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 a nonlinear relationship is suspected, researchers explore nonparametric models such as regression splines, smoothing splines and penalized regression splines (Korevaar et al., Lancet: Diabetes Endocrinol. 4, 35–43 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 technique based on mixed effects regression spline to analyze 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 prenatal screening program data set.