# Sample size determination for time-to-event endpoints in randomized selection trials with generalized exponential distribution

## TL;DR

This paper introduces a new method for calculating sample sizes in clinical trials using a generalized exponential distribution for time-to-event endpoints.

## Contribution

The novelty is proposing a sample size calculation method based on the generalized exponential distribution to improve trial design.

## Key findings

- Using the generalized exponential distribution can result in smaller required sample sizes compared to the Weibull distribution.
- Traditional methods using exponential or Weibull distributions may not accurately reflect real-world time-to-event data.
- The proposed method aims to achieve desired statistical power more effectively.

## Abstract

Randomized selection trials are frequently used to compare experimental treatments that have the potential to be beneficial, but they often do not include a control group. While time-to-event endpoints are commonly applied in clinical investigations, methodologies for determining the required sample size for such endpoints, except exponential distribution, are lacking. In recent times, there has been a shift in clinical trials, with a growing emphasis on progression-free survival as a primary endpoint. However, the utilization of this measure has typically been restricted to specific time points for both sample size determination and analysis. This alteration in approach could wield a substantial influence on the clinical trial process, potentially diminishing the capacity to discern variances between treatment groups. In the calculation of sample sizes for randomized trials, this investigation operates under the assumption that the time-to-event endpoint conforms to either an exponential, Weibull, or generalized exponential distribution.

•Sample size calculation for time-to-event endpoints is discussed using a generalized exponential distribution.•Comparing results with Weibull distribution, a smaller sample size is achieved with the proposal.•Problem: Time-to-event endpoints may not follow well-known distributions like exponential or Weibull.•What is Already Known: Computing sample size using Weibull distribution ignored previously the ineffectiveness of the maximum likelihood estimation.•What This Paper Adds: This study proposed a sample size calculation based on a generalized exponential distribution to achieve the desired power.

Sample size calculation for time-to-event endpoints is discussed using a generalized exponential distribution.

Comparing results with Weibull distribution, a smaller sample size is achieved with the proposal.

Problem: Time-to-event endpoints may not follow well-known distributions like exponential or Weibull.

What is Already Known: Computing sample size using Weibull distribution ignored previously the ineffectiveness of the maximum likelihood estimation.

What This Paper Adds: This study proposed a sample size calculation based on a generalized exponential distribution to achieve the desired power.