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Statistica Sinica 28 (2018), 1333-1349

SEMIPARAMETRIC RANDOM-EFFECTS CONDITIONAL
DENSITY MODELS FOR LONGITUDINAL ANALYSIS
WITH CONCOMITANT INTERVENTION
Tianqing Liu, Colin O. Wu, Zhaohai Li and Yuanzhang Li
Jilin University, National Heart Lung and Blood Institute, The George
Washington University and Walter Reed Army Institute of Research

Abstract: Longitudinal data in biomedical studies often involve concomitant interventions in addition to the pre-specified repeatedly measured outcome and covariate variables. Since a concomitant intervention is often initiated when a patient exhibits an undesirable health trend, adequate statistical methods should properly incorporate the starting time of a concomitant intervention in order to reduce the potential bias of the estimated intervention effects. We propose in this paper a class of semiparametric random-effects conditional density models for evaluating the distributions and concomitant intervention effects with longitudinal observations. These models simultaneously incorporate concomitant intervention effects and intra-subject longitudinal dependence structures, and quantify the change of the distribution functions through the ratio of two conditional density functions. The conditional density ratio is assumed to have a parametric form, while the baseline density function is nonparametric. We develop a likelihood-based method for estimating the parameters and a goodness-of-fit test for testing the validity of the models. Finite sample properties of our estimation and testing procedures are illustrated through a simulation study and an application to a longitudinal clinical trial in depression and heart disease.

Key words and phrases: Concomitant intervention, conditional density ratio, conditional likelihood, longitudinal data, random-effects conditional density model.

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