Logistic regression error‐in‐covariate models for longitudinal high‐dimensional covariates

Abstract

We consider a logistic regression model for a binary response where part of its covariates are subject‐specific random intercepts and slopes from a large number of longitudinal covariates. These random effect covariates must be estimated from the observed data, and therefore, the model essentially involves errors in covariates. Because of high dimension and high correlation of the random effects, we employ longitudinal principal component analysis to reduce the total number of random effects to some manageable number of random effects. To deal with errors in covariates, we extend the conditional‐score equation approach to this moderate dimensional logistic regression model with random effect covariates. To reliably solve the conditional‐score equations in moderate/high dimension, we apply a majorization on the first derivative of the conditional‐score functions and a penalized estimation by the smoothly clipped absolute deviation. The method was evaluated through a set of simulation studies and applied to a data set with longitudinal cortical thickness of 68 regions of interest to identify biomarkers that are related to dementia transition.