A Bivariate Pseudo-Likelihood for Incomplete Longitudinal Binary Data with Nonignorable Non-monotone Missingness

For analyzing longitudinal binary data with nonignorable and non-monotone missing responses, a full likelihood method is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. As an alternative, a pseudo-likelihood approach has been proposed in the literature under minimal parametric assumptions. This formulation only requires specification of the marginal distributions of the responses and missing data mechanism, and uses an independence working assumption. However, this estimator can be inefficient for estimating both time-varying and time-stationary effects under moderate to strong within-subject associations among repeated responses. In this article, we propose an alternative estimator, based on a bivariate pseudo-likelihood, and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudo-likelihood obtained under the assumption of independence. We illustrate the method using longitudinal data on CD4 counts from two clinical trials of HIV-infected patients.