Tables_Figures_v4.Rmd

---
title: "Tables_Figures_TDR"
author: "Yujia Wang"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
	echo = FALSE,
	message = FALSE,
	warning = FALSE
)
library(dplyr)
library(ggplot2)
library(tidyverse)
library(kableExtra)
library(readr)
library(ggpubr)
library(ggthemes)
library(latex2exp)

# install.packages("magick")
# install.packages("webshot")
# webshot::install_phantomjs()
library(magick)
library(webshot)

```

## Read Data
### TDR
```{r}
# read TDR data
# 1:1 randomizatin, alpha at p0=pc
tdr_alpha10_1s2by2_alphaonly_files = (Sys.glob('results/TDR_alpha10_1s_2by2_alphaonly*.csv'))
tdr_alpha10_1s2by2_alphamax30_files = (Sys.glob('results/TDR_alpha10_1s_2by2_alphamax30*.csv'))
tdr_alpha20_1s2by2_alphaonly_files = (Sys.glob('results/TDR_alpha20_1s_2by2_alphaonly*.csv'))
tdr_alpha20_1s2by2_alphamax30_files = (Sys.glob('results/TDR_alpha20_1s_2by2_alphamax30*.csv'))

tdr_alpha10_1s3by2_alphaonly_files = (Sys.glob('results/TDR_alpha10_1s_3by2_alphaonly*.csv'))
tdr_alpha10_1s3by2_alphamax30_files = (Sys.glob('results/TDR_alpha10_1s_3by2_alphamax30*.csv'))
tdr_alpha20_1s3by2_alphaonly_files = (Sys.glob('results/TDR_alpha20_1s_3by2_alphaonly*.csv'))
tdr_alpha20_1s3by2_alphamax30_files = (Sys.glob('results/TDR_alpha20_1s_3by2_alphamax30*.csv'))

tdr_alpha10_2s2by2_alphaonly_files = (Sys.glob('results/TDR_alpha10_2s_2by2_alphaonly*.csv'))
tdr_alpha10_2s2by2_alphamax30_files = (Sys.glob('results/TDR_alpha10_2s_2by2_alphamax30*.csv'))
tdr_alpha20_2s2by2_alphaonly_files = (Sys.glob('results/TDR_alpha20_2s_2by2_alphaonly*.csv'))
tdr_alpha20_2s2by2_alphamax30_files = (Sys.glob('results/TDR_alpha20_2s_2by2_alphamax30*.csv'))

tdr_alpha10_2s3by2_alphaonly_files = (Sys.glob('results/TDR_alpha10_2s_3by2_alphaonly*.csv'))
tdr_alpha10_2s3by2_alphamax30_files = (Sys.glob('results/TDR_alpha10_2s_3by2_alphamax30*.csv'))
tdr_alpha20_2s3by2_alphaonly_files = (Sys.glob('results/TDR_alpha20_2s_3by2_alphaonly*.csv'))
tdr_alpha20_2s3by2_alphamax30_files = (Sys.glob('results/TDR_alpha20_2s_3by2_alphamax30*.csv'))

readTDRfiles = function(filenames) {
  TDRdat = data.frame()
  Nfiles = length(filenames)
  print(Nfiles)
  for (i in 1:Nfiles) {
  dat = read.csv(filenames[i], skip = 2)
  TDRdat = rbind(TDRdat, dat)
  }
  return(TDRdat)
}

tdr_alpha10_1s2by2_alphaonly = readTDRfiles(tdr_alpha10_1s2by2_alphaonly_files)
tdr_alpha10_1s2by2_alphamax30 = readTDRfiles(tdr_alpha10_1s2by2_alphamax30_files)
tdr_alpha20_1s2by2_alphaonly = readTDRfiles(tdr_alpha20_1s2by2_alphaonly_files)
tdr_alpha20_1s2by2_alphamax30 = readTDRfiles(tdr_alpha20_1s2by2_alphamax30_files)

tdr_alpha10_1s3by2_alphaonly = readTDRfiles(tdr_alpha10_1s3by2_alphaonly_files) 
tdr_alpha10_1s3by2_alphamax30 = readTDRfiles(tdr_alpha10_1s3by2_alphamax30_files)
tdr_alpha20_1s3by2_alphaonly = readTDRfiles(tdr_alpha20_1s3by2_alphaonly_files) 
tdr_alpha20_1s3by2_alphamax30 = readTDRfiles(tdr_alpha20_1s3by2_alphamax30_files)

tdr_alpha10_2s2by2_alphaonly = readTDRfiles(tdr_alpha10_2s2by2_alphaonly_files) 
tdr_alpha10_2s2by2_alphamax30 = readTDRfiles(tdr_alpha10_2s2by2_alphamax30_files)
tdr_alpha20_2s2by2_alphaonly = readTDRfiles(tdr_alpha20_2s2by2_alphaonly_files) 
tdr_alpha20_2s2by2_alphamax30 = readTDRfiles(tdr_alpha20_2s2by2_alphamax30_files)

tdr_alpha10_2s3by2_alphaonly = readTDRfiles(tdr_alpha10_2s3by2_alphaonly_files) 
tdr_alpha10_2s3by2_alphamax30 = readTDRfiles(tdr_alpha10_2s3by2_alphamax30_files)
tdr_alpha20_2s3by2_alphaonly = readTDRfiles(tdr_alpha20_2s3by2_alphaonly_files)
tdr_alpha20_2s3by2_alphamax30 = readTDRfiles(tdr_alpha20_2s3by2_alphamax30_files)
```

### HW, LBR, Conventional
```{r}
# Read reference data
# read hong
# code: hong_reproduce.R
hong_alpha10_alphaonly = read.csv('results/hong_alpha10_alphaonly_eta10_gam10_confidence90.csv',skip=2)
hong_alpha10_alphamax30 = read.csv('results/hong_alpha10_alphamax30_eta10_gam10_confidence30.csv',skip=2)

hong_alpha20_alphaonly_etagam10 = read.csv('results/hong_alpha20_alphaonly_eta10_gam10_confidence90.csv',skip=2)
hong_alpha20_alphamax30_etagam10 = read.csv('results/hong_alpha20_alphamax30_eta10_gam10_confidence30.csv',skip=2)
hong_alpha20_alphaonly_etagam20 = read.csv('results/hong_alpha20_alphaonly_eta20_gam20_confidence90.csv',skip=2) # Hong relaxed criteria on eta and gamma
hong_alpha20_alphamax30_etagam20 = read.csv('results/hong_alpha20_alphamax30_eta20_gam20_confidence30.csv',skip=2) # Hong relaxed criteria on eta and gamma

# read litwin
# code: litwin_1s_reproduce.R
# code: litwin_2s_reproduce.R
litwin_alpha10_1s_alphaonly = read.csv('results/Litwin_alpha10_1s_alphaonly_1to1_confidence90.csv', skip=2)
litwin_alpha10_1s_alphamax30 = read.csv('results/Litwin_alpha10_1s_alphamax30_1to1_confidence30.csv', skip=2)

litwin_alpha10_2s_alphaonly = read.csv('results/Litwin_alpha10_2s_alphaonly_1to1_confidence90.csv', skip=0)
litwin_alpha10_2s_alphaonly = litwin_alpha10_2s_alphaonly %>% mutate(gam = 0, eta = 0) 
litwin_alpha10_2s_alphamax30 = read.csv('results/Litwin_alpha10_2s_alphamax30_1to1_confidence30.csv', skip=0)
litwin_alpha10_2s_alphamax30 = litwin_alpha10_2s_alphamax30 %>% mutate(gam = 0, eta = 0)

litwin_alpha20_1s_alphaonly = read.csv('results/Litwin_alpha20_1s_alphaonly_1to1_confidence90.csv', skip=2)
litwin_alpha20_1s_alphamax30 = read.csv('results/Litwin_alpha20_1s_alphamax30_1to1_confidence30.csv', skip=2)

litwin_alpha20_2s_alphaonly = read.csv('results/Litwin_alpha20_2s_alphaonly_1to1_confidence90.csv', skip=0)
litwin_alpha20_2s_alphaonly = litwin_alpha20_2s_alphaonly %>% mutate(gam = 0, eta = 0)
litwin_alpha20_2s_alphamax30 = read.csv('results/Litwin_alpha20_2s_alphamax30_1to1_confidence30.csv', skip=0)
litwin_alpha20_2s_alphamax30 = litwin_alpha20_2s_alphamax30 %>% mutate(gam = 0, eta = 0)

