Binary Endpoints

In many clinical trials, the primary endpoint is binary, such as response vs. no response to a treatment.
Most commonly, these studies compare two parallel arms: a control group receiving the standard of care, and an experimental group receiving a new drug expected to improve outcomes. In such settings, the natural parameter of interest is the proportion of responders in each arm, and the key statistical question is whether these proportions differ.

This chapter focuses on methods for testing differences in proportions and on how various statistical software implement these methods under different trial designs.

More specifically:

• In Binary Tests, we introduce the main hypothesis tests used in two-arm trials with binary endpoints (Z-test, exact test) and briefly discuss their assumptions and limitations.

• In Two-Arm Fixed Design with Binary Endpoints, we compare sample size calculations and test results across commonly used software and R packages for trials without interim analyses.

• In Two-Arm Group-Sequential Design with Binary Endpoints, we extend the previous comparison to designs including interim analyses (group-sequential designs), highlighting differences in spending functions, boundary calculations, and implementation across tools.

• Finally, in One-Arm Fixed Design with Binary Endpoints, we compare sample size calculations in single-arm studies, which are frequently employed in rare diseases where recruitment is limited and comparing two groups becomes impractical.