Inference for a two-stage enrichment design

Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients' biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture of normal distributions. Using random normings, we obtain asymptotically standard normal MLEs and construct hypothesis tests. Finally, in a simulation study, we demonstrate that our proposed design is more powerful than a single stage design when outcomes and biomarkers are correlated; the model-based estimators have smaller bias and mean square error (MSE) than weighted average estimators.