This document is an introduction to heemod's basic steps to define and run a model.

When building a Markov model for health economic evaluation, the following steps must be performed:

Other vignettes provide more details and examples on specific topics:

Transition probabilities

The probability to change from one state to another during a time period is called a transition probability. The time period is called a cycle.

Transition probabilities between states can be specified through a 2-way table where the lines correspond to the states at the beginning of a cycle and the columns to the states at the end of a cycle. For example consider a model with 2 states A and B:

A B
A 1 2
B 3 4

When starting a cycle in state A (row A), the probability to still be in state A at the end of the cycle is found in colunm A (row 1) and the probability to change to state B is found in column B (cell 2).

Similarly, when starting a cycle from state B (row B), the probability to be in state A or B at the end of the cycle are found in cells 3 or 4 respectively.

In the context of Markov models, this 2-way table is called a transition matrix. A transition matrix can be defined easily in heemod with the define_matrix function. If we consider the previous example, where cell values have been replaced by actual probabilities:

A B
A 0.9 0.1
B 0.2 0.8

This transition matrix can be defined with the following command:

mat_trans <- define_matrix(
  .9, .1,
  .2, .8
)
mat_trans
## An unevaluated matrix, 2 states.
## 
##   A   B  
## A 0.9 0.1
## B 0.2 0.8

Attach values to states

In health economic evaluation, values are attached to states. Cost and utility are classical examples of such values. To continue with the previous example, the following values can be attachd to state A and B:

A state and its values can be defined with define_state:

state_A <- define_state(
  cost = 1234,
  utility = 0.85
)
state_A
## An unevaluated state with 2 values.
## 
## cost = 1234
## utility = 0.85
state_B <- define_state(
  cost = 4321,
  utility = 0.50
)
state_B
## An unevaluated state with 2 values.
## 
## cost = 4321
## utility = 0.5

In order to specify that both states belong to the same model they must be combined together with define_state_list:

state_list <- define_state_list(
  state_A,
  state_B
)
## No named state -> generating names.
state_list
## A list of 2 unevaluated states with 2 values each.
## 
## State names:
## 
## A
## B
## 
## State values:
## 
## cost
## utility

Combine information in a model

Now that the transition matrix and the state values are defined, we can combine them to create a Markov model with define_model:

mod_1 <- define_model(
  transition_matrix = mat_trans,
  states = state_list
)
mod_1
## An unevaluated Markov model:
## 
##     0 parameter,
##     2 states,
##     2 state values.

Run a model

The model can then be run with run_model for a given number of cycles:

res_mod_1 <- run_model(
  mod_1,
  cycles = 5
)
## No named model -> generating names.
res_mod_1
## 1 Markov model, run for 5 cycles.
## 
## Model names:
## 
## A

The result can be explored with summary:

summary(res_mod_1)
## 1 Markov model run for 5 cycles.
## 
## Initial states:
## 
##   N
## A 1
## B 0
##       cost  utility
## A 9317.536 3.893137

By default the model is run for one person starting in the first state (here state A).