Random Effects Logistic Regression Analysis with Auxiliary Covariates

We study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable. We extend the semiparametric estimator of Pepe and Fleming (1991, Journal of the American Statistical Association86, 108–113) to the random effects model using the best linear unbiased prediction approach of Henderson (1975, Biometrics31, 423–448). The method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications. Simulation study results show that the proposed method outperforms the existing methods. We analyzed a data set from the Collaborative Perinatal Project using the proposed method and found that the use of DDT increases the risk of preterm births among US. children.