# read conventional
# code: conventional.R
conventional_alpha10 <- read_csv("results/conventional_alpha10_1to1.csv")
conventional_alpha20 <- read_csv("results/conventional_alpha20_1to1.csv")

```

## Functions
```{r}
loss_func_1s <- function(x, alpha, beta, w=0.5) {
  # 1:1 randomization
  # calculate conventional reference sample size
  # w: weight coefficient for adjusting the relative importance of sample size saving and power increase
  # larger w will give more priority to sample size saving
  # smaller w will give more priority to power gain.
  # score = 0.5: conventional method
  # score > 0.5: unacceptable (no sample size saving at the same power or no power increase at the same sample size)
  # score < 0.5: sample size saving or power improvement or both; the smaller the better
  p0 = x['p0']
  p1 = x['p1']
  n = x['N']
  pwr0 = 0.80
  pwr = x['power']
  N0 = 2*ceiling(((qnorm(1-alpha)+qnorm(1-beta))/(p1 - p0))^2*(p0*(1-p0)+p1*(1-p1)))
  loss_score = w*n/(0.5*N0)+(1-w)*(pwr0/pwr)-1.5
  loss_score = 1/(1+exp(-loss_score))
  return(loss_score)
}

loss_func_2s <- function(x, alpha, beta, w=0.5) {
  # 1:1 randomization
  # calculate conventional reference sample size
  # w: weight coefficient for adjusting the relative importance of sample size saving and power increase
  # larger w will give more priority to sample size saving
  # smaller w will give more priority to power gain.
  # score = 0.5: conventional method
  # score > 0.5: unacceptable (no sample size saving at the same power or no power increase at the same sample size)
  # score < 0.5: sample size saving or power improvement or both; the smaller the better
  
  p0 = x['p0']
  p1 = x['p1']
  n = x['N2']
  pwr0 = 0.80
  pwr = x['power']
  N0 = 2*ceiling(((qnorm(1-alpha)+qnorm(1-beta))/(p1 - p0))^2*(p0*(1-p0)+p1*(1-p1)))
  loss_score = w*n/(0.5*N0)+(1-w)*(pwr0/pwr)-1.5 # conventional will give 0 here
  loss_score = 1/(1+exp(-loss_score)) # conventional will give 0.5 here
  return(loss_score)
}

# percentage formatting
fmt_diffperc = function(x,y, d=2) {
  fmtted = paste(round(x-y,2),' (',round((x-y)/x*100,d),'%)',sep='')
  return(fmtted)
}

fmt_p0p1 = function(p0,p1) {
  return(paste(format(round(p0, 2), nsmall = 2),format(round(p1, 2), nsmall = 2), sep = ', '))
}
```

## Designs
```{r}
p0p1_list = c('0.10, 0.25',
              '0.10, 0.30',
              '0.10, 0.35',
              
              '0.20, 0.35',
              '0.20, 0.40',
              '0.20, 0.45',
              
              '0.35, 0.50',
              '0.35, 0.55',
              '0.35, 0.60',
              
              '0.30, 0.45',
              '0.30, 0.50',
              
              '0.40, 0.60',
              '0.40, 0.65',
              
              '0.50, 0.65',
              '0.50, 0.70',
              
              '0.55, 0.70',
              '0.55, 0.75',
              
              '0.60, 0.85',
              '0.65, 0.85',
              '0.70, 0.85'
)

```

## 1. One-Stage 2-by-2 alpha <= 0.20, beta <= 0.20, control alpha only
```{r}
# maximum 5% power reduction
score = apply(tdr_alpha20_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly
tdr_alpha20_1s2by2_alphaonly_score$loss_score = score
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly_score %>% filter(power>=0.75) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

tdr_alpha20_1s2by2_alphaonly_9 = tdr_alpha20_1s2by2_alphaonly_score %>% select(p0, p1, s, m, N, power, beta, alpha, gam,eta)

litwin_alpha20_1s_alphaonly_1_9 = litwin_alpha20_1s_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(litwin_alpha20_1s_alphaonly_1_9) = c('p0','p1','N_litwin','power_litwin','beta_litwin', 'alpha_litwin', 'gam_litwin', 'eta_litwin')
hong_alpha20_alphaonly_etagam10_1_9 = hong_alpha20_alphaonly_etagam10 %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(hong_alpha20_alphaonly_etagam10_1_9) = c('p0','p1','N_hong','power_hong','beta_hong', 'alpha_hong', 'gam_hong', 'eta_hong')
conventional_alpha20_1_9 = conventional_alpha20 %>% select(p0, p1, n_alphaonly)
colnames(conventional_alpha20_1_9) = c('p0','p1','N_conventional')
table_9_1 =  tdr_alpha20_1s2by2_alphaonly_9 %>% left_join(litwin_alpha20_1s_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(hong_alpha20_alphaonly_etagam10_1_9, on=c('p0','p1')) %>% 
  left_join(conventional_alpha20_1_9, on=c('p0','p1')) %>%
  mutate(NvsLitwin=fmt_diffperc(N_litwin,N,2),
         NvsHong = fmt_diffperc(N_hong,N,2),
         NvsConventional=fmt_diffperc(N_conventional,N,2),
         powervsLitwin = power_litwin - power,
         powervsHong = power_hong - power,
         betavsLitwin = beta_litwin - beta,
         betavsHong = beta_hong - beta,
         alphavsLitwin = alpha_litwin - alpha,
         alphavsHong = alpha_hong - alpha,
         
         )

write.csv(table_9_1, 'tdr_one_stage_2by2_alpha20.csv', row.names = F)

kable(table_9_1 %>% select(p0, p1, NvsLitwin, NvsHong, NvsConventional, powervsLitwin, betavsLitwin, alphavsLitwin), booktab=T, align='c', digits=2, 
      caption='One-Stage 2-by-2 Method Full') %>% kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))


```

```{r}
tdr1s6075 = tdr_alpha20_1s2by2_alphaonly %>% filter(p0==0.60, p1==0.75)
score = apply(tdr1s6075, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr1s6075$loss_score = score
tdr1s6075 = tdr_alpha20_1s2by2_alphaonly_score %>% filter(power>=0.80*0.95) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

write.csv(tdr1s6075, 'example_one_stage_loss_scores_6075.csv', row.names = F)
```


#### selected cases
```{r}
# maximum 1% power reduction
score = apply(tdr_alpha20_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly
tdr_alpha20_1s2by2_alphaonly_score$loss_score = score
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly_score %>% filter(power>=0.80*0.95, alpha<=0.20) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

tdr_alpha20_1s2by2_alphaonly_9 = tdr_alpha20_1s2by2_alphaonly_score %>% select(p0, p1, s, m, N, power, beta, alpha, gam,eta)

litwin_alpha20_1s_alphaonly_1_9 = litwin_alpha20_1s_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(litwin_alpha20_1s_alphaonly_1_9) = c('p0','p1','N_litwin','power_litwin','beta_litwin', 'alpha_litwin', 'gam_litwin', 'eta_litwin')
hong_alpha20_alphaonly_etagam10_1_9 = hong_alpha20_alphaonly_etagam10 %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(hong_alpha20_alphaonly_etagam10_1_9) = c('p0','p1','N_hong','power_hong','beta_hong', 'alpha_hong', 'gam_hong', 'eta_hong')
conventional_alpha20_1_9 = conventional_alpha20 %>% select(p0, p1, n_alphaonly)
colnames(conventional_alpha20_1_9) = c('p0','p1','N_conventional')
table_9_1 =  tdr_alpha20_1s2by2_alphaonly_9 %>% left_join(litwin_alpha20_1s_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(hong_alpha20_alphaonly_etagam10_1_9, on=c('p0','p1')) %>% 
  left_join(conventional_alpha20_1_9, on=c('p0','p1')) %>%
  mutate(NvsLitwin=fmt_diffperc(N_litwin,N,2),
         NvsHong = fmt_diffperc(N_hong,N,2),
         NvsConventional=fmt_diffperc(N_conventional,N,2),
         powervsLitwin = power_litwin - power,
         powervsHong = power_hong - power,
         betavsLitwin = beta_litwin - beta,
         betavsHong = beta_hong - beta,
         alphavsLitwin = alpha_litwin - alpha,
         alphavsHong = alpha_hong - alpha,
         )


table_9_1 = table_9_1 %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1),
                                               s/(N/2), m/(N/2)) 
table_9_1 = table_9_1 %>% 
  filter(p0_p1 %in% c('0.10, 0.25',
                      '0.10, 0.30',
                      '0.10, 0.35',
                      
                      '0.20, 0.35',
                      '0.20, 0.40',
                      '0.20, 0.45',
                      
                      '0.35, 0.50',
                      '0.35, 0.55',
                      '0.35, 0.60',
                      
