Fixed Effects Models for Longitudinal Binary Data with Drop-outs Missing at Random

We consider the problem of attrition under a logistic regression model for longitudinal binary data in which each subject has his own intercept parameter, and where parameters are eliminated via conditional logistic regression. This is a fixed-effects, subject-specific model which exploits the longitudinal data by allowing subjects to act as their own controls. By modeling and conditioning on the drop-out process, we develop a valid but inefficient conditional likelihood using the completerecord data. Then, noting that the drop-out process is ancillary in this model, we use a projection argument to develop a score with improved efficiency over the conditional likelihood score, and embed both of these scores in a more general class of estimating functions. We then propose a member of this class that approximates the projected score, while being much more computationally feasible. We study the efficiency gains that are possible using a small simulation, and present an example analysis from aging research.