Conditional power, predictive power and probability of success in clinical trials with continuous, binary and time-to-event endpoints

Abstract

Assessment of study success using conditional power (CP), the predictive power of success (PPoS) and probability of success (PoS) is becoming increasingly common for resource optimization and adaption of trials in clinical investigation. Determination of these measures is often a non-trivial mathematical task. Further, the terminologies used across the literature are not consistent, and there is no consolidated presentation on this. Lastly, certain types of trials received more attention where others (e.g., single-arm trial with time-to-event endpoints) were completely ignored. We attempted to fill these gaps. This paper first provides a detailed derivation of CP, PPoS and PoS in a general setting with normally distributed test statistics and normal prior. Subsequently, expressions for these measures are obtained for continuous, binary, and time-to-event endpoints in single-arm and two-arm trial settings. We have discussed both clinical success and trial success. Importantly, we have derived the expressions for CP, PPoS and PoS in a single-arm trial with a time-to-event endpoint that was never addressed in the literature to our knowledge. In that discussion, we have also shown that commonly recommended 1/d consistently under-estimates the variance of log(median) and alternative expression for variance was derived. We have also presented the PPoS calculation for the binomial endpoint with a beta prior. Examples are given along with the comparison of CP and PPoS. Expressions presented in this paper are implemented in LongCART package in R. An R shiny app is also available at https://ppos.herokuapp.com/ .