A Two-Step Test to Identify Zero-Inflated Biomarkers in Early-Phase Clinical Trials

In early-phase clinical trials, a predictive biomarker may identify subgroups that benefit from an experimental therapy, even when the overall average treatment effect is negligible. Recently proposed nonparametric interaction tests such as the Average Kolmogorov-Smirnov Approach (AKSA) avoid prespecified biomarker cutting points and model assumptions, but their power degrades when the biomarker distribution is zero-inflated. We propose a two-step test that partitions the analysis into a spike test for biomarker-negative patients and a tail test for biomarker-positive patients, then combines the resulting p-values using Fisher's or Brown's method. This design isolates distinct sources of predictive effects, mitigates dilution, and preserves exact type I error control through permutation calibration. We derive theoretical properties showing that the proposed test retains nominal size and improves power over AKSA when predictive effects are concentrated in either the spike or tail subpopulation. Extensive simulations confirm robust type I error control under various zero-inflation rates, sample sizes, and skewed biomarker distributions. We also demonstrate consistent power gains across spike-only, tail-only, and mixed-effect scenarios. Our method provides a practical and flexible tool for early-phase trials with sparse biomarker distributions, enabling more reliable identification of predictive biomarkers to guide later-phase development.