# Optimal designs for discrete-time survival models with competing risks

## TL;DR

This paper introduces new optimal design methods for clinical trials with multiple competing outcomes, improving trial efficiency and accuracy.

## Contribution

The paper develops a novel cost-based D_A-optimal design criterion for discrete-time survival models with competing risks.

## Key findings

- Equal allocation of subjects to treatment groups is generally optimal unless hazard rates are low in both groups.
- Optimal designs depend critically on parameter values in the parametric competing risks model.
- The methodology is applied to the SANAD trial, demonstrating practical advantages of the proposed strategies.

## Abstract

Current methodological research on randomized controlled trial design has predominantly focused on studies with a single primary endpoint. However, many trials in practice involve multiple competing target events. The optimal designs for survival trials with competing target events have not been systematically addressed in the statistical literature. This paper fills this significant gap by developing design methodologies for randomized discrete-time-to-event trials with competing endpoints. We derive the Fisher information matrix for the general discrete-time survival model (DTSM) by transforming the original discrete-time survival data into proper multinomial responses. By introducing a cost-based generalized \documentclass[12pt]{minimal}
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\begin{document}$$D_A$$\end{document}-optimal design criterion, we identify various types of optimal designs for estimating the treatment effects. Under the assumption of a parametric competing risks model for the underlying survival process, we demonstrate that the optimal treatment allocation scheme is critically influenced by the parameter values within this model. Our methodology is applied to the redesign of the SANAD trial, which examines withdrawal times from anti-epileptic drugs, thereby highlighting the advantages of our optimal design strategies. A key finding is that assigning subjects equally to the different groups in a two-arm DTSM trial with competing risks is generally a favorable choice, unless the hazard rates over the duration of the trial in both groups are low.

The online version contains supplementary material available at 10.1007/s10985-026-09695-0.