Maximum likelihood analysis of logistic regression models with incomplete covariate data and auxiliary information

This article presents a new method for maximum likelihood estimation of log istic regression models with incomplete covariate data where auxiliary info rmation is available. This auxiliary information is extraneous to the regre ssion model of interest but predictive of the covariate with missing data. Ibrahim (1990, Journal of the American Statistical Association 85, 765-769) provides a general method for estimating generalized linear regression mod els with missing covariates using the EM algorithm that is easily implement ed when there is no auxiliary data. Vach (1997, Statistics in Medicine 16, 57-72) describes how the method can be extended when the outcome and auxili ary data are conditionally independent given the covariates in the model. T he method allows the incorporation of auxiliary data without making the con ditional independence assumption. We suggest tests of conditional independe nce and compare the performance of several estimators in an example concern ing mental health service utilization in children. Using an artificial data set, we compare the performance of several estimators when auxiliary data a re available.