Methods for longitudinal binary data with time-dependent covariates

We consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time. Our analysis goal is to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject. However, additional care must be taken to adjust for the association between the repeated measurements on each subject. In this dissertation, we propose the new first-order Markov maximum likelihood (MARK1ML) method for covariates that may be fixed or time-varying. We also implement and make comparisons with two other approaches: generalized estimating equations, which may be more robust to misspecification of the true correlation structure, and alternating logistic regression, which models association via odds-ratios, that are subject to less-restrictive constraints than are correlations. We prove that the proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters, if the correlation on consecutive measurements on a subject is correctly specified. Simulations (conducted with a new and simple approach that we present in this dissertation) demonstrate that our approach can yield improved efficiency in estimation of the regression parameter; for equally spaced and complete data, the gains in efficiency were greatest for the parameter associated with a time by group interaction term and for higher values of the correlation. For unequally spaced data and with drop-out according to a missing at random mechanism, MARK1ML with correctly specified consecutive correlations yielded substantial improvements both in terms of bias and efficiency. We present analyzes from longitudinal studies in psychiatry and cancer prevention to demonstrate application of the methods we consider. We also offer an R function for easy implementation of our approach