                      '0.30, 0.45',
                      '0.30, 0.50',
                      
                      '0.40, 0.60',
                      '0.40, 0.65',
                      
                      '0.50, 0.65',
                      '0.50, 0.70',
                      
                      '0.55, 0.70',
                      '0.55, 0.75',
                      
                      '0.60, 0.85',
                      '0.65, 0.85',
                      '0.70, 0.85'
  ))
kable(table_9_1, booktab=T, align='c', digits=2, 
      caption='One-Stage 2-by-2 Method Full') %>% kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
```


### Table 1
```{r}

# p0p1_list = c('0.05, 0.20',
#               '0.15, 0.30',
#               '0.25, 0.40',
#               '0.35, 0.50',
#               '0.50, 0.65',
#               '0.70, 0.85',
#               
#               '0.20, 0.40',
#               '0.20, 0.45',
#               '0.30, 0.50',
#               '0.30, 0.55',
#               '0.40, 0.60',
#               '0.40, 0.65',
#               '0.50, 0.70',
#               '0.50, 0.75',
#               '0.60, 0.80',
#               '0.60, 0.85'
# )
score = apply(tdr_alpha20_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly
tdr_alpha20_1s2by2_alphaonly_score$loss_score = score
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly_score %>% 
  filter(power>=0.8*0.95) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_1 = tdr_alpha20_1s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

table_1_ltx = table_1
table_1_ltx[,8:13] = round(table_1_ltx[,8:13],2)
# colnames(table_1_ltx) = c("$p_C$","$p_E$","$\\gamma_{max}$","$\\lambda_{max}$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")
write.csv(table_1_ltx, 'manuscript/tbl_1.csv', row.names = F)

tbl1 = kable(table_1, booktab=T, align='c', digits=2, 
      caption='Table 1: TDR one-stage 2-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl1
```

```{r}
sort(fig1_dat$beta - fig1_dat$beta.LBR)

sort(fig1_dat$N.reduce.perc.TDR - fig1_dat$N.reduce.perc.LBR)



sd(fig1_dat$N.reduce.perc.TDR - fig1_dat$N.reduce.perc.LBR)

sort(fig1_dat$power - fig1_dat$power.LBR)
fig1_dat %>% filter(p0==0.10, p1==0.30) %>% mutate(beta_diff = beta.LBR - beta, alpha_diff = alpha.LBR - alpha) %>% select(alpha_diff, beta_diff)

fig1_dat %>% filter(p0==0.30, p1==0.50) %>% mutate(beta_diff = beta.LBR - beta, alpha_diff = alpha.LBR - alpha) %>% select(alpha_diff, beta_diff)
```

### Figure 1a
```{r}
table_1 = tdr_alpha20_1s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

fig1_dat = table_1 %>% left_join(litwin_alpha20_1s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) %>% 
  left_join(hong_alpha20_alphaonly_etagam10, by=c("p0","p1"), suffix=c("", ".HW")) %>% 
  left_join(conventional_alpha20, by=c("p0","p1"))

fig1_dat = fig1_dat %>% rowwise() %>% mutate(N.reduce.TDR = n_alphaonly - N,
                                             N.reduce.HW = n_alphaonly - N.HW,
                                             N.reduce.LBR = n_alphaonly - N.LBR,
                                             N.reduce.perc.TDR = (N.reduce.TDR/n_alphaonly)*100,
                                             N.reduce.perc.HW = (N.reduce.HW/n_alphaonly)*100,
                                             N.reduce.perc.LBR = (N.reduce.LBR/n_alphaonly)*100)
fig1_dat = fig1_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1)) 

fig1_dat_tdr = fig1_dat %>% select(p0_p1, N,N.reduce.TDR,N.reduce.perc.TDR)
colnames(fig1_dat_tdr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_dat_tdr$design = 'TDR'
fig1_dat_hw = fig1_dat %>% select(p0_p1, N.HW,N.reduce.HW,N.reduce.perc.HW)
colnames(fig1_dat_hw) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_dat_hw$design = 'HW'
fig1_dat_lbr = fig1_dat %>% select(p0_p1, N.LBR,N.reduce.LBR,N.reduce.perc.LBR)
colnames(fig1_dat_lbr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_dat_lbr$design = 'LBR'


fig1_dat_long = rbind(fig1_dat_tdr,fig1_dat_hw,fig1_dat_lbr)
```


```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9","#E69F00",  "#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig1_dat_long$design = ordered(fig1_dat_long$design, levels=c('TDR', 'HW', 'LBR'))
fig1_dat_long$N.reduce.perc = ifelse(fig1_dat_long$N.reduce.perc < 0, 0, fig1_dat_long$N.reduce.perc)
fig1a = fig1_dat_long %>% ggplot(aes(x=p0_p1, y=N.reduce.perc,fill=design)) + 
  geom_col(color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction from conventional design $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,60,5), limits = c(0, 60)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig1a
```
### Figure 1b

```{r}
table_1 = tdr_alpha20_1s2by2_alphaonly_score %>% rowwise() %>%
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>%
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

fig1b_dat = table_1 %>% left_join(litwin_alpha20_1s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) %>%
  left_join(hong_alpha20_alphaonly_etagam10, by=c("p0","p1"), suffix=c("", ".HW")) %>%
  left_join(conventional_alpha20, by=c("p0","p1"))

fig1b_dat = fig1b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig1b_dat_tdr = fig1b_dat %>% select(p0_p1, power, alpha, beta, eta, gam) %>%
  mutate(design="TDR")

fig1b_dat_hw = fig1b_dat %>% select(p0_p1, power.HW, alpha.HW, beta.HW, eta.HW, gam.HW)
colnames(fig1b_dat_hw) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig1b_dat_hw = fig1b_dat_hw %>%
  mutate(design="HW")

fig1b_dat_lbr = fig1b_dat %>% select(p0_p1, power.LBR,alpha.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig1b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig1b_dat_lbr = fig1b_dat_lbr %>%
  mutate(design="LBR", eta=NA, gam=NA) # no inconclusive region in LBR method, thus eta & gam = 0

fig1b_dat_long = rbind(fig1b_dat_tdr,fig1b_dat_hw,fig1b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
fig1b_dat_long$design = ordered(fig1b_dat_long$design, levels=c('TDR', 'HW', 'LBR'))
cbPalette <- c("#56B4E9","#E69F00",  "#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig1b1 = fig1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.65,0.90,0.05), limits = c(0.65, 0.90)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig1b2 = fig1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig1b3 = fig1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\beta$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#  theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig1b4 = fig1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=eta, color=design, group=design), alpha=0.75) +
#   geom_point(aes(y=eta, color=design), alpha=0.75) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.35,0.05), limits = c(0.0, 0.35)) +
#   labs(y = TeX("$\\eta$")) +
#   # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#   theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig1b5 = fig1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=gam, color=design, group=design), alpha=0.5) +
#   geom_point(aes(y=gam, color=design), alpha=0.5) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.2,linetype='dashed', color='grey', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
#  labs(x = TeX("Response rates: ($p_0, p_1$)"), y = TeX("$\\gamma$")) +
  labs(x = TeX("Response rates: ($p_0, p_1$)")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

# fig1b = ggarrange(fig1b1, fig1b2, fig1b3, fig1b4, fig1b5, align='v', heights=c(1.5,1,1,1.5,2), nrow=5)
fig1b = ggarrange(fig1b1, fig1b2, fig1b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig1b
```
### Figure 1
```{r, fig.height=3, fig.width=5}
fig1 = ggarrange(fig1a, fig1b, nrow=1, legend = 'bottom')
fig1
```

### write to pdf
```{r}
FILENAME = 'manuscript/tbl1_fig1_v2.pdf'
# save_kable(tbl1, FILENAME)
# kableExtra::kable_styling(tbl1) %>% save_kable('manuscript/tbl1.png')
pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig1
dev.off()

```




## 1.2. One-Stage 2-by-2 alpha <= 0.20, beta <= 0.20, alphamax30
### Table 1.1
```{r}

score = apply(tdr_alpha20_1s2by2_alphamax30, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s2by2_alphamax30_score = tdr_alpha20_1s2by2_alphamax30
tdr_alpha20_1s2by2_alphamax30_score$loss_score = score
tdr_alpha20_1s2by2_alphamax30_score = tdr_alpha20_1s2by2_alphamax30_score %>% filter(power>=0.80*0.95, alpha<=0.20) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_1_1 = tdr_alpha20_1s2by2_alphamax30_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, alphamax, gam, eta, expic)

table_S2_ltx = table_1_1
table_S2_ltx[,8:14] = round(table_S2_ltx[,8:14],2)
write.csv(table_S2_ltx, 'manuscript/tbl_S2.csv', row.names = F)

