In n8thangreen/CEdecisiontree: Cost-effectiveness decision tree analysis

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

Introduction

For small decision trees it is simple to directly write down structure of the tree and its values.

However, for larger trees this may become unwieldy and error prone. We can take advantage of some of the tree characteristics though:

Sections of the tree may be repeated
A particular unit cost or health measure may be used on multiple edges
Multiple trees may use the same cost and health values
Tree structure and labeling may remain the same but values assigned change e.g. in sensitivity analysis or alternative interventions

Thus, we can separate the structure of the tree, the labeling of edges and the values assigned to those labels. In this way we have flexibility in modify any one of these and better adhere to the DRY principle and the benefits it offers.

For instance, we can think of the value assignment like a relational table with key-value pairs where the key is Label. For the decision tree tree with cost values, edges are labeled as follows:

| Label | From node | To node | |-----------|-----------|---------| | vaccinate | 1 | 2 | | disease | 2 | 4 | | disease | 3 | 6 |

and joined with the values table:

| Label | Cost | Prob | Health | |--------------|------|------|--------| | vaccinate | 10 | 0.7 | 0 | | vacc_disease | - | 0.1 | - | | disease | 100 | 0.9 | 0.5 |

Example

Let us demonstrate this approach using a simple tree.

library(CEdecisiontree)
library(dplyr)

First, we define the structure of the tree in list format without any additional information. Let's make a two-step binary tree.

tree_struc <-
  list(
    '1' = c(2,3),
    '2' = c(4,5),
    '3' = c(6,7))

Now we can add labels and values to this tree. Define the set of cost, health values and probabilities, independent of the tree structure.

label_cost <-
  list(
    "vaccinate" = 10,
    "disease" = 100)

label_probs <- 
  list(
    "vaccinate" = 0.7,
    "vacc_disease" = 0.1,
    "disease" = 0.9)

label_health <- 
  list(
    "disease" = 0.5)

Next, assign cost, probability and health labels to particular branches.

library(tibble)

cost_label_branch <- 
  tribble(~name,      ~from, ~to,
          "vaccinate", 1,    2,
          "disease",   2,    4,
          "disease",   3,    6)

prob_label_branch <- 
  tribble(~name,      ~from, ~to,
          "vaccinate",    1,  2,
          "vacc_disease", 2,  4,
          "disease",      3,  6)

health_label_branch <- 
  tribble(~name,     ~from, ~to,
          "disease", 2,     4,
          "disease", 3,     6)

Finally, we can pull it all together and create a single decision tree long format data frame.

tree_dat <-
  create_ce_tree_long_df(
    tree_list = tree_struc,
    label_probs = label_probs,
    label_costs = label_cost,
    label_health = label_health,
    pname_from_to = prob_label_branch,
    cname_from_to = cost_label_branch,
    hname_from_to = health_label_branch)

tree_dat

The above example may seem a little over-elaborate. This demonstrates an example where all of the components are defined separately and then combined to obtain a single object with all the input values. Alternatively, we could define the label look up table and the values look up table outside of R and simply read this in and join to obtain an equivalent object.

library(reshape2)

label_branch_tab <- read.csv(here::here("data-raw/label-branch table.csv"))
label_branch_tab

label_val_tab <- read.csv(here::here("data-raw/label-val table.csv"))
label_val_tab

tree_dat2 <-
  create_ce_tree_df(label_branch_tab,
                    label_val_tab,
                    tree_struc)
tree_dat2

This data frame can now be used in the main cost-effectiveness analysis.

tree_costs <- tree_dat2
names(tree_costs)[names(tree_costs) == "cost"] <- "vals"

treemod <- define_model(dat_long = tree_costs)

dectree_expected_values(model = treemod)