Vaccination Markov Model - issue with initial cost

[zaddyzad]

I'm running a simple time-homogeneous Markov model. It's unclear why the final cost of drugs is $3,960 rather than $4,000. The cost of vaccination is $4 and the initial state count for A == 1,000 (i.e., healthy children). Could this be a bug?

My abridged code is below:

`dr=0.03

#Transition
vacc=define_transition(
  .97995,.00005,0,.02,
  0,.97,.01,.02,
  0,0,.9,.1,
  0,0,0,1)

#Healthy
state_A <- define_state(
  cost_health = discount(15, dr),
  cost_drugs = discount(dispatch_strategy(
    vaccination = ifelse(model_time == 1, 4, 0),
    no_vaccination = 0), dr),
  cost_total = cost_health + cost_drugs,
  QALY = discount(1,dr)
)

#running the model
res_mod <- run_model(
  vaccination = strat_vacc,
  no_vaccination = strat_no_vacc,
  cycles = 80,
  cost = cost_total,
  effect = QALY
);summary(res_mod)

Initial state counts:

A = 1000L
B = 0L
C = 0L
D = 0L

Counting method: 'life-table'.

Values:

               cost_health cost_drugs cost_total     QALY
vaccination       304360.2       3960   308320.2 20011.43
no_vaccination    316803.2          0   316803.2 20005.90

[KZARCA]

Hi,
I cannot reproduce your error as I do not have your full code. If you need help, please send it to me.
Best,
Kevin

[zaddyzad]

Hi,
I cannot reproduce your error as I do not have your full code. If you need help, please send it to me.
Best,
Kevin

Hi Kevin, thanks for the help, the full code is here

dr=0.03

#Transition
vacc=define_transition(
  .97995,.00005,0,.02,
  0,.97,.01,.02,
  0,0,.9,.1,
  0,0,0,1)

no.vacc=define_transition(
  .9798,.0002,0,.02,
  0,.97,.01,.02,
  0,0,.9,.1,
  0,0,0,1)

#Healthy
state_A <- define_state(
  cost_health = discount(15, dr),
  cost_drugs = discount(dispatch_strategy(
    vaccination = ifelse(model_time == 1, 4, 0),
    no_vaccination = 0), dr),
  cost_total = cost_health + cost_drugs,
  QALY = discount(1,dr)
)

#chronic HBV
state_B <- define_state(
  cost_health = discount(15, dr),
  cost_drugs = discount(dispatch_strategy(
    vaccination = ifelse(model_time == 1, 4, 0),
    no_vaccination = cost_no_vaccination), dr),
  cost_total = cost_health + cost_drugs,
  QALY = discount(1,dr)
)

#compensated cirrhosis 
state_C <- define_state(
  cost_health = discount(3500, dr),
  cost_drugs = discount(dispatch_strategy(
    vaccination = ifelse(model_time == 1, 4, 0),
    no_vaccination = cost_no_vaccination), dr),
  cost_total = cost_health + cost_drugs,
  QALY = discount(0.75,dr)
)

#dead 
state_D <- define_state(
  cost_health = 0,
  cost_drugs = 0,
  cost_total = 0,
  QALY = 0
)

#defining strategies
strat_vacc <- define_strategy(
  transition = vacc,
  state_A,
  state_B,
  state_C,
  state_D
)

#defining strategies
strat_no_vacc <- define_strategy(
  transition = no.vacc,
  state_A,
  state_B,
  state_C,
  state_D
)

#running the model
res_mod <- run_model(
  vaccination = strat_vacc,
  no_vaccination = strat_no_vacc,
  cycles = 80,
  cost = cost_total,
  effect = QALY
);summary(res_mod)

[KZARCA]

It's not a bug, heemod uses a first-cycle correction named "life-table" by default. You can read more on https://journals.sagepub.com/doi/10.1177/0272989X09340585

If you want the transition to occur at the beginning of the cycle, you can choose method = "beginning".
Best

[zaddyzad]

It's not a bug, heemod uses a first-cycle correction named "life-table" by default. You can read more on https://journals.sagepub.com/doi/10.1177/0272989X09340585

If you want the transition to occur at the beginning of the cycle, you can choose method = "beginning".
Best

'beginning' and 'end' may be inversed in heemod. Per the article 'beginning' should yield an overestimate and 'end' should yield an underestimate.

This is not reflected in the model.

