A weighted combination of pseudo-likelihood estimators for longitudinal binary data subject to non-ignorable non-monotone missingness.

For longitudinal binary data with non-monotone non-ignorably missing outcomes over time, a full likelihood approach is complicated algebraically, and with many follow-up times, maximum likelihood estimation can be computationally prohibitive. As alternatives, two pseudo-likelihood approaches have been proