# Inference in group sequential designs with causal mechanisms: implications for power and mediation analysis

## TL;DR

This paper explores how mediation analysis works in group sequential trials, showing that ignoring causal mechanisms can reduce power and introduce bias.

## Contribution

The paper introduces a simulation study to evaluate mediation analysis under group sequential designs, revealing biases and power implications.

## Key findings

- Ignoring causal mechanisms in sample size calculations reduces power in group sequential designs.
- Maximum likelihood estimators are unbiased only for the mediator-outcome path.
- Conditional maximum likelihood estimators show smaller bias for total and direct effects.

## Abstract

Group sequential designs are increasingly employed to allow trials to stop early with statistical rigor. While existing work focuses on intention-to-treat effect on clinical endpoints, the properties of mediation analysis (commonly conducted in psychological trials to understand a causal mechanism) remain unknown under group sequential designs.

Considering a group sequential design with one interim analysis for early stopping for efficacy, we conduct a simulation study to evaluate existing analysis techniques when the treatment effect on a continuous outcome is partially or fully mediated by a continuous intermediate variable measuring a casual mechanism. We study the probability of rejecting the null hypotheses on the total effect (i.e., intention-to-treat effect), direct effect and indirect effect, respectively. We examine the bias of maximum likelihood estimator for these effects. We investigate if the penalized (and conditional) maximum likelihood estimator has smaller bias than the maximum likelihood estimator when a trial stopped (did not stop) early.

The presence of an intermediate variable reduces the power of a group sequential design when sample size calculation ignores the causal mechanism, though type I error control remains unaffected. The maximum likelihood estimator is unbiased only for the mediator-outcome path, impacting the properties of mediation analysis since existing methods typically rely on it to estimate the pathways. The penalized maximum likelihood estimator for other pathways has similar bias to the stage-one maximum likelihood estimator, while the conditional maximum likelihood estimator shows negligible or smaller bias than the usual maximum likelihood estimator for estimating the total and the direct effects only.

Mediation analysis needs additional consideration in group sequential designs. As with fixed trial designs, the sample size calculation of group sequential designs should account for the total variability underlying a causal mechanism when the treatment effect is hypothesized to be mediated by an intermediate variable, or risk the overall power to detect an intention-to-treat (total) effect being lower than the nominal value. We suggest reporting several estimators and acknowledging that they may be biased for some mediation pathways. More research is needed to develop methods for the analysis of indirect effect under group sequential designs.

The online version contains supplementary material available at 10.1186/s12874-025-02714-y.