r4asme09 further cox.Rmd

---
title: "9: Further analysis with Cox regression"
subtitle: "R 4 ASME"
authors: Authors – Lakmal Mudalige & Andrea Mazzella [(GitHub)](https://github.com/andreamazzella)
output: html_notebook
---

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## Contents

* Examine the proportionality assumption in Cox models
  * graphically, with Nelson-Aalen plots
  * with a test for interaction
  * with a test for residuals
 
* Cox regression with multiple covariates

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## 0. Packages and options

```{r message=FALSE, warning=FALSE}
# Load packages
library("haven")
library("magrittr")
library("survival")
library("survminer")
library("epiDisplay")
library("tidyverse")

# Limit significant digits to 3, reduce scientific notation
options(digits = 3, scipen = 9)
```

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# Diet and heart disease

This dataset contains information on dietary energy intake and subsequent incidence of coronary heart disease.


**Outcome*: `chd` (coronary heart disease mortality)
**Exposure*: `hieng` (high-energy diet)
**Time*:
 -`doe` (date of entry)
 -`dox` (date of exit)
 -`dob` (date of birth)
 -`agein` (age at entry)
 -`ageout` (age at exit)
 -`fup` (follow-up time)
**Other*
- `fibre` (daily dietary fibre, g)
            
Data import and management. The practical asks later to categorise the `fibre` variable, let's do it now.
```{r include=FALSE}
diet <- read_dta("dietlsh.dta") %>% mutate_if(is.labelled, as_factor)

glimpse(diet)

diet %<>% mutate(hieng = factor(hieng,
                                levels = c(0, 1),
                                labels = c("normal", "high-energy")),
                 fibre_cat = cut_number(fibre, 3))
summary(diet$fibre_cat)
summary(diet$fibre)
glimpse(diet)
```

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## 1. Cox regression

Set the timescale as time since entry, and analyse the effect of a high-energy diet on the CHD mortality with Cox regression.

```{r}
# Create survival object
surv_diet <- Surv(diet$fup, diet$chd)
summary(surv_diet)

# Cox model
(cox_hieng <- coxph(surv_diet ~ hieng, data = diet))
cox_hieng$coefficients %>% exp()
confint(cox_hieng) %>% exp()
```
The longest follow-up period was 20 years.
People following a high-energy diet half the rate of CHD than people not on that diet (HR 0.52, 0.29-0.95).

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## 2. Nelson-Aalen plot

Cox regression carries an assumption that the rate ratio remains constant over time. We can check this visually with a Nelson-Aalen plot. Do you think the proportionality assumption is valid?

N-A plots are built with function `ggsurvplot()` from package "survminer"; it uses ggplot to visualise survival objects made with `Surv()` and fitted to data with `survfit()`. Unlike Stata, the confidence interval bands are semi-transparent, which makes the graph much more readable.
```{r message=FALSE, warning=FALSE}
# Create Survfit object
sf_diet <- survfit(surv_diet ~ hieng, data = diet)

# Nelson-Aalen graph
ggsurvplot(sf_diet,
           data = diet,
           fun = "cumhaz",
           conf.int = T,
           yscale = "log2",
           title = "Nelson-Aalen plot", xlab = "Time since entry (years)")
```
On the logarithm scale, the lines seem to remain equidistant through time: the relative effects of diet seem proportional.

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## 3. Interaction test

Let's now formally assess this with an interaction test.

Let's first split the data in two: before and after the median follow-up period.
*Issue*: I don't know how to calculate the median (equivalent of centile in Stata) for the Surv object.
```{r}
# Calculate median follow-up ???
summary(surv_diet)

# plot(surv_diet)

sf_diet

# Split the dataset into two time-bands
split_diet <- survSplit(surv_diet ~ ., diet, cut = c(6.8), episode = "timegroup")
```

We add the newly created timegroup variable in `strata()`, and we use `*` to indicate interaction with high-energy diet. In the output, R knows not to estimate an effect for time, so it doesn't, unlike Stata.


We compare this model with another model without strata() with a LRT.

NB: you need to fit a new basic model to the split dataset!
```{r}
# Model with interaction
(cox_hieng_inter <- coxph(surv_diet ~ hieng * strata(timegroup), data = split_diet))

# Model without interaction
cox_hieng_basic <- coxph(surv_diet ~ hieng, data = split_diet) 

# Likelihood ratio test
lrtest(cox_hieng_basic, cox_hieng_inter)
```
There is no evidence that the effect of diet is not proportional using time in the study (LRT p = 0.38).