Counting method: 'beginning'.

Values:

               cost_health cost_drugs cost_total     QALY
vaccination       301399.5       3920   305319.5 19809.24
no_vaccination    314056.4          0   314056.4 19803.60

Counting method: 'end'.

Values:

               cost_health cost_drugs cost_total     QALY
vaccination       307320.9       4000   311320.9 20213.62
no_vaccination    319550.0          0   319550.0 20208.21

[KZARCA]

OK thanks for your input, I will change it in the next heemod version.
Best

[zaddyzad]

OK thanks for your input, I will change it in the next heemod version.
Best

Thank you.

[zaddyzad]

@KZARCA, I am facing another issue with the run_dsa function. It works well when I define only 1 sensitivity analyses to be done (i.e., cost_vacc, discount_rate [dr]); however, when I define multipe, I get the following error:

Running DSA on strategy 'vaccination'...
Error: Can't subset columns that don't exist.
x Columns care_cirrohosis, dr, and rr don't exist.

Code is below:

library(heemod)
library(tidyverse)
dr=0.03
cost_vacc=4
care_cirrohosis=3500
rr=0.25

#Transition
vacc=define_transition(
  C,0.0002*rr,0,.02,
  0,.97,.01,.02,
  0,0,.9,.1,
  0,0,0,1)

no.vacc=define_transition(
  .9798,.0002,0,.02,
  0,.97,.01,.02,
  0,0,.9,.1,
  0,0,0,1)

#Healthy
state_A <- define_state(
  cost_health = discount(15, dr),
  cost_drugs = dispatch_strategy(
    vaccination = ifelse(model_time == 1, cost_vacc, 0),
    no_vaccination = 0),
  cost_total = cost_health + cost_drugs,
  QALY = discount(1,dr)
)

#chronic HBV
state_B <- define_state(
  cost_health = discount(15, dr),
  cost_drugs = dispatch_strategy(
    vaccination = ifelse(model_time == 1, cost_vacc, 0),
    no_vaccination = 0),
  cost_total = cost_health + cost_drugs,
  QALY = discount(1,dr)
)

#compensated cirrhosis 
state_C <- define_state(
  cost_health = discount(care_cirrohosis, dr),
  cost_drugs = dispatch_strategy(
    vaccination = ifelse(model_time == 1, cost_vacc, 0),
    no_vaccination = 0),
  cost_total = cost_health + cost_drugs,
  QALY = discount(0.75,dr)
)

#dead 
state_D <- define_state(
  cost_health = 0,
  cost_drugs = 0,
  cost_total = 0,
  QALY = 0
)

#defining strategies
strat_vacc <- define_strategy(
  transition = vacc,
  state_A,
  state_B,
  state_C,
  state_D
)

#defining strategies
strat_no_vacc <- define_strategy(
  transition = no.vacc,
  state_A,
  state_B,
  state_C,
  state_D
)

#running the model
res_mod <- run_model(
  vaccination = strat_vacc,
  no_vaccination = strat_no_vacc,
  cycles = 80,
  init=c(1000000,0,0,0),
  cost = cost_total,
  effect = QALY,
  method='end'
);summary(res_mod)

##plot
plot(res_mod, type = "counts", panel = "by_strategy") +
  xlab("Time") +
  theme_bw() +
  scale_color_brewer(
    name = "State",
    palette = "Set1"
  )

##sensitivity analyses and tornado plot
ds=define_dsa(
    cost_vacc, 2, 30,
    care_cirrohosis,1000,5000,
    dr, 0.015, 0.06,
    rr, 0.3,0.5
 )

print(ds)

x=run_dsa(res_mod,ds)
plot(x,type='difference',result='icer')

`
```

[KZARCA]

Hi, all your variables should be encapsulated within the function define_parameters

params <- define_parameters(
dr=0.03,
cost_vacc=4,
care_cirrohosis=3500,
rr=0.25
)

[minakabiri]

Hi There. I am using heemod for a simulation and I realized that the update related to this issue has changed the results. I checked (by looking at the counts -numebr of people in each state- in each cycle) and realized that the update has changed the package such that with the "beginning" method, transitions happen at the end of the cycle, and with the "end" method, transitions happened at the beginning of the cycle. I think this is probably incorrect though. Maybe there is an error in calculating costs and effects related to the method chosen, but the counts were correct, and now incorrect with this update.

Thanks for your consideration.