# Decision Tree Herpes Virus Encephalopathy

This is an example that we use to illustrate decision trees in our DARTH teaching materials. The example involves the treatment of herpes simplex ecncephalopathy (HVE) by either treating everyone without biopsy (Treat), not treating or taking biopsy (DoNotTreat), and Taking biopsy and treat if biopsy posivite (Biopsy).

We will first define the twig model and the parameters and then we will show how one would code the model direclty in R and compare the outcomes.

# twig

    library(twig)

## twig model definition

    mytwig <- twig() +
      decisions(names=c(DoNotTreat, Treat, Biopsy)) +  # treatment options
      event(name = DIE,  # first event
            options = c(yes, none), # either occurs or doesn't occur
            probs = c(pDie, leftover),  # occurs with prob pDie and doesn't occur with 1-pDie (leftover)
            transitions = c(Death, HVE_event)) + # if it occurs, transitions to Death, otherwise the HVE_event
      event(name = HVE_event,  # similarly, HVE_event occurs with f_HVE but if not it will be OVE
            options = c(yes, none),
            probs = c(f_HVE, leftover),
            transitions = c(get_HVE_comp, get_OVE_comp)) +
      event(name = get_HVE_comp, # evaluate whether HVE complications occured
            options = c(yes, none),
            probs = c(p_comp, leftover),
            transitions = c(HVE_comp, no_HVE_comp))  +
      event(name = get_OVE_comp, # evaluate whether other viral encephalitis (OVE) complications occured
            options = c(yes, none),
            probs = c(p_comp, leftover),
            transitions = c(OVE_comp, no_OVE_comp)) +
      payoffs(names = c(cost, utility)) # finally measure the cost and utilities

## DecisionTwig

In DecisionTwig, this decision tree looks like this:

# Model parameters

Define a data frame for model parameters as a list of scalar values. This can also ve a dataset for running a probabilistic analysis.

    params <- list(
      # Probabilities,
      p_HVE          = 0.52   ,# prevalence of HVE
      p_HVE_comp     = 0.71   ,# complications with untreated HVE
      p_OVE_comp     = 0.01   ,# complications with untreated OVE
      p_HVE_comp_tx  = 0.36   ,# complications with treated HVE
      p_OVE_comp_tx  = 0.20   ,# complications with treated OVE
      p_biopsy_death = 0.005  ,# probability of death due to biopsy

      # Costs,
      c_VE           = 1200   ,# cost of viral encephalitis care without complications
      c_VE_comp      = 9000   ,# cost of viral encephalitis care with complications
      c_tx           = 9500   ,# cost of treatment
      c_biopsy       = 25000  ,# cost of brain biopsy

      # QALYs,
      q_VE           = 20     ,# remaining QALYs for those without VE-related complications
      q_VE_comp      = 19     ,# remaining QALYs for those with VE-related complications
      q_loss_biopsy  = 0.01   ,# one-time QALY loss due to brain biopsy
      q_death_biopsy = 0      # remaining QALYs for those who died during biopsy
    )

# Functions

## Probability of death

We only look into death from biopsy in this decision tree.

    pDie <- function(decision, p_biopsy_death){
      p_biopsy_death * (decision == "Biopsy")
    }

## Probability of complications

This depends on whether treatment received or not, HVE vs. OVE, and whether either HVE or OVE complications occured.

    p_comp <- function(decision, HVE_event, p_HVE_comp, p_OVE_comp,
                       p_HVE_comp_tx, p_OVE_comp_tx) {

        # complication of untreated HVE
        p_HVE_comp * (decision == "DoNotTreat" & HVE_event=="yes") +

        # complication of untreated OVE
        p_OVE_comp * (decision %in% c("DoNotTreat", "Biopsy") & HVE_event=="none") +

        # complications of treated HVE
        p_HVE_comp_tx * (decision %in% c("Treat", "Biopsy") & HVE_event=="yes") +

        # complications of treated OVE
        p_OVE_comp_tx * (decision == "Treat" & HVE_event=="none")
    }

## Probability of HVE

All event probabilities must be function names. So, we can just create a simple wrapper around the p_HVE variable.

    f_HVE <- function(p_HVE){
      p_HVE
    }

## Cost function

Cost is a function of the decision and the final model outcomes.

    cost <- function(decision, outcome, c_biopsy, c_tx, c_VE_comp, c_VE){

      # cost of biopsy
      c_biopsy*(decision=="Biopsy") +

        # cost of treatment if treated or biopsy was +ve for HVE
        c_tx*(decision=="Treat" | (decision=="Biopsy" & outcome %in% c("HVE_comp", "no_HVE_comp"))) +

        # cost of complication if outcomes are in either HVE or OVE complications
        c_VE_comp*(outcome %in% c("HVE_comp", "OVE_comp")) +

        # cost of viral encephalitis if complications didn't occur
        c_VE*(outcome %in% c("no_HVE_comp", "no_OVE_comp"))
    }

## utility

Is a function of the decision and final outcome.

    utility <- function(decision, outcome, q_loss_biopsy, q_VE_comp, q_VE){

      # apply utility discount for biopsy
      -q_loss_biopsy*(decision=="Biopsy") +

      # apply utility values for complications
        q_VE_comp*(outcome %in% c("HVE_comp", "OVE_comp")) +

        # apply utility values if complications didn't occur
        q_VE*(outcome %in% c("no_HVE_comp", "no_OVE_comp"))
    }

# Running the `twig`

We can run the model and check the results of the single parameter set under `results$sim_ev`

    results <- run_twig(twig_obj = mytwig, params = params, parallel = FALSE, progress_bar = FALSE)
    #> Checking Twig syntax ....
    #> A states layer was not detected - Treatign the twig as a Decision Tree. Event transitions include the following event names:  HVE_event, get_HVE_comp, get_OVE_comp . These are valid.
    #> The following transitions are not event names and will be treated as final outcomes:  Death, HVE_comp, no_HVE_comp, OVE_comp, no_OVE_comp .
    #> Twig syntax validation completed successfully.
    #> Preprocessing started ...
    #> Preprocessing completed. Starting simulation...
    #>
    #> Total time: 0.00065 secs

    results$sim_ev
    #> , , sim = 1
    #>
    #>             payoff
    #> decision         cost  utility
    #>   DoNotTreat  4117.20 19.62600
    #>   Treat      12908.96 19.71680
    #>   Biopsy     32599.41 19.69896

## Incremental Cost-Effectiveness Ratio (ICER)

using the `calculate_icers` function adapted from the dampack package, we can retrieve ICER table by passing the payoffs summary table.

    calculate_icers(results$mean_ev)
    #>              decision     cost  utility inc_cost inc_utility     ICER status
    #> DoNotTreat DoNotTreat  4117.20 19.62600       NA          NA       NA     ND
    #> Treat           Treat 12908.96 19.71680  8791.76      0.0908 96825.55     ND
    #> Biopsy         Biopsy 32599.41 19.69896       NA          NA       NA      D

## Summary

This example illustrated the following features of `twig` * Decision tree * Multiple decisions * Multiple sequential events * probability dependency on prior events * transition payoffs * using sequential events to model complications * ICER

In addition, various intermediate objects and computations can be returned by enabling `verbose`.