hazard_sub: Hazard Function for Sub Population

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

Hazard Function for Sub Population

Description

Computes the hazard function of a piecewise exponential (pwexp) distribution for the biomarker negative sub population, such that the resulting survival function for the ITT population closely matches a given pwexp survival function.

Usage

hazard_sub(
  piecewiseSurvivalTime = 0,
  hazard_itt = 0.0578,
  hazard_pos = 0.02,
  p_pos = 0.5
)

Arguments

piecewiseSurvivalTime	A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: [0, 6) and [6, Inf). Defaults to 0 for exponential distribution.
hazard_itt	A scalar or numeric vector specifying the hazard(s) for the ITT population based on a pwexp distribution.
hazard_pos	A scalar or numeric vector specifying the hazard(s) for the biomarker positive sub population based on a pwexp distribution.
p_pos	A numeric value specifying the prevalence of the biomarker positive sub population.

Details

This function determines the hazard vector \lambda_{\text{neg}} for the pwexp distribution of the biomarker negative sub population, so that the implied survival function for the ITT population closely matches the specified pwexp distribution with hazard vector \lambda_{\text{itt}}.

Let p_{\text{pos}} be the prevalence of the biomarker positive sub population, then the survival function for the ITT population is given by

S_{\text{itt}}(t) = p_{\text{pos}} S_{\text{pos}}(t) + (1 - p_{\text{pos}}) S_{\text{neg}}(t)

where S_{\text{pos}}(t) and S_{\text{neg}}(t) are the survival functions for the biomarker positive and biomarker negative sub populations, respectively.

Matching is performed sequentially at the internal cutpoints u_2, ..., u_J and at the point u_J + \log(2)/\lambda_{\text{itt},J} for the final interval to solve for \lambda_{\text{neg},1}, \ldots, \lambda_{\text{neg},J-1} and \lambda_{\text{neg},J}, respectively.

Value

A numeric vector representing the estimated hazard rates for the pwexp distribution of the biomarker negative sub population.

Author(s)

Kaifeng Lu ([e-mail])

Examples

u <- c(0, 1, 3, 4)
lambda_itt <- c(0.0151, 0.0403, 0.0501, 0.0558)
lambda_pos <- c(0.0115, 0.0302, 0.0351, 0.0404)
p_pos <- 0.3
hazard_sub(u, lambda_itt, lambda_pos, p_pos)

lrstat documentation built on Aug. 8, 2025, 7:36 p.m.