tbl1_1 = kable(table_1_1, booktab=T, align='c', digits=2, 
      caption='Table S2: TDR one-stage 2-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$, $p_0$ CI 30%',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\alpha_{max}$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl1_1
```

### Figure 1.1a
```{r}
table_1_1 = tdr_alpha20_1s2by2_alphamax30_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, alphamax, gam, eta, expic)

fig1_1_dat = table_1_1 %>% left_join(litwin_alpha20_1s_alphamax30, by=c("p0","p1"), suffix=c("", ".LBR")) %>% 
  left_join(hong_alpha20_alphamax30_etagam10, by=c("p0","p1"), suffix=c("", ".HW")) %>% 
  left_join(conventional_alpha20, by=c("p0","p1"))

fig1_1_dat = fig1_1_dat %>% rowwise() %>% mutate(N.reduce.TDR = n_alphaonly - N,
                                             N.reduce.HW = n_alphaonly - N.HW,
                                             N.reduce.LBR = n_alphaonly - N.LBR,
                                             N.reduce.perc.TDR = (N.reduce.TDR/n_alphaonly)*100,
                                             N.reduce.perc.HW = (N.reduce.HW/n_alphaonly)*100,
                                             N.reduce.perc.LBR = (N.reduce.LBR/n_alphaonly)*100)
fig1_1_dat = fig1_1_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1)) 

fig1_1_dat_tdr = fig1_1_dat %>% select(p0_p1, N,N.reduce.TDR,N.reduce.perc.TDR)
colnames(fig1_1_dat_tdr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_1_dat_tdr$design = 'TDR'
fig1_1_dat_hw = fig1_1_dat %>% select(p0_p1, N.HW,N.reduce.HW,N.reduce.perc.HW)
colnames(fig1_1_dat_hw) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_1_dat_hw$design = 'HW'
fig1_1_dat_lbr = fig1_1_dat %>% select(p0_p1, N.LBR,N.reduce.LBR,N.reduce.perc.LBR)
colnames(fig1_1_dat_lbr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig1_1_dat_lbr$design = 'LBR'


fig1_1_dat_long = rbind(fig1_1_dat_tdr,fig1_1_dat_hw,fig1_1_dat_lbr)
```


```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9","#E69F00",  "#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig1_1_dat_long$design = ordered(fig1_1_dat_long$design, levels=c('TDR', 'HW', 'LBR'))
fig1_1_dat_long$N.reduce.perc = ifelse(fig1_1_dat_long$N.reduce.perc < 0, 0, fig1_1_dat_long$N.reduce.perc)
fig1_1a = fig1_1_dat_long %>% ggplot(aes(x=p0_p1, y=N.reduce.perc,fill=design)) + 
  geom_col(color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction from conventional design $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,50,5), limits = c(0, 50)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig1_1a
```
### Figure 1.1b

```{r}
table_1_1 = tdr_alpha20_1s2by2_alphamax30_score %>% rowwise() %>%
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>%
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, alphamax, gam, eta, expic)

fig1_1b_dat = table_1_1 %>% left_join(litwin_alpha20_1s_alphamax30, by=c("p0","p1"), suffix=c("", ".LBR")) %>%
  left_join(hong_alpha20_alphamax30_etagam10, by=c("p0","p1"), suffix=c("", ".HW")) %>%
  left_join(conventional_alpha20, by=c("p0","p1"))

fig1_1b_dat = fig1_1b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig1_1b_dat_tdr = fig1_1b_dat %>% select(p0_p1, power, alpha, alphamax, beta, eta, gam) %>%
  mutate(design="TDR")

fig1_1b_dat_hw = fig1_1b_dat %>% select(p0_p1, power.HW, alpha.HW, alphamax.HW, beta.HW, eta.HW, gam.HW)
colnames(fig1_1b_dat_hw) = c('p0_p1', 'power', 'alpha', 'alphamax', 'beta', 'eta', 'gam')
fig1_1b_dat_hw = fig1_1b_dat_hw %>%
  mutate(design="HW")

fig1_1b_dat_lbr = fig1_1b_dat %>% select(p0_p1, power.LBR,alpha.LBR, alphamax.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig1_1b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'alphamax', 'beta', 'eta', 'gam')
fig1_1b_dat_lbr = fig1_1b_dat_lbr %>%
  mutate(design="LBR", eta=NA, gam=NA) # no inconclusive region in LBR method, thus eta & gam = 0

fig1_1b_dat_long = rbind(fig1_1b_dat_tdr,fig1_1b_dat_hw,fig1_1b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
fig1_1b_dat_long$design = ordered(fig1_1b_dat_long$design, levels=c('TDR', 'HW', 'LBR'))
cbPalette <- c("#56B4E9","#E69F00",  "#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig1_1b1 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.65,0.90,0.05), limits = c(0.65, 0.90)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig1_1b2 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig1_1b3 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alphamax, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alphamax, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha_{max}$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )


fig1_1b4 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\beta$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#   theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig1_1b4 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=eta, color=design, group=design), alpha=0.75) +
#   geom_point(aes(y=eta, color=design), alpha=0.75) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.35,0.05), limits = c(0.0, 0.35)) +
#   labs(y = TeX("$\\eta$")) +
#   # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#   theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig1_1b5 = fig1_1b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=gam, color=design, group=design), alpha=0.5) +
#   geom_point(aes(y=gam, color=design), alpha=0.5) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.2,linetype='dashed', color='grey', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
# , y = TeX("$\\gamma$")
  labs(x = TeX("Response rates: ($p_0, p_1$)")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig1_1b = ggarrange(fig1_1b1, fig1_1b2, fig1_1b3, fig1_1b4, align='v', heights=c(1.5,1,1,1.5), nrow=4)
fig1_1b
```
### Figure 1.1
```{r, fig.height=3.5, fig.width=5}
fig1_1 = ggarrange(fig1_1a, fig1_1b, nrow=1, legend = 'bottom')
fig1_1
```

### write to pdf
```{r}
FILENAME = 'manuscript/fig1_1.pdf'
save_kable(tbl1_1, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig1_1
dev.off()

```






## 2. One-Stage 2-by-2 alpha <= 0.10, beta <= 0.10
### 2.1. control alpha only
```{r}
# maximum 5% power reduction
score = apply(tdr_alpha10_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.10, beta=0.10, w=0.50)
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly
tdr_alpha10_1s2by2_alphaonly_score$loss_score = score
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly_score %>% filter(power>=0.90*0.95, alpha<=0.10) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

tdr_alpha10_1s2by2_alphaonly_9 = tdr_alpha10_1s2by2_alphaonly_score %>% select(p0, p1, s, m, N, power, beta, alpha, gam,eta)

litwin_alpha10_1s_alphaonly_1_9 = litwin_alpha10_1s_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(litwin_alpha10_1s_alphaonly_1_9) = c('p0','p1','N_litwin','power_litwin','beta_litwin', 'alpha_litwin', 'gam_litwin', 'eta_litwin')
hong_alpha10_alphaonly_1_9 = hong_alpha10_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(hong_alpha10_alphaonly_1_9) = c('p0','p1','N_hong','power_hong','beta_hong', 'alpha_hong', 'gam_hong', 'eta_hong')
conventional_alpha10_1_9 = conventional_alpha10 %>% select(p0, p1, n_alphaonly)
colnames(conventional_alpha10_1_9) = c('p0','p1','N_conventional')
table_9_1 =  tdr_alpha10_1s2by2_alphaonly_9 %>% left_join(litwin_alpha10_1s_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(hong_alpha10_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(conventional_alpha10_1_9, on=c('p0','p1')) %>%
  mutate(NvsLitwin=fmt_diffperc(N_litwin,N,2),
         NvsHong = fmt_diffperc(N_hong,N,2),
         NvsConventional=fmt_diffperc(N_conventional,N,2),
         powervsLitwin = power_litwin - power,
         powervsHong = power_hong - power,
         betavsLitwin = beta_litwin - beta,
         betavsHong = beta_hong - beta,
         alphavsLitwin = alpha_litwin - alpha,
         alphavsHong = alpha_hong - alpha,
         
