In n8thangreen/CEdecisiontree: Cost-effectiveness decision tree analysis

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Introduction

Scenario (or deterministic) sensitivity analysis is a common part of any cost-effectiveness analysis [@Briggs2012]. Here we will carry this out for a simple decision tree. This involves explicitly specifying values for particular branch probability and/or values and calculating the total expected value.

Example

library(CEdecisiontree, quietly = TRUE)
library(assertthat, quietly = TRUE)
library(tibble, quietly = TRUE)
library(tidyverse, quietly = TRUE)
library(purrr, quietly = TRUE)

We create a complete design meaning all combinations on the grid of input values. Alternatively, we may only want to do a one-way analysis and so would set the non-varied term to some common baseline distribution or fixed value. In our example, we will choose three values for each parameter. We can think of this as a worst-, most likely and best-case scenario.

p <- c(NA_real_, 0.4, 0.6)

c2 <- c(10, 50, 100)
c3 <- c(5, 40, 150)

c_grid <-
  expand.grid(c2 = c2,
              c3 = c3) %>% 
  cbind(c1 = 0L, .) %>% 
  t() %>% 
  as.data.frame()

c_grid

Then define the decision tree structure as just a basic binary tree.

child <- list("1" = c(2, 3),
              "2" = NULL,
              "3" = NULL)

We can now loop over the inputs and generate a complete tree object for each cost combination.

tree_dat_sa <- list()

for (i in seq_along(c_grid)) {

  tree_dat_sa[[i]] <-
    define_model(
      tree_dat =
        list(child = child,
             dat = data.frame(
               node = names(child),
               prob = p,
               vals = c_grid[[i]])
        ))
}

This results in a list of trees.

tree_dat_sa[[1]]

Now, it is straightforward to map over each of these trees to obtain the total expected values.

res <- map_dbl(tree_dat_sa, dectree_expected_values)
res

Tornado plot

Lets create a tornado plot showing a one-way sensitivity analysis. We'll use my ceplot. By specifying the output data as a model frame it is handled appropriately.

library(ceplot)
library(reshape2)
library(magrittr)
library(plyr)
library(purrr)
library(dplyr)
library(ggplot2)

sa_dat <- as.data.frame(cbind(t(c_grid), res))

sa_model_dat <- model.frame(formula = res ~ c1 + c2 + c3,
                            data = sa_dat)

##TODO: ceplot package build error
# sa_model_dat %>%
#   ceplot::create_tornado_data() %>%
#   ceplot::ggplot_tornado()