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记物价值的患者获得不同的治疗益处，则患者的特征被称为预测性生物标记物。生物标志物的检测对于为个体寻找最佳治疗方案具有重要意义。这促使我在两个方向上开发新的统计方法。在方向1中，我将通过搜索切入点来离散化生物标记物，并在生物标记物切割点指定的间隔上模拟不同的治疗效果阈值。这导致了一个生物标记物切点模型，它实际上是回归模型的混合，由于模型的不规则性，传统的统计推断很难进行。我将开发测试方法和生物标记物切点模型的分层贝叶斯推断，以研究生物标记物定义的患者亚组治疗效果的异质性。我预计研究结果将是有理论支持的新测试方法，以及用于估计和可信区间的新贝叶斯技术，两者都克服了模型的不规则性。生物标记物切点模型方法因其清晰的解释而受到医学研究人员的青睐。在方向2中，我将开发一张图表，显示连续生物标记物在其整个范围内的不同治疗效果。将使用局部回归和/或非参数方法来估计没有预先指定的函数形式的治疗效果路径。为了得出统计结论，将为治疗效果路径构建同时的置信带。我预计研究结果将成为新的可视化工具，通过统计推断来增强，以全面了解不同生物标记物价值的治疗效果。这种方法有可能成为医学研究人员的新宠，因为它提取了更多的信息，对模型假设的依赖更少。在这两个方向上，我将探索具有单个或多个生物标志物或其组合的情况。拟议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，并解决生物标记物辅助临床试验研究中新出现的统计学挑战。我计划将新的思路扩展到统计研究中，这将促进混合模型、非参数统计和局部回归的理论和方法的发展。我将培养研究生在这一领域进行扎实的统计学研究，并分析真实的临床试验数据。它们将为今后改进相关领域的统计应用和研究做出贡献。

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.