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.
The authors thank an anonymous Associate Editor and referees for helpful comments that greatly improved the manuscript.
"Inference for a two-stage enrichment design." Ann. Statist. 49 (5) 2697 - 2720, October 2021. https://doi.org/10.1214/21-AOS2051