An Approximate Generalized Linear Model with Random Effects for Informative Missing Data

TLDR

Models for handling missing data in longitudinal studies have been developed in econometrics and biostatistics for Gaussian primary responses. This paper develops a class of models to address missing data in longitudinal studies. The authors link separate models for the primary response and missingness through a common random parameter, allowing the response to follow a generalized linear model conditioned on this parameter and approximating the GLM by conditioning on missingness data, with an example and simulations illustrating the approach for repeated binary data. The approximation yields a mixed generalized linear model with heterogeneous random effects, and simulations suggest its adequacy for repeated binary data.

Abstract

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.