# Sample size recalculation in three-stage clinical trials and its evaluation

## TL;DR

This paper explores how to adjust sample sizes in three-stage clinical trials and evaluates the benefits of such adjustments.

## Contribution

The paper extends sample size recalculation methods to three-stage trials and evaluates their performance.

## Key findings

- Three-stage designs show notable improvements in power and expected sample size compared to two-stage designs.
- The benefits of recalculation depend on the performance measures and trial characteristics considered.
- Recalculation rules can be applied in three-stage trials but their advantages are not always clear.

## Abstract

In clinical trials, the determination of an adequate sample size is a challenging task, mainly due to the uncertainty about the value of the effect size and nuisance parameters. One method to deal with this uncertainty is a sample size recalculation. Thereby, an interim analysis is performed based on which the sample size for the remaining trial is adapted. With few exceptions, previous literature has only examined the potential of recalculation in two-stage trials.

In our research, we address sample size recalculation in three-stage trials, i.e. trials with two pre-planned interim analyses. We show how recalculation rules from two-stage trials can be modified to be applicable to three-stage trials. We also illustrate how a performance measure, recently suggested for two-stage trial recalculation (the conditional performance score) can be applied to evaluate recalculation rules in three-stage trials, and we describe performance evaluation in those trials from the global point of view. To assess the potential of recalculation in three-stage trials, we compare, in a simulation study, two-stage group sequential designs with three-stage group sequential designs as well as multiple three-stage designs with recalculation.

While we observe a notable favorable effect in terms of power and expected sample size by using three-stage designs compared to two-stage designs, the benefits of recalculation rules appear less clear and are dependent on the performance measures applied.

Sample size recalculation is also applicable in three-stage designs. However, the extent to which recalculation brings benefits depends on which trial characteristics are most important to the applicants.

The online version contains supplementary material available at 10.1186/s12874-024-02337-9.