Statistical Methods and Theory for Predictive Biomarker Study in Clinical Trials via Modeling and Analysis of Covariate Interactions

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In a clinical trial study, a patient characteristic is called a predictive biomarker if patients with different biomarker values gain different treatment benefits. Biomarker detection is important for finding the optimal treatments for individuals. This motivates me to develop new statistical methodologies in two directions. In Direction 1, I will discretize the biomarker by searching for cut-points, and model different treatment effect thresholds on the biomarker cut-point specified intervals. This leads to a biomarker cut-point model, which is in fact a mixture of regression models, that is difficult for traditional statistical inference because of model irregularities. I will develop testing methods, and hierarchical Bayesian inference for biomarker cut-point models, for studying the heterogeneity in treatment effects for biomarker-defined patient subgroups. I expect the research outcomes to be new testing methods with theoretical support, and new Bayesian techniques for estimation and confidence intervals, both overcoming model irregularities. The biomarker cut-point model approach is appealing among medical researchers for its clear interpretation. In Direction 2, I will develop a graph displaying the varying treatment effects for a continuous biomarker in its entire range. Local regression and/or non-parametric methods will be utilized to estimate the treatment-effect paths without pre-specified functional forms. Simultaneous confidence bands will be constructed for the treatment-effect path for drawing statistical conclusions. I expect the research outcomes to be new visualization tools enhanced by statistical inference for a complete understanding of the treatment-effects varying across biomarker values. This approach has the potential to become the new favorite among medical researchers for extracting more information and relying on less model assumptions. In both directions, I will explore the situations with single or multiple biomarkers or their combinations. The proposed research will provide new statistical tools for medical researchers and applied statisticians and address emerging statistical challenges in biomarker-aided clinical trial studies. I plan to extend the new ideas to statistical research, which will advance the theory and methods in mixture models, nonparametric statistics and local regression. I will train graduate students for solid statistical research in this area, and also for analyzing real clinical trial data. They will contribute to improving the statistical application and research in the related areas in the future.