Predicting Pregnancy Outcomes Using Longitudinal Information: A Penalized Splines Mixed–Effects Model Approach

Abstract

We propose a semiparametric mixed–effects model (SNMM) using penalized splines to clas- sify longitudinal data and improve the prediction of a binary outcome. The work is motivated by a study in which different hormone levels were measured during the early stages of preg- nancy, and the challenge is using this information to predict normal versus abnormal pregnancy outcomes. The aim of this paper is to compare models and estimation strategies based on alternative formulations of SNMMs depending on the characteristics of the data set under con- sideration. For our motivating example, we address the classification problem using a particular case of the SNMM in which the parameter space has a finite dimensional component (fixed effects and variance components) and an infinite dimensional component (unknown function) that need to be estimated. The nonparametric component of the model is estimated using pe- nalized splines. For the parametric component, we compare the advantages of using random effects versus direct modeling of the correlation structure of the errors. Numerical studies show that our approach improves over other existing methods for the analysis of this type of data. Furthermore, the results obtained using our method support the idea that explicit modeling of the serial correlation of the error term improves the prediction accuracy with respect to a model with random effects, but independent errors.