Efficient semiparametric mean-association estimation for longitudinal binary responses

Semiparametric methods for longitudinal data with association within subjects have recently received considerable attention. However, existing methods for semiparametric longitudinal binary regression modeling (i) mainly concern mean structures with association parameters treated as nuisance; (ii) generally require a correct specification of the covariance structure for misspecified covariance structure may lead to inefficient mean parameter estimates; and (iii) usually run into computation and estimation problems when the time points are irregularly and possibly subject specific. In this article, we propose a semiparametric logistic regression model, which simultaneously takes into account both the mean and response-association structures (via conditional log-odds ratio) for multivariate longitudinal binary outcomes. Our main interest lies in efficient estimation of both the marginal and association parameters. The estimators of the parameters are obtained via the profile kernel approach. We evaluate the proposed methodology through simulation studies and apply it to a real dataset. Both theoretical and empirical results demonstrate that the proposed method yields highly efficient estimators and performs satisfactorily.