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.
First, we define the structure of the tree in list format without any additional information. Let’s make a two-step binary tree.
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
FALSE from to name.cost cost name.prob prob name.health health
FALSE 1 1 2 vaccinate 10 vaccinate 0.7 <NA> NA
FALSE 2 1 3 <NA> NA <NA> 0.3 <NA> NA
FALSE 3 2 4 disease 100 vacc_disease 0.1 disease 0.5
FALSE 4 2 5 <NA> NA <NA> 0.9 <NA> NA
FALSE 5 3 6 disease 100 disease 0.9 disease 0.5
FALSE 6 3 7 <NA> NA <NA> 0.1 <NA> NAThe 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
#> unit label from to
#> 1 cost vaccinate 1 2
#> 2 cost disease 2 4
#> 3 cost disease 3 6
#> 4 prob vaccinate 1 2
#> 5 prob vacc_disease 2 4
#> 6 prob disease 3 6
#> 7 health disease 2 4
#> 8 health disease 3 6
label_val_tab <- read.csv(here::here("data-raw/label-val table.csv"))
label_val_tab
#> unit label val
#> 1 cost vaccinate 10.0
#> 2 cost disease 100.0
#> 3 prob vaccinate 0.7
#> 4 prob vacc_disease 0.1
#> 5 prob disease 0.9
#> 6 health disease 0.5
tree_dat2 <-
create_ce_tree_df(label_branch_tab,
label_val_tab,
tree_struc)
tree_dat2
#> # A tibble: 6 × 5
#> from to cost health prob
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 1 2 10 NA 0.7
#> 2 1 3 NA NA 0.3
#> 3 2 4 100 0.5 0.1
#> 4 2 5 NA NA 0.9
#> 5 3 6 100 0.5 0.9
#> 6 3 7 NA NA 0.1This 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)
#> Removing column(s) health
dectree_expected_values(model = treemod)
#> vals used for calculation.
#> 1 2 3 4 5 6 7 8
#> 41 20 90 100 0 100 0 0We can run both the cost and health analyses together.
run_cedectree(tree_dat2)
#> vals used for calculation.
#> vals used for calculation.
#> $cost
#> $cost$ev_point
#> 1 2 3 4 5 6 7 8
#> 41 20 90 100 0 100 0 0
#>
#> $cost$term_pop_point
#> NULL
#>
#>
#> $health
#> $health$ev_point
#> 1 2 3 4 5 6 7 8
#> 0.17 0.05 0.45 0.50 0.00 0.50 0.00 0.00
#>
#> $health$term_pop_point
#> NULL