Shape Detection using Semi-parametric Shape-Restricted Mixed Effects Regression Spline with Applications

Linear models are widely used in the field of epidemiology to model the relationship between placental-fetal hormone and fetal/infant outcome. 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 this paper, we focus on the regression spline technique and develop a method to help researchers select the most suitable shape to describe their data among increasing, decreasing, convex and concave shapes. Specifically, we develop a mixed effects regression spline to model hormonal data described in this paper. The proposed methodology is general enough to be applied to other similar problems. We illustrate the method using a state-wide prenatal screening program data set.