# Decision Tree Modelling for Cost Effectiveness Analysis in R

**R – Jacob Smith Economics**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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## Motivation for this blog

I have seen several packages and frameworks used for the development of decision analytic models for cost effectiveness analysis in R. Some can be hard to understand and are often paywalled behind some sort of training that is associated with using package. Even after attending some sort of training, some run into more issues with debugging this type of code.

After struggling with some of these packages for some time, I thought to myself why not try coding my own solution. I decided to start simple beginning with defining functions needed for decision tree modelling.

## The Main Code

For coding a decision tree model in R we require two unique functions:

1) A function defining a chance node.

2) A function defining net monetary benefit.

The code for each of these functions are given below:

#Net Benefits NB<-function(Threshold,Costs,Effects){ Threshold*Effects-Costs } #chance node c_node<-function(p,x,y){ if(p>1|p<0){ print('p must be a value on the interval [0,1]') }else{ p*x+(1-p)*y }}

These two functions will simplify much of the modelling process as we will be building decision tree models by each branch.

## Coding a Decision Tree Model

We will consider the following decision tree model of vaccination. In this case we have an individual who is making a decision to vaccinate or to not vaccinate. A special note about this model is that with vaccination there is a risk of experience side effects due to the vaccine.

The way we will code up this model will be seen in the block below:

#Threshold Value L<-5000 #Costs SickCost<-2500 InjuryCost<-1000 VaxCost<-50 #Utilities Sick<-0.5 SickAE<-0.4 Well<-1 WellAE<-0.9 #Payoffs SickNoVax<-NB(L,SickCost,Sick) WellNoVax<-NB(L,0,Well) SickVaxAE<-NB(L,VaxCost+InjuryCost,Sick) WellVaxAE<-NB(L,VaxCost+InjuryCost,WellAE) SickVaxNoAE<-NB(L,VaxCost,Sick) WellVaxNoAE<-NB(L,VaxCost,Well) #ChanceNodes NoVax_SWRisk<-c_node(0.6,SickNoVax,WellNoVax) VaxAE_SWRisk<-c_node(0.6,SickVaxAE,WellVaxAE) VaxNoAE_SWRisk<-c_node(0.6,SickVaxNoAE,WellVaxNoAE) #Decisions Vax<-c_node(0.5,VaxAE_SWRisk,VaxNoAE_SWRisk) NoVax<-NoVax_SWRisk #Organizing as a DataFrame data1<-c("Vaccinate","Dont Vaccinate") data2<-c(Vax, NoVax) DecisionTree<-data.frame(Decisions=data1,Scores=data2) #Optimal Choice DecisionTree$Decisions[which.max(DecisionTree$Scores)]

## Notes

- We define our Threshold, Costs, Utilities and Payoffs before building out the branches of our decision trees using the
`c_node()`

function. Better practice would be to define probabilities used in this function before as well. - The decisions you are considering should be organized in a data frame.
`which.max()`

is essential to defining optimal treatment. In our context we read our code as “Define the decision which provides the maximum net benefits score”.

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**R – Jacob Smith Economics**.

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