Modified weights based generalized quasilikelihood inferences in incomplete longitudinal binary models

Abstract

AbstractIn an incomplete longitudinal set up, a small number of repeated responses subject to an appropriate missing mechanism along with a set of covariates are collected from a large number of independent individuals over a small period of time. In this set up, the regression effects of the covariates are routinely estimated by solving certain inverse weights based generalized estimating equations. These inverse weights are introduced to make the estimating equation unbiased so that a consistent estimate of the regression parameter vector may be obtained. In the existing studies, these weights are in general formulated conditional on the past responses. Since the past responses follow a correlation structure, the present study reveals that if the longitudinal data subject to missing mechanism are generated by accommodating the longitudinal correlation structure, the conditional weights based on past correlated responses may yield biased and hence inconsistent regression estimates. The bias appears to get larger as the correlation increases. As a remedy, in this paper the authors proposed a modification to the formulation of the existing weights so that weights are not affected directly or indirectly by the correlations. They have then exploited these modified weights to form a weighted generalized quasi‐likelihood estimating equation that yields unbiased and hence consistent estimates for the regression effects irrespective of the magnitude of correlation. The efficiencies of the regression estimates follow due to the use of the true correlation structure as a separate longitudinal weights matrix in the estimating equation. The Canadian Journal of Statistics © 2010 Statistical Society of Canada