         )
kable(table_9_1, booktab=T, align='c', digits=2, 
      caption='One-Stage 2-by-2 Method Full') %>% kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))


```

#### selected cases
```{r}
# maximum 1% power reduction
score = apply(tdr_alpha10_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.10, beta=0.10, w=0.50)
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly
tdr_alpha10_1s2by2_alphaonly_score$loss_score = score
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly_score %>% filter(power>=0.90*0.95, alpha<=0.10) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

tdr_alpha10_1s2by2_alphaonly_9 = tdr_alpha10_1s2by2_alphaonly_score %>% select(p0, p1, s, m, N, power, beta, alpha, gam,eta)

litwin_alpha10_1s_alphaonly_1_9 = litwin_alpha10_1s_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(litwin_alpha10_1s_alphaonly_1_9) = c('p0','p1','N_litwin','power_litwin','beta_litwin', 'alpha_litwin', 'gam_litwin', 'eta_litwin')
hong_alpha10_alphaonly_1_9 = hong_alpha10_alphaonly %>% select(p0, p1, N, power, beta, alpha, gam, eta)
colnames(hong_alpha10_alphaonly_1_9) = c('p0','p1','N_hong','power_hong','beta_hong', 'alpha_hong', 'gam_hong', 'eta_hong')
conventional_alpha10_1_9 = conventional_alpha10 %>% select(p0, p1, n_alphaonly)
colnames(conventional_alpha10_1_9) = c('p0','p1','N_conventional')
table_9_1 =  tdr_alpha10_1s2by2_alphaonly_9 %>% left_join(litwin_alpha10_1s_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(hong_alpha10_alphaonly_1_9, on=c('p0','p1')) %>% 
  left_join(conventional_alpha10_1_9, on=c('p0','p1')) %>%
  mutate(NvsLitwin=fmt_diffperc(N_litwin,N,2),
         NvsHong = fmt_diffperc(N_hong,N,2),
         NvsConventional=fmt_diffperc(N_conventional,N,2),
         powervsLitwin = power_litwin - power,
         powervsHong = power_hong - power,
         betavsLitwin = beta_litwin - beta,
         betavsHong = beta_hong - beta,
         alphavsLitwin = alpha_litwin - alpha,
         alphavsHong = alpha_hong - alpha,
         )

fmt_p0p1 = function(p0,p1) {
  return(paste(format(round(p0, 2), nsmall = 2),format(round(p1, 2), nsmall = 2), sep = ', '))
}
table_9_1 = table_9_1 %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1),
                                               s/(N/2), m/(N/2)) 
table_9_1 = table_9_1 %>% 
  filter(p0_p1 %in% c('0.05, 0.20',
                      '0.15, 0.30',
                      '0.25, 0.40',
                      '0.35, 0.50',
                      '0.50, 0.65',
                      '0.70, 0.85',
                      
                      '0.20, 0.40',
                      '0.20, 0.45',
                      '0.30, 0.50',
                      '0.30, 0.55',
                      '0.40, 0.60',
                      '0.40, 0.65',
                      '0.50, 0.70',
                      '0.50, 0.75',
                      '0.60, 0.80',
                      '0.60, 0.85'
  ))
kable(table_9_1, booktab=T, align='c', digits=2, 
      caption='One-Stage 2-by-2 Method Full') %>% kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
```


### Table 2
```{r}

score = apply(tdr_alpha10_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.10, beta=0.10, w=0.50)
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly
tdr_alpha10_1s2by2_alphaonly_score$loss_score = score
tdr_alpha10_1s2by2_alphaonly_score = tdr_alpha10_1s2by2_alphaonly_score %>% filter(power>=0.90*0.95, alpha<=0.10) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_2 = tdr_alpha10_1s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

table_2_ltx = table_2
table_2_ltx[,8:13] = round(table_2_ltx[,8:13],2)
# colnames(table_1_ltx) = c("$p_C$","$p_E$","$\\gamma_{max}$","$\\lambda_{max}$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")
write.csv(table_2_ltx, 'manuscript/tbl_2.csv', row.names = F)


tbl2 = kable(table_2, booktab=T, align='c', digits=2, 
      caption='Table 2: TDR one-stage 2-by-2 design, $\\alpha\\leq0.10$, $\\beta\\leq0.10$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl2
```
```{r}
sort(fig2_dat$beta - fig2_dat$beta.LBR)

sort(fig2_dat$N.reduce.perc.TDR - fig2_dat$N.reduce.perc.LBR)



sd(fig2_dat$N.reduce.perc.TDR - fig2_dat$N.reduce.perc.LBR)

sort(fig2_dat$power - fig2_dat$power.LBR)
fig2_dat %>% filter(p0==0.20, p1==0.45) %>% mutate(beta_diff = beta.LBR - beta, alpha_diff = alpha.LBR - alpha) %>% select(alpha_diff, beta_diff)

fig2_dat %>% filter(p0==0.65, p1==0.85) %>% mutate(beta_diff = beta.LBR - beta, alpha_diff = alpha.LBR - alpha) %>% select(alpha_diff, beta_diff)
```
### Figure 2a
```{r}
table_2 = tdr_alpha10_1s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

fig2_dat = table_2 %>% left_join(litwin_alpha10_1s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) %>% 
  left_join(hong_alpha10_alphaonly, by=c("p0","p1"), suffix=c("", ".HW")) %>% 
  left_join(conventional_alpha10, by=c("p0","p1"))

fig2_dat = fig2_dat %>% rowwise() %>% mutate(N.reduce.TDR = n_alphaonly - N,
                                             N.reduce.HW = n_alphaonly - N.HW,
                                             N.reduce.LBR = n_alphaonly - N.LBR,
                                             N.reduce.perc.TDR = (N.reduce.TDR/n_alphaonly)*100,
                                             N.reduce.perc.HW = (N.reduce.HW/n_alphaonly)*100,
                                             N.reduce.perc.LBR = (N.reduce.LBR/n_alphaonly)*100)
fig2_dat = fig2_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1)) 

fig2_dat_tdr = fig2_dat %>% select(p0_p1, N,N.reduce.TDR,N.reduce.perc.TDR)
colnames(fig2_dat_tdr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig2_dat_tdr$design = 'TDR'
fig2_dat_hw = fig2_dat %>% select(p0_p1, N.HW,N.reduce.HW,N.reduce.perc.HW)
colnames(fig2_dat_hw) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig2_dat_hw$design = 'HW'
fig2_dat_lbr = fig2_dat %>% select(p0_p1, N.LBR,N.reduce.LBR,N.reduce.perc.LBR)
colnames(fig2_dat_lbr) = c('p0_p1', 'N', 'N.reduce', 'N.reduce.perc')
fig2_dat_lbr$design = 'LBR'


fig2_dat_long = rbind(fig2_dat_tdr,fig2_dat_hw,fig2_dat_lbr)
```



```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9","#E69F00",  "#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig2_dat_long$design = ordered(fig2_dat_long$design, levels=c('TDR', 'HW', 'LBR'))
fig2_dat_long$N.reduce.perc = ifelse(fig2_dat_long$N.reduce.perc < 0, 0, fig2_dat_long$N.reduce.perc)
fig2a = fig2_dat_long %>% ggplot(aes(x=p0_p1, y=N.reduce.perc,fill=design)) + 
  geom_col(color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction from conventional design $(\\alpha\\leq$ 0.10, $\\beta\\leq$ 0.10)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,60,5), limits = c(0, 60)) + 
  scale_fill_manual(values=cbPalette) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig2a
```

### Figure 2b

```{r}
table_2 = tdr_alpha10_1s2by2_alphaonly_score %>% rowwise() %>%
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>%
  select(p0, p1, gammax, expicmax, s, m, N, power, beta, alpha, gam, eta, expic)

fig2b_dat = table_2 %>% left_join(litwin_alpha10_1s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) %>%
  left_join(hong_alpha10_alphaonly, by=c("p0","p1"), suffix=c("", ".HW")) %>%
  left_join(conventional_alpha10, by=c("p0","p1"))

fig2b_dat = fig2b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig2b_dat_tdr = fig2b_dat %>% select(p0_p1, power, alpha, beta, eta, gam) %>%
  mutate(design="TDR")

fig2b_dat_hw = fig2b_dat %>% select(p0_p1, power.HW, alpha.HW, beta.HW, eta.HW, gam.HW)
colnames(fig2b_dat_hw) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig2b_dat_hw = fig2b_dat_hw %>%
  mutate(design="HW")

fig2b_dat_lbr = fig2b_dat %>% select(p0_p1, power.LBR,alpha.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig2b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig2b_dat_lbr = fig2b_dat_lbr %>%
  mutate(design="LBR",eta=NA, gam=NA) # no inconclusive region in LBR method, thus eta & gam = 0

fig2b_dat_long = rbind(fig2b_dat_tdr,fig2b_dat_hw,fig2b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
fig2b_dat_long$design = ordered(fig2b_dat_long$design, levels=c('TDR', 'HW', 'LBR'))

