Predicting pregnancy outcomes using longitudinal information: a penalized splines mixed-effects model approach

Abstract

We propose a semiparametric nonlinear mixed-effects model (SNMM) using penalized splines to classify 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 pregnancy, 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 on the basis of alternative formulations of SNMMs depending on the characteristics of the data set under consideration. 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 penalized 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. ; The first author was supported by Proyecto DI Regular 37.0/2016 VRIEA PUCV; FONDECYT grants 1120739, 1130233, and 1141256; Ministerio de Economía y Competitividad and FEDER, Spain, grants MTM2013-40941-P and MTM2016-74931-P; FONDAP grant 15130011; and grant 16-MATH-03 SIDRE from CONICYT MATH-AmSud Program. The third author was supported by FONDECYT grant 1141256; and grant 16-MATH-03 SIDRE from CONICYT MATH-AmSud Program. The fourth author was supported by the Basque Government through the BERC 360 2014-2017 and the Department of Education, Language Policy and Culture of the Basque Government IT-620-13 programs and Basque Government Industry Department under the ELKARTEK Program, by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and MTM2014-52184-P, and by the RISE Horizon 2020 European Project GEAGAM (644602). The fifth author was funded by grants MTM2014-56535-R and ECO2015-66593-P of the Ministerio de Economía y Competitividad, Spain. Contributions of the second, fourth, and fifth authors were partially supported by grants FONDECYT1120739 and 1141256 while visiting PUCV and CIMFAV-UV.