Event-driven planning of two-armed trials with a binary endpoint

Abstract

Background/Aims:

In randomized two-armed clinical trials with binary endpoints, there may be uncertainty about the event probability, which is needed for sample size calculation. Survival trials are powered based on number of events rather than people, and this is advantageous because the number of events needed to achieve a desired power is less sensitive to an unknown parameter than is the number of people needed. We investigate and quantify this relative stability of number of events compared to number of people in the context of a randomized two-armed trial with equal sample sizes and a binary endpoint. In binary endpoint settings with such relative stability, we consider (1) enhancement of traditional adaptive trial design and (2) potential benefits of a simple event-driven strategy.

Methods:

Using sample size formulas, we determine the relative stability of the expected number of events compared to the sample size for binary outcome trials using the relative risk, odds ratio, or risk difference. Simulations consider a simple event-driven design when there is relative stability; we evaluate type I error rate and power under various analysis methods and approaches to halting the trial.

Results:

We find that the number of events is at least three times more stable than the sample size to achieve a specified power for the relative risk when the overall event probability is less than 1/3, and for the odds ratio when the overall event probability is less than 0.20. We show that this relative stability is independent of the type 1 and type 2 error rates and magnitude of the treatment effect. In a setting where the overall event probability is consistent with relative stability, simulations of an event-driven design show that asymptotic methods may have modestly high type I error rates, but that other approaches appear to have good operating characteristics.

Conclusion:

In settings with moderately low event probabilities, thinking in terms of the number of events instead of sample size may (1) facilitate the planning of clinical trials and help determine whether a trial is futile, and (2) lead to a simple event-driven design for binary endpoints that may be feasible and appealing.