fig2b1 = fig2b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.90,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.75,1,0.05), limits = c(0.75,1)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.10, $\\beta\\leq$0.10)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig2b2 = fig2b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.10,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.15,0.05), limits = c(0.0, 0.15)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig2b3 = fig2b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.10,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.15,0.05), limits = c(0.0, 0.15)) +
  labs(y = TeX("$\\beta$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#   theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig2b4 = fig2b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=eta, color=design, group=design), alpha=0.75) +
#   geom_point(aes(y=eta, color=design), alpha=0.75) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.50,0.05), limits = c(0.0, 0.50)) +
#   labs(y = TeX("$\\eta$")) +
#   # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
#   theme_light() +
#   theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
#         axis.title.x = element_blank(),
#         axis.text.x = element_blank(),
#         axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
#         axis.text.y = element_text(size=rel(0.8)),
#         text = element_text(),
#         panel.background = element_rect(colour = NA),
#         plot.background = element_rect(colour = NA),
#         panel.border = element_rect(colour = NA),
#         axis.text = element_text(),
#         axis.line = element_line(colour="black"),
#         axis.line.x = element_blank(),
#         axis.ticks = element_line(),
#         axis.ticks.x = element_blank(),
#         panel.grid.major = element_line(colour="#f0f0f0"),
#         panel.grid.minor = element_blank(),
#         legend.key = element_rect(colour = NA),
#         legend.position = "none",
#         legend.margin = margin(0,0,0,0), # unit(0, "cm"),
#         legend.title = element_text(face="italic"),
#         plot.margin=unit(c(0,5,0,5),"mm"),
#         strip.background=element_rect(colour="#999999",fill="#999999"),
#         strip.text = element_text(face="bold")
#         )
# 
# fig2b5 = fig2b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
#   geom_line(aes(y=gam, color=design, group=design), alpha=0.5) +
#   geom_point(aes(y=gam, color=design), alpha=0.5) +
#   scale_color_manual(values=cbPalette) +
#   # geom_hline(yintercept = 0.2,linetype='dashed', color='grey', alpha=0.5) +
#   scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
# , y = TeX("$\\gamma$")
  labs(x = TeX("Response rates: ($p_0, p_1$)")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig2b = ggarrange(fig2b1, fig2b2, fig2b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig2b
```

### Figure 2
```{r, fig.height=3.5, fig.width=5}
fig2 = ggarrange(fig2a, fig2b, nrow=1, legend = 'bottom')
fig2
```

### write to pdf
```{r}
FILENAME = 'manuscript/tbl2_fig2.pdf'
save_kable(tbl2, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig2
dev.off()

```





## 3. Two-Stage 2-by-2 alpha <= 0.20, beta <= 0.20
### 1.1. control alpha only
#### selected cases
### Table 3
```{r}

score = apply(tdr_alpha20_2s2by2_alphaonly, 1, loss_func_2s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_2s2by2_alphaonly_score = tdr_alpha20_2s2by2_alphaonly
tdr_alpha20_2s2by2_alphaonly_score$loss_score = score
tdr_alpha20_2s2by2_alphaonly_score = tdr_alpha20_2s2by2_alphaonly_score %>% 
  filter(power>=0.8*0.95) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_3 = tdr_alpha20_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, s, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

table_3_ltx = table_3
table_3_ltx[,8:17] = round(table_3_ltx[,8:17],2)
write.csv(table_3_ltx, 'manuscript/tbl_3.csv', row.names = F)

tbl3 = kable(table_3, booktab=T, align='c', digits=2, 
      caption='Table 3: TDR two-stage 2-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$s_1$","$m_1$","$s_2$","$m_2$","$EN$", "$N_1$","$N_2$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl3
```

### Figure 3a
```{r}
fig3_dat_tdr = tdr_alpha20_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='TDR') %>% filter(p0_p1 %in% p0p1_list) %>% ungroup() %>%
  select(p0_p1, En, N2, power, beta, alpha, gam, eta, design)

fig3_dat_lbr = litwin_alpha20_2s_alphaonly %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='LBR') %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0_p1, En, N1, N2, power, beta, alpha, gam, eta, design) %>%
  mutate(N2-N1)

fig3_dat = left_join(fig3_dat_tdr, fig3_dat_lbr, by='p0_p1', suffix=c("",".LBR"))
fig3_dat = fig3_dat %>% rowwise() %>% mutate(En.reduce.perc=(En.LBR - En)/En.LBR*100,
                                             Nmax.reduce.perc = (N2.LBR - N2)/N2.LBR*100)
fig3_dat_long = pivot_longer(fig3_dat, cols = c('En.reduce.perc', 'Nmax.reduce.perc'), names_to = 'metric')
```

```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9", "#009E73", "#E69F00","#F0E442", "#0072B2", "#D55E00", "#CC79A7")

fig3_dat_long$metric = ordered(fig3_dat_long$metric, levels=c('En.reduce.perc', 'Nmax.reduce.perc'))
fig3a = fig3_dat_long %>% ggplot(aes(x=p0_p1,fill=metric)) + 
  geom_col(aes(y=value), color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction vs LBR $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,20,5), limits = c(0, 20)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig3a
```
```{r}
tdr2s3560 = tdr_alpha20_2s2by2_alphaonly %>% filter(p0==0.35, p1==0.60)
score = apply(tdr2s3560, 1, loss_func_2s, alpha=0.20, beta=0.20, w=0.50)

tdr2s3560$loss_score = score
tdr_alpha20_2s2by2_alphaonly_score = tdr_alpha20_2s2by2_alphaonly_score %>% 
  filter(power>=0.8*0.95) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

```


### Figure 3b
```{r}
table_3 = tdr_alpha20_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, s, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

fig3b_dat = table_3 %>% left_join(litwin_alpha20_2s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) 

fig3b_dat = fig3b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig3b_dat_tdr = fig3b_dat %>% select(p0_p1, power, alpha, beta, eta, gam) %>%
  mutate(design="TDR")

fig3b_dat_lbr = fig3b_dat %>% select(p0_p1, power.LBR,alpha.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig3b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig3b_dat_lbr = fig3b_dat_lbr %>%
  mutate(design="LBR")

fig3b_dat_long = rbind(fig3b_dat_tdr,fig3b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
cbPalette <- c("#56B4E9","#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig3b_dat_long$design = ordered(fig3b_dat_long$design, levels=c('TDR', 'LBR'))

fig3b1 = fig3b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.65,0.90,0.05), limits = c(0.65, 0.90)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig3b2 = fig3b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig3b3 = fig3b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(x = TeX("Response rates: ($p_0, p_1$)"), y = TeX("$\\beta$")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig3b = ggarrange(fig3b1, fig3b2, fig3b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig3b
```
### Figure 3
```{r, fig.height=2.5, fig.width=5}
fig3 = ggarrange(fig3a, fig3b, nrow=1, legend = 'bottom')
fig3
```

### write to pdf
```{r}
FILENAME = 'manuscript/fig3.pdf'
save_kable(tbl3, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig3
dev.off()

```

## 4. One-Stage 2-by-2 vs 3-by-2 alpha <= 0.20, beta <= 0.20, control alpha only
### Table 4
```{r}


score = apply(tdr_alpha20_1s2by2_alphaonly, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly
tdr_alpha20_1s2by2_alphaonly_score$loss_score = score
tdr_alpha20_1s2by2_alphaonly_score = tdr_alpha20_1s2by2_alphaonly_score %>% filter(power>=0.80*0.95, alpha<=0.20) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

score = apply(tdr_alpha20_1s3by2_alphaonly, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_1s3by2_alphaonly_score = tdr_alpha20_1s3by2_alphaonly
tdr_alpha20_1s3by2_alphaonly_score$loss_score = score
tdr_alpha20_1s3by2_alphaonly_score = tdr_alpha20_1s3by2_alphaonly_score %>% filter(power>=0.80*0.95, alpha<=0.20) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_4 = tdr_alpha20_1s3by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, r, s, m, N, power, beta, alpha, gam, eta, expic)

table_S3_ltx = table_4
table_S3_ltx[,9:14] = round(table_S3_ltx[,9:14],2)
write.csv(table_S3_ltx, 'manuscript/tbl_S3.csv', row.names = F)

tbl4 = kable(table_4, booktab=T, align='c', digits=2, 
      caption='Table S3: TDR one-stage 3-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$r$","$s$","$m$","$N$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl4
```

### Figure 4a
```{r}
table_4_2by2 = tdr_alpha20_1s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='2by2') %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0_p1, design, N, power, beta, alpha, gam, eta, expic)
table_4_3by2 = tdr_alpha20_1s3by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='3by2') %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0_p1, design, N, power, beta, alpha, gam, eta, expic)


fig4_dat_long = rbind(table_4_2by2,table_4_3by2)
```

```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9", "#009E73", "#E69F00","#F0E442", "#0072B2", "#D55E00", "#CC79A7")

