goldilocks (version 0.3.0)

pwe_impute: Impute piecewise exponential time-to-event outcomes

Description

Imputation of time-to-event outcomes using the piecewise constant hazard exponential function conditional on observed exposure.

Usage

pwe_impute(time, hazard, cutpoints = 0, maxtime = NULL)

Arguments

time

vector. The observed time for patient that have had no event or passed maxtime.

hazard

vector. The constant hazard rates for exponential failures.

cutpoints

vector. The change-point vector indicating time when the hazard rates change. Note the first element of cutpoints should always be 0.

maxtime

scalar. Maximum time before end of study.

Value

A data frame with simulated follow-up times (time) and respective event indicator (event, 1 = event occurred, 0 = censoring).

Details

If a subject is event-free at time \(s < t\), then the conditional probability \(F_{T \| s}|(t \| s) = P[T \le \| T > s] = (F(t) - F(s)) / (1 - F(s))\), where \(F(\cdot)\) is the cumulative distribution function of the piecewise exponential (PWE) distribution. Equivalently, \(F(t) = 1 - S(t)\), where S(t) is the survival function. If \(U \sim Unif(0, 1)\), then we can generate an event time (conditional on being event free up until \(s\)) as \(F^{-1}(U(1-F(s)) + F(s))\). Note: if \(s = 0\), then this is the equivalent of a direct (unconditional) sample from the PWE distribution.

Examples

# NOT RUN {
pwe_impute(time = c(3, 4, 5), hazard = c(0.002, 0.01), cutpoints = c(0, 12))
pwe_impute(time = c(3, 4, 5), hazard = c(0.002, 0.01), cutpoints = c(0, 12),
           maxtime = 36)
pwe_impute(time = 19.621870008, hazard = c(2.585924e-02, 3.685254e-09),
           cutpoints = c(0, 12), maxtime = 36)
# }