Functional methods for logistic regression on random-effect-coefficients for longitudinal measurements

We study logistic regression analysis when covariate variables are the underlying regression coefficients of another random effects model. For each subject, the covariate variables to the primary regression model are not observed, but can be estimated from observed longitudinal measurements. Wang et al. (Biometrics 56 (2000) 487-495) investigated estimation methods based on the regression calibration approximation and the expected estimating equations conditional on observed data. In this paper, we extend the sufficiency score and conditional score estimators of Stefanski and Carroll (Biometrics 74 (1987) 703-716) to this problem. These methods do not need the assumption of the underlying distribution of the random effects for each subject. We apply a robust sandwich covariance estimation procedure for both methods. Simulation results are provided for various random effects distributions.