fig4_dat_long$design = ordered(fig4_dat_long$design, levels=c('2by2', '3by2'))
fig4a = fig4_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) + 
  geom_col(aes(y=N), color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size: one-stage 2-by-2 vs 3-by-2 $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "Sample size") + 
  scale_y_continuous(breaks=seq(0,80,5), limits = c(0, 80)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig4a
```


### Figure 4b
```{r, fig.height=3, fig.width=2}
cbPalette <- c("#56B4E9", "#009E73", "#E69F00","#F0E442", "#0072B2", "#D55E00", "#CC79A7")

fig4b_dat_long = fig4_dat_long

fig4b1 = fig4b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.65,0.90,0.05), limits = c(0.65, 0.90)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig4b2 = fig4b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig4b3 = fig4b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(x = TeX("Response rates: ($p_0, p_1$)"), y = TeX("$\\beta$")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig4b = ggarrange(fig4b1, fig4b2, fig4b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig4b
```


### Figure 4
```{r, fig.height=2.5, fig.width=5}
fig4 = ggarrange(fig4a, fig4b, nrow=1, legend = 'bottom')
fig4
```
### delta
```{r}
fig4_dat_long = fig4_dat_long %>% rowwise() %>% mutate(d = p1-p0)
fig4_dat_long %>% group_by(round(d,2), design) %>% summarise(mean(N), mean(power), mean(alpha), mean(beta))
```


### write to pdf
```{r}
FILENAME = 'manuscript/tbl4_fig4.pdf'
save_kable(tbl4, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig4
dev.off()

```

## 5. Loss function case study
```{r}
case1 = tdr_alpha20_1s2by2_alphaonly %>% filter(p0==0.35,p1==0.55) %>% 
  select(p0,p1,power, N, gammax, expicmax) %>% 
group_by(p0,p1,power, N) %>%
  arrange(gammax,expicmax) %>%
  filter(row_number() %in% c(1)) 

score = apply(case1, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.40)
case1$score_w40 = score
score = apply(case1, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
case1$score_w50 = score
score = apply(case1, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.60)
case1$score_w60 = score



# case1_dat_1 = case1 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
# case1_dat_1
# 
# score = apply(case1, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
# case1$loss_score = score
# case1_dat_2 = case1 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
# case1_dat_2
# 
# score = apply(case1, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.60)
# case1$loss_score = score
# case1_dat_3 = case1 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
# case1_dat_3

case1

case1[,3] = round(case1[,3],2)
case1[,7:9] = round(case1[,7:9],5)

table_S1_ltx = case1[,3:9]
# table_S1_ltx[,8:13] = round(table_3_ltx[,8:13],2)
write.csv(table_S1_ltx, 'manuscript/tbl_S1.csv', row.names = F)

tbl5 = kable(case1[,3:9], booktab=T, align='c', # digits=5, 
      caption='Table 5: example of loss scores at w=0.40, 0.50, 0.60',
      col.names = c("$\\pi$","$N$","$\\gamma_{max}$", "$\\lambda_{max}$", "$w=0.40$","$w=0.50$","$w=0.60$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl5
```
```{r}
case2 = tdr_alpha20_1s2by2_alphaonly %>% filter(p0==0.50,p1==0.65)
score = apply(case2, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.10)
case2$loss_score = score
case2_dat = case2 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
case2_dat

score = apply(case2, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.50)
case2$loss_score = score
case2_dat = case2 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
case2_dat

score = apply(case2, 1, loss_func_1s, alpha=0.20, beta=0.20, w=0.90)
case2$loss_score = score
case2_dat = case2 %>% distinct(N, power, loss_score) %>% arrange(loss_score)
case2_dat

```

## 6. Two-Stage 3-by-2 alpha <= 0.20, beta <= 0.20
### 1.1. control alpha only
#### selected cases
### Table 6
```{r}

score = apply(tdr_alpha20_2s3by2_alphaonly, 1, loss_func_2s, alpha=0.20, beta=0.20, w=0.50)
tdr_alpha20_2s3by2_alphaonly_score = tdr_alpha20_2s3by2_alphaonly
tdr_alpha20_2s3by2_alphaonly_score$loss_score = score
tdr_alpha20_2s3by2_alphaonly_score = tdr_alpha20_2s3by2_alphaonly_score %>% filter(power>=0.80*0.95, alpha<=0.20) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_6 = tdr_alpha20_2s3by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, b1,b2, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

tbl6 = kable(table_6, booktab=T, align='c', digits=2, 
      caption='Table 6: TDR two-stage 3-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$a_1$","$m_1$","$b_1$","$b_2$","$m_2$","$EN$", "$N_1$","$N_2$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl6
```

### Figure 6a
```{r}
fig6_dat_tdr = tdr_alpha20_2s3by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='TDR') %>% filter(p0_p1 %in% p0p1_list) %>% ungroup() %>%
  select(p0_p1, En, N2, power, beta, alpha, gam, eta, design)

fig6_dat_lbr = litwin_alpha20_2s_alphaonly %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='LBR') %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0_p1, En, N2, power, beta, alpha, gam, eta, design)

fig6_dat = left_join(fig6_dat_tdr, fig6_dat_lbr, by='p0_p1', suffix=c("",".LBR"))
fig6_dat = fig6_dat %>% rowwise() %>% mutate(En.reduce.perc=(En.LBR - En)/En.LBR*100,
                                             Nmax.reduce.perc = (N2.LBR - N2)/N2.LBR*100)
fig6_dat_long = pivot_longer(fig6_dat, cols = c('En.reduce.perc', 'Nmax.reduce.perc'), names_to = 'metric')
```

```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9", "#009E73", "#E69F00","#F0E442", "#0072B2", "#D55E00", "#CC79A7")

fig6_dat_long$metric = ordered(fig6_dat_long$metric, levels=c('En.reduce.perc', 'Nmax.reduce.perc'))
fig6a = fig6_dat_long %>% ggplot(aes(x=p0_p1,fill=metric)) + 
  geom_col(aes(y=value), color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction vs LBR $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,20,5), limits = c(0, 20)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig6a
```
### Figure 6b
```{r}
table_6 = tdr_alpha20_2s3by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, b1,b2, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

fig6b_dat = table_6 %>% left_join(litwin_alpha20_2s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) 

fig6b_dat = fig6b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig6b_dat_tdr = fig6b_dat %>% select(p0_p1, power, alpha, beta, eta, gam) %>%
  mutate(design="TDR")

fig6b_dat_lbr = fig6b_dat %>% select(p0_p1, power.LBR,alpha.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig6b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig6b_dat_lbr = fig6b_dat_lbr %>%
  mutate(design="LBR")

fig6b_dat_long = rbind(fig6b_dat_tdr,fig6b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
cbPalette <- c("#56B4E9","#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig6b_dat_long$design = ordered(fig6b_dat_long$design, levels=c('TDR', 'LBR'))

fig6b1 = fig6b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.65,0.90,0.05), limits = c(0.65, 0.90)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig6b2 = fig6b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.20, $\\beta\\leq$0.20)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig6b3 = fig6b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(x = TeX("Response rates: ($p_0, p_1$)"), y = TeX("$\\beta$")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig6b = ggarrange(fig6b1, fig6b2, fig6b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig6b
```
### Figure 6
```{r, fig.height=2.5, fig.width=5}
fig6 = ggarrange(fig6a, fig6b, nrow=1, legend = 'bottom')
fig6
```

### write to pdf
```{r}
FILENAME = 'manuscript/tbl6_fig6.pdf'
save_kable(tbl6, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig6
dev.off()

```



## 7. Two-Stage 2-by-2 alpha <= 0.10, beta <= 0.10
### 1.1. control alpha only
#### selected cases
### Table 7
```{r}

score = apply(tdr_alpha10_2s2by2_alphaonly, 1, loss_func_2s, alpha=0.10, beta=0.10, w=0.50)
tdr_alpha10_2s2by2_alphaonly_score = tdr_alpha10_2s2by2_alphaonly
tdr_alpha10_2s2by2_alphaonly_score$loss_score = score
tdr_alpha10_2s2by2_alphaonly_score = tdr_alpha10_2s2by2_alphaonly_score %>% 
  filter(power>=0.8*0.95) %>%
  group_by(p0,p1,gammax) %>%
  arrange(p0,p1,loss_score,expicmax) %>%
  filter(row_number() %in% c(1)) %>%
  group_by(p0,p1) %>%
  arrange(p0,p1,loss_score) %>%
  filter(row_number() %in% c(1)) 

