Median Regression Models for Longitudinal Data with Dropouts

Abstract

Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease (Volberding et al., 1990, The New England Journal of Medicine 322, 941-949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined.