Time-varying values

How to specify time-dependency

These variables takes increasing values with each cycles, starting from 1. For example the age of individuals at any moment can be defined as Initial age + model_time. The time an individual spends in a state is equal to state_time.

Both variables can be used in define_parameters(), define_state(), or define_transition():

define_parameters(
  mr = exp(- state_time * lambda),
  age = 50 + model_time
)

## 2 unevaluated parameters.
## 
## mr = exp(-state_time * lambda)
## age = 50 + model_time

define_state(
  cost = 100 - state_time,
  effect = 10
)

## A state with 2 values.
## 
## cost = 100 - state_time
## effect = 10

f <- function(x) abs(sin(x))

define_transition(
  C,  f(state_time),
  .1, .9
)

## No named state -> generating names.

## A transition matrix, 2 states.
## 
##   A   B            
## A C   f(state_time)
## B 0.1 0.9

Details

Using model_time in a model does not change the execution speed of the analysis. On the other hand adding state_time may slow down the analysis, especially if the model is run for many cycles and a transition probability depends on state_time.¹

To mitigate this drawback it is possible to limit the number of state expansion with state_time_limit. Because most time-varying values reach an asymptotic value quite fast, it is unnecessary to expand the states any further. The last cycle value is repeated until the end.

The limit can be defined globally, per state, or per model and state. In the following example probabilities are kept constant after 10 cycles for state B and 20 cycles for state D in strategy I, and 15 cycles in state B in strategy II.

run_model(
  I =  strat_1,
  II = strat_2,
  cycles = 100,
  state_time_limit = list(
    I = c(B = 10, D = 20),
    II = c(B = 15)
  )
)