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

在临床试验研究中，如果具有不同生物标志物值的患者获得不同的治疗益处，则将患者特征称为预测性生物标志物。生物标志物检测对于找到适合个体的最佳治疗方法非常重要。这促使我从两个方向发展新的统计方法。在方向1中，我将通过寻找切割点来离散生物标志物，并在生物标志物切割点指定的间隔上建模不同的处理效果阈值。这就产生了一个生物标志物切点模型，它实际上是一个回归模型的混合物，由于模型的不规则性，传统的统计推断很困难。我将开发测试方法，以及生物标志物切割点模型的分层贝叶斯推断，以研究生物标志物定义的患者亚组治疗效果的异质性。我希望研究成果是有理论支持的新的检验方法，以及新的贝叶斯估计和置信区间技术，两者都克服了模型的不规则性。生物标志物切割点模型方法因其清晰的解释而受到医学研究人员的欢迎。在方向2中，我将开发一个图表，显示连续生物标志物在其整个范围内的不同治疗效果。局部回归和/或非参数方法将被用来估计治疗效果路径，没有预先指定的功能形式。同时构建治疗-效果路径的置信带，以得出统计结论。我希望研究成果能够成为新的可视化工具，通过统计推断来增强对不同生物标志物值的治疗效果的全面理解。这种方法有可能成为医学研究人员的新宠，因为它可以提取更多的信息，并且依赖更少的模型假设。在这两个方向上，我将探讨单个或多个生物标志物或其组合的情况。提出的研究将为医学研究人员和应用统计学家提供新的统计工具，并解决生物标志物辅助临床试验研究中出现的统计挑战。我计划将新的思想扩展到统计研究中，这将推动混合模型，非参数统计和局部回归的理论和方法。我将培养研究生在这一领域进行扎实的统计研究，并分析真实的临床试验数据。他们将为今后提高统计在相关领域的应用和研究水平作出贡献。

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.