solveMixtureExponentialDistribution: Solve Parameters in a Mixture Exponential Distribution

In TrialSimulator: Clinical Trial Simulator

Solve Parameters in a Mixture Exponential Distribution

Description

This is a helper function to explore parameters for endpoint generator, likely in an enrichment design.

Assume that the overall population in an arm is a mixture of two exponential distributions with medians median1 (m_1) and median2 (m_2). Given the proportion of the first component (p_1) and the overall median m, we have

p_1 (1 - e^{-\log(2)m/m_1}) + (1 - p_1) (1 - e^{-\log(2)m/m_2}) = 1/2

This function computes m_2 or m given p_1 and m_1. These parameters can be used in custom random number generator to define exponential distributed endpoints.

Note that the math formula above may not be displayed correctly on a html page. You can read it with better format by running ?solveMixtureExponentialDistribution.

Usage

solveMixtureExponentialDistribution(
  weight1,
  median1,
  median2 = NULL,
  overall_median = NULL
)

Arguments

weight1	numeric. The proportion of the first component.
median1	numeric. Median of the first component.
median2	numeric. Median of the second component. If NULL, then overall_median must be specified, and this function will calculate and return median2.
overall_median	numeric. Median of the overall population. If NULL, then median2 must be specified, and this function will calculate and return overall_median.

Value

a named vector of median2 or overall_median.

Examples

library(dplyr)

median2 <-
  solveMixtureExponentialDistribution(
    weight1 = .3,
    median1 = 10,
    overall_median = 8)

median2

n <- 1e6
ifelse(
  runif(n) < .3,
  rexp(n, rate=log(2)/10),
  rexp(n, rate=log(2)/median2)) %>%
  median() ## should be close to 8

overall_median <-
  solveMixtureExponentialDistribution(
    weight1 = .4,
    median1 = 12,
    median2 = 4)

overall_median

ifelse(
  runif(n) < .4,
  rexp(n, rate=log(2)/12),
  rexp(n, rate=log(2)/4)) %>%
  median() ## should be close to overall_median

TrialSimulator documentation built on Nov. 5, 2025, 7:22 p.m.