Doctoral Candidate Qing Yin defends his dissertation on "Shape detection and mediation analysis using semi-parametric shape-restricted regression spline with applications"

Advisor: Jong H. Jeong, PhD, Department of Biostatistics

Committee Members: 

• Jennifer Adibi, PhD, Department of Epidemiology
• Jeanine Buchanich, PhD, Department of Biostatistics
• Gong Tang, PhD, Department of Biostatistics

ABSTRACT:

Linear models are widely used in the field of epidemiology to model the relationship between two continuous variables, such as circulating levels of the placental hormone human chorionic gonadotropin (hCG) and infant genital size (Adibi et al., 2015). When researchers suspect curvilinear relationship exists, some nonparametric techniques, including regression splines, smoothing splines and penalized regression splines, can be used to model the relationship (Korevaar et al., 2016; Wu and Zhang, 2006). By applying these nonparametric techniques, researchers can relax the linearity assumption and capture scientifically meaningful or appropriate shapes.

 In the first part of the dissertation, a shape detection method based on the regression splines technique is developed. The proposed method can help researchers select the most suitable shape to describe their data among increasing, decreasing, convex and concave shapes. Specifically, we develop a technique based on mixed effects regression spline to analyze hormonal data, but the method is general enough to be applied to other similar problems. We conduct the simulation study to evaluate the performance of the method by examining the family-wise error rate and power. The results from simulation study suggest that the proposed method controls the family-wise error rate while maintaining good power in detecting the correct shape. The method is applied to a population-level prenatal screening program data set to evaluate the relationship between placental-fetal hormones and birth weight.

 Analyzing the association between two variables is usually the first step of some research project. Researchers also want to explore the causal relationship between an exposure and a potential outcome caused by the exposure. In many cases, the exposure may not directly lead to the outcome, but instead, it induces the outcome through a process. Mediation analysis is designed to explain the causal relationship between the exposure and the outcome by examining the intermediate stage, which helps researchers understand the pathway whereby the exposure affects the outcome. The regression-based mediation analysis has been formulated and developed in the last decade (VanderWeele, 2015), and several papers discussed the situation where the relationship between the mediator and the outcome is curvilinear (Imai et al., 2010).

 In the second part of the dissertation, we develop a method to analytically estimate the direct and indirect effects when we have some prior knowledge on the relationship between the mediator and the outcome (increasing, decreasing, convex or concave). In order to make suitable inferences, the asymptotic confidence intervals of those effects are obtained via delta method. We perform the simulation study to evaluate the performance of the method by measuring the coverage probability, average absolute relative bias and average mean squared error. If the relationship between the mediator and the outcome is curvilinear, the results from simulation study suggest that the proposed method results in around 95% coverage probability and outperforms the existing method based on linear regression in general. The method is applied to a population-level prenatal screening program data set to evaluate the relationship among pesticides, placental-fetal hormones and birth weight.

 Public health significance: The shape detection technique can help public health researchers make judgements on the potential relationship between the exposure and the outcome while controlling for confounders. With such judgements, researchers can avoid the bias caused by model misspecification when building models. The regression-based mediation analysis within the shape-restricted framework offers public health researchers a flexible and efficient approach to perform the causal inference. The method helps researchers estimate causal effects using reasonable models.