# Simulation‐Based Bayesian Predictive Probability of Success for Interim Monitoring of Clinical Trials With Competing Event Data: Two Case Studies

## TL;DR

This paper introduces a simulation-based Bayesian method to calculate the probability of success in clinical trials with competing events, using two real-world trials as examples.

## Contribution

The novel contribution is a simulation-based Bayesian predictive probability of success method for clinical trials with competing event data.

## Key findings

- A simulation-based Bayesian approach was developed to compute PPoS for trials with competing events.
- The method was applied to two clinical trials (I-SPY COVID and STHLM3) with competing event data.
- Different modeling choices and prior distributions were explored to assess PPoS under various scenarios.

## Abstract

Bayesian predictive probabilities of success (PPoS) use interim trial data to calculate the probability of trial success. These quantities can be used to optimise trial size or to stop for futility. In this paper, we describe a simulation‐based approach to compute the PPoS for clinical trials with competing event data, for which no specific methodology is currently available. The proposed procedure hinges on modelling the joint distribution of time to event and event type by specifying Bayesian models for the cause‐specific hazards of all event types. This allows the prediction of outcome data at the conclusion of the trial. The PPoS is obtained by numerically averaging the probability of success evaluated at fixed parameter values over the posterior distribution of the parameters. Our work is motivated by two randomised clinical trials: the I‐SPY COVID phase II trial for the treatment of severe COVID‐19 (NCT04488081) and the STHLM3 prostate cancer diagnostic trial (ISRCTN84445406), both of which are characterised by competing event data. We present different modelling alternatives for the joint distribution of time to event and event type and show how the choice of the prior distributions can be used to assess the PPoS under different scenarios. The role of the PPoS analyses in the decision‐making process for these two trials is also discussed.