Topics in modeling multilevel and longitudinal data

Part of this work is devoted to multilevel modeling of binary response variables. Specifically, the maximum pairwise likelihood (MPL) estimator is investigated in multilevel probit models where it is computationally easy to obtain. The asymptotic efficiency of the MPL estimator versus the maximum likelihood (ML) estimator is investigated in two particular models and the issue of weighting the log PL is examined as well. A simulation study was further conducted to compare MPL to ML and PQL2 estimators.;An illustration of the MPL estimation method is presented in the context of surrogate endpoint validation. We use the methodology developed by Buyse et al. (2000) for two normally distributed endpoints, where the surrogate validation issue is approached from a meta-analytic standpoint and studied at each of two levels (individual and trial levels), and we propose an extension to the case of two binary endpoints. This approach entails fitting of a three-level probit model for which MPL estimation is well suited.;An extension of the standard multilevel probit model is also discussed for modeling of longitudinal binary outcomes. Using a latent variable model formulation, the (latent) error terms are assumed to be realizations of a stationary Gaussian process with some autocorrelation function, which affords a possible way of correcting for residual correlation left in the data even after correction for fixed and random effects. Although ML estimation is impractical with this model, MPL is straightforward to use. The model is used to estimate reliability in clinical trial data with longitudinal binary outcomes.;Finally, we examine the surrogate endpoint validation issue when a longitudinally measured biomarker is considered as a surrogate for a time-to-event endpoint. To extend the approach of Buyse et al. (2000), we need to formulate a joint model for longitudinal measurements and event time data. To this end, the model of Henderson, Diggle and Dobson (2000) is adopted. It is shown how trial- and individual-level surrogacy measures can be adapted in this context and clinical trial data in advanced prostate cancer are used to evaluate the usefulness of prostate-specific antigen (PSA) level as a surrogate for survival.