# Study Design
table_7 = tdr_alpha10_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, s, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

table_7_ltx = table_7
table_7_ltx[,8:17] = round(table_7_ltx[,8:17],2)
write.csv(table_7_ltx, 'manuscript/tbl_7.csv', row.names = F)

tbl7 = kable(table_7, booktab=T, align='c', digits=2, 
      caption='Table 3: TDR two-stage 2-by-2 design, $\\alpha\\leq0.20$, $\\beta\\leq0.20$',
      col.names = c("$p_0$","$p_1$","$\\gamma_{max}$","$\\lambda_{max}$","$s_1$","$m_1$","$s_2$","$m_2$","$EN$", "$N_1$","$N_2$","$\\pi$", "$\\beta$", "$\\alpha$", "$\\gamma$", "$\\eta$", "$\\lambda$")) %>% 
  kable_classic_2() %>%
  kable_styling(latex_options=c("scale_down","HOLD_position"))
tbl7
```

### Figure 7a
```{r}
fig7_dat_tdr = tdr_alpha10_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='TDR') %>% filter(p0_p1 %in% p0p1_list) %>% ungroup() %>%
  select(p0_p1, En, N2, power, beta, alpha, gam, eta, design)

fig7_dat_lbr = litwin_alpha10_2s_alphaonly %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1), design='LBR') %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0_p1, En, N1, N2, power, beta, alpha, gam, eta, design) %>%
  mutate(N2-N1)

fig7_dat = left_join(fig7_dat_tdr, fig7_dat_lbr, by='p0_p1', suffix=c("",".LBR"))
fig7_dat = fig7_dat %>% rowwise() %>% mutate(En.reduce.perc=(En.LBR - En)/En.LBR*100,
                                             Nmax.reduce.perc = (N2.LBR - N2)/N2.LBR*100)
fig7_dat_long = pivot_longer(fig7_dat, cols = c('En.reduce.perc', 'Nmax.reduce.perc'), names_to = 'metric')
```

```{r, fig.width=6, fig.height=3}
cbPalette <- c("#56B4E9", "#009E73", "#E69F00","#F0E442", "#0072B2", "#D55E00", "#CC79A7")

fig7_dat_long$metric = ordered(fig7_dat_long$metric, levels=c('En.reduce.perc', 'Nmax.reduce.perc'))
fig7a = fig7_dat_long %>% ggplot(aes(x=p0_p1,fill=metric)) + 
  geom_col(aes(y=value), color='black', size=0.05, width=0.5, position = position_dodge(0.5)) + # stat = 'identity', 
  # geom_text(aes(label = N.reduce), vjust = -0.5, size=2, position = position_dodge(width= 0.5)) + 
    ggtitle(TeX("Sample size reduction vs LBR $(\\alpha\\leq$ 0.20, $\\beta\\leq$ 0.20)")) + 
    labs(x = TeX("Response rates: ($p_0, p_1$)"), y = "% reduction") + 
  scale_y_continuous(breaks=seq(0,20,5), limits = c(0, 20)) + 
  scale_fill_manual(values=cbPalette) + 
  
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,5,5),"mm"),
        strip.background=element_rect(colour="#f0f0f0",fill="#f0f0f0"),
        strip.text = element_text(face="bold")
        )
fig7a
```
```{r}
# tdr2s3560 = tdr_alpha10_2s2by2_alphaonly %>% filter(p0==0.35, p1==0.60)
# score = apply(tdr2s3560, 1, loss_func_2s, alpha=0.20, beta=0.20, w=0.50)
# 
# tdr2s3560$loss_score = score
# tdr_alpha10_2s2by2_alphaonly_score = tdr_alpha10_2s2by2_alphaonly_score %>% 
#   filter(power>=0.8*0.95) %>%
#   group_by(p0,p1,gammax) %>%
#   arrange(p0,p1,loss_score,expicmax) %>%
#   filter(row_number() %in% c(1)) %>%
#   group_by(p0,p1) %>%
#   arrange(p0,p1,loss_score) %>%
#   filter(row_number() %in% c(1)) 

```


### Figure 7b
```{r}
table_7 = tdr_alpha10_2s2by2_alphaonly_score %>% rowwise() %>% 
  mutate(p0_p1 = fmt_p0p1(p0,p1)) %>% filter(p0_p1 %in% p0p1_list) %>% 
  select(p0, p1, gammax, expicmax, a1, m1, s, m2, En, N1, N2, power, beta, alpha, gam, eta, expic)

fig7b_dat = table_7 %>% left_join(litwin_alpha10_2s_alphaonly, by=c("p0","p1"), suffix=c("", ".LBR")) 

fig7b_dat = fig7b_dat %>% rowwise() %>% mutate(p0_p1 = fmt_p0p1(p0,p1))

fig7b_dat_tdr = fig7b_dat %>% select(p0_p1, power, alpha, beta, eta, gam) %>%
  mutate(design="TDR")

fig7b_dat_lbr = fig7b_dat %>% select(p0_p1, power.LBR,alpha.LBR, beta.LBR, eta.LBR, gam.LBR)
colnames(fig7b_dat_lbr) = c('p0_p1', 'power', 'alpha', 'beta', 'eta', 'gam')
fig7b_dat_lbr = fig7b_dat_lbr %>%
  mutate(design="LBR")

fig7b_dat_long = rbind(fig7b_dat_tdr,fig7b_dat_lbr)

```

```{r, fig.height=3, fig.width=2}
cbPalette <- c("#56B4E9","#999999", "#F0E442", "#009E73", "#0072B2", "#D55E00", "#CC79A7")

fig7b_dat_long$design = ordered(fig7b_dat_long$design, levels=c('TDR', 'LBR'))

fig7b1 = fig7b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=power, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=power, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.80,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0.70,0.95,0.05), limits = c(0.70, 0.95)) +
  labs(y = TeX("$\\pi$")) +
  ggtitle(TeX("Operating characteristics $(\\alpha\\leq$0.10, $\\beta\\leq$0.10)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(10,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig7b2 = fig7b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=alpha, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=alpha, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(y = TeX("$\\alpha$")) +
  # ggtitle(TeX("Performance comparison $(\\alpha\\leq$0.10, $\\beta\\leq$0.10)")) + 
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1.2), hjust = 0.5, vjust=0.5),
        axis.title.x = element_blank(),
        axis.text.x = element_blank(),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.line.x = element_blank(),
        axis.ticks = element_line(),
        axis.ticks.x = element_blank(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "none",
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,0,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig7b3 = fig7b_dat_long %>% ggplot(aes(x=p0_p1,fill=design)) +
  geom_line(aes(y=beta, color=design, group=design), alpha=0.75) +
  geom_point(aes(y=beta, color=design), alpha=0.75) +
  scale_color_manual(values=cbPalette) +
  geom_hline(yintercept = 0.20,linetype='dashed', color='black', alpha=0.5) +
  scale_y_continuous(breaks=seq(0,0.25,0.05), limits = c(0.0, 0.25)) +
  labs(x = TeX("Response rates: ($p_0, p_1$)"), y = TeX("$\\beta$")) +
  theme_light() +
  theme(plot.title = element_text(face = "bold", size = rel(1), hjust = 0.5, vjust=0.5),
        axis.text.x = element_text(angle = 60, vjust=0.5, size=rel(0.8)),
        axis.title.y = element_text(angle=90,vjust =2, size=rel(0.8)),
        axis.text.y = element_text(size=rel(0.8)),
        text = element_text(),
        panel.background = element_rect(colour = NA),
        plot.background = element_rect(colour = NA),
        panel.border = element_rect(colour = NA),
        axis.text = element_text(),
        axis.line = element_line(colour="black"),
        axis.ticks = element_line(),
        panel.grid.major = element_line(colour="#f0f0f0"),
        panel.grid.minor = element_blank(),
        legend.key = element_rect(colour = NA),
        legend.position = "bottom",
        legend.direction = "horizontal",
        legend.key.size= unit(0.2, "cm"),
        legend.margin = margin(0,0,0,0), # unit(0, "cm"),
        legend.title = element_text(face="italic"),
        plot.margin=unit(c(0,5,5,5),"mm"),
        strip.background=element_rect(colour="#999999",fill="#999999"),
        strip.text = element_text(face="bold")
        )

fig7b = ggarrange(fig7b1, fig7b2, fig7b3, align='v', heights=c(1.5,1,1.5), nrow=3)
fig7b
```
### Figure 7
```{r, fig.height=2.5, fig.width=5}
fig7 = ggarrange(fig7a, fig7b, nrow=1, legend = 'bottom')
fig7
```

### write to pdf
```{r}
FILENAME = 'manuscript/fig7.pdf'
save_kable(tbl7, FILENAME)

pdf(file = FILENAME,   # The directory you want to save the file in
        width = 10, # The width of the plot in inches
        height = 5) # The height of the plot in inches
fig7
dev.off()

```