# Flexible Spline Models for Blinded Sample Size Reestimation in Event‐Driven Clinical Trials

## TL;DR

This paper introduces a flexible statistical method to adjust sample sizes in clinical trials based on event rates, helping ensure trials finish on time even if initial assumptions are wrong.

## Contribution

A new flexible spline-based method for blinded sample size reestimation in event-driven trials is proposed and validated.

## Key findings

- Parametric models can over- or underestimate event numbers, while the proposed flexible spline method avoids this.
- The Royston–Parmar spline model improves accuracy in sample size reestimation for event-driven trials.
- The method was successfully applied to a multiple sclerosis trial, showing improved performance over traditional approaches.

## Abstract

In event‐driven trials, the target power under a certain treatment effect is maintained as long as the required number of events is obtained. The misspecification of the survival function in the planning phase does not result in a loss of power. However, the trial might take longer than planned if the event rate is lower than assumed. Blinded sample size reestimation (BSSR) uses non‐comparative interim data to adjust the sample size if some planning assumptions are wrong. In the setting of an event‐driven trial, the sample size may be adjusted to maintain the chances to obtain the required number of events within the planned time frame. For the purpose of BSSR, the survival function is estimated based on the interim data and often needs to be extrapolated. The current practice is to fit standard parametric models, which may however not always be suitable. Here we propose a flexible spline‐based BSSR method. Specifically, we propose to carry out the extrapolation based on the Royston–Parmar spline model. To compare the proposed procedure with parametric approaches, we carried out a simulation study. Although parametric approaches might seriously over‐ or underestimate the expected number of events, the proposed flexible approach avoided such undesirable behavior. This is also observed in an application to a secondary progressive multiple sclerosis trial. Overall, if planning assumptions are wrong this more robust flexible BSSR method could help event‐driven designs to more accurately adjust recruitment numbers and to finish on time.