Robust Inference for Incomplete Binary Longitudinal Data

Missing data occur in many longitudinal studies. When data are nonignorably missing, it is necessary to incorporate the missing data mechanism into the observed data likelihood function. A full likelihood analysis of nonignorable missing data is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. To avoid such computational difficulties, pseudo-likelihood methods have been proposed in the literature under minimal parametric assumptions. However, like the classical maximum likelihood estimators, these pseudo-likelihood estimators are also sensitive to potential outliers in the data. In this article, we propose and explore a robust method in the framework of a pseudo-likelihood function that is derived under the working assumption that the longitudinal responses are independent over time. The performance of the proposed robust method is investigated in simulations. The method is also illustrated in an example using actual data on CD4 counts from clinical trials of HIV-infected patients.