Combination of longitudinal biomarkers in predicting binary events.

In disease screening, the combination of multiple biomarkers often substantially improves the diagnostic accuracy over a single marker. This is particularly true for longitudinal biomarkers where individual trajectory may improve the diagnosis. We propose a pattern mixture model (PMM) framework to predict a binary disease status from a longitudinal sequence of biomarkers. The marker distribution given the disease status is estimated from a linear mixed effects model. A likelihood ratio statistic is computed as the combination rule, which is optimal in the sense of the maximum receiver operating characteristic (ROC) curve under the correctly specified mixed effects model. The individual disease risk score is then estimated by Bayes' theorem, and we derive the analytical form of the 95% confidence interval. We show that this PMM is an approximation to the shared random effects (SRE) model proposed by Albert (2012. A linear mixed model for predicting a binary event from longitudinal data under random effects mis-specification. Statistics in Medicine 31: (2), 143-154). Further, with extensive simulation studies, we found that the PMM is more robust than the SRE model under wide classes of models. This new PPM approach for combining biomarkers is motivated by and applied to a fetal growth study, where the interest is in predicting macrosomia using longitudinal ultrasound measurements.