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## 4. Nelson-Aalen plot with age timescale

Now do the same analyses in Q1-2 but using age as the time scale. 


```{r}
# Create survival object with age as the time scale 
surv_diet_age <- diet %$% Surv(time = as.numeric(doe) / 365.25,
                               time2 = as.numeric(dox) / 365.25,
                               event = chd,
                               origin = as.numeric(dob) / 365.25)
summary(surv_diet_age)
```

```{r message=FALSE}
# Nelson-Aalen plot
sf_diet_age <- survfit(surv_diet_age ~ hieng, data = diet)
ggsurvplot(sf_diet_age,
           data = diet,
           fun = "cumhaz",
           conf.int = T,
           yscale = "log2",
           title = "Nelson-Aalen plot", xlab = "Age (years)")
```
The lines are not equidistant, so the effect does not *appear* to be proportional; but the confidence intervals are very wide, because there are few observations particularly at the start (among younger people). So, a NA plot is not very helpful. 

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## 5. Interaction test on age timescale

Now do the same analyses in Q3 but using age as the time scale. 

```{r}
# Split the age timeaxis into two, at 59.7
split_diet_age <- survSplit(surv_diet_age ~ ., diet, cut = c(59.7), episode = "agegroup")

# Cox with interaction for age
(cox_hieng_age_inter <- coxph(surv_diet_age ~ hieng * strata(agegroup), data = split_diet_age))

# Cox without interaction
cox_hieng_age_basic <- coxph(surv_diet_age ~ hieng, data = split_diet_age) 

# LRT
lrtest(cox_hieng_age_inter, cox_hieng_age_basic)
```
There is no evidence against proportionality using age as timescale.

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## 6. Non-binary exposures

Investigate the effect of dietary fibre (`fibre_cat`) on CHD mortality, first with follow-up time scale.

```{r}
# Create survfit object
sf_diet_fibre <- survfit(surv_diet ~ fibre_cat, data = diet)

# Nelson-Aalen plot
ggsurvplot(sf_diet_fibre, data = diet, fun = "cumhaz", conf.int = T, yscale = "log2", title = "Nelson-Aalen plot", xlab = "Time of follow-up (years)")
```

The plot becomes very difficult to interpret, and the confidence intervals greatly overlap.

```{r}
# Fit a Cox model 
(cox_fibre <- coxph(surv_diet ~ fibre_cat, data = split_diet))

# Cox with interaction
(cox_fibre_inter <- coxph(surv_diet ~ fibre_cat * strata(timegroup), data = split_diet))

# LRT
lrtest(cox_fibre, cox_fibre_inter)
```

Now let's do the same analyses (except NA plot) but using age time-scale.
```{r}
# Cox model
(cox_fibre_age <- coxph(surv_diet_age ~ fibre_cat, data = split_diet_age))

# Cox model adjusting for age
(cox_fibre_age_inter <- coxph(surv_diet_age ~ fibre_cat * strata(agegroup), data = split_diet_age))

# LRT
lrtest(cox_fibre_age, cox_fibre_age_inter)
```

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# Primary Biliary Cirrhosis

## 7. Cox with multiple covariates


Read in pbc1bas.dta and set the analysis on a follow-up timescale.

```{r}
# Read in the pbc1bas.dta dataset 
pbc <- read_dta("pbc1bas.dta")

# Data management
pbc %<>% mutate(death = d,
               treat = factor(treat, levels = c(1, 2), labels = c("placebo", "azath")),
               cenc0 = factor(cenc0, levels = c(0, 1), labels = c("no", "yes")),
               cir0 = factor(cir0, levels = c(0, 1), labels = c("no", "yes")),
               gh0 = factor(gh0, levels = c(0, 1), labels = c("no", "yes")),
               asc0 = factor(asc0, levels = c(0, 1), labels = c("no", "yes"))) %>% 
         select(-d)

# Survival object
surv_pbc <- Surv(pbc$time, pbc$death)
```

Firstly, examine the effect of treatment (`treat`), then add bilirubin (`logb0`) and cirrhosis (`cir0`) to the model, one by one.
```{r}
# Univariate
coxph(surv_pbc ~ treat, data = pbc)

# Adding bilirubin
coxph(surv_pbc ~ treat + logb0, data = pbc)

# Fully adjusted model
coxph(surv_pbc ~ treat + logb0 + cir0, data = pbc)
```

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## Bonus 1: Forest plots

Package survminer has a great function to visually represent the rate ratios in a Cox model via a Forest plot: `ggforest()`. It takes as argument a Cox model. (Alternatively, you can use `sjPlot::plot_model()`)
```{r}
ggforest(cox_fibre_age, data = diet)
# sjPlot::plot_model(cox_fibre_age)
```


## Bonus 2: test of proportional hazards with residuals

There is a quicker way of testing the assumption of proportional hazards: testing of residuals, with function `cox.zph()`.
```{r}
# Test 
(pr_haz <- cox.zph(cox_hieng))

# Plot curves
ggcoxzph(pr_haz)
```

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