Two equivalent formulations of conditional power and predictive probability of success in interim monitoring

Conditional power (CP) and predictive probability of success (PPoS) are key metrics used for interim monitoring, futility or efficacy stopping, and sample size re-estimation in clinical trials. CP is defined as the probability of achieving a successful final outcome given the current interim data under a specified assumed treatment effect. PPoS extends this concept by averaging CP over the distribution of the true treatment effect, typically using the posterior or predictive distribution. In this article, we compare two formulations: a traditional approach (Jennison and Turnbull, 2000) and a post-interim-data-based approach (Kundu et al., 2024). We demonstrate that, under a normal model with matching priors, the two approaches yield identical CP and PPoS values. We provide a practical example demonstrating the use of these approaches and conclude with guidance on how to pre-specify the effect size and prior, as well as how to interpret results using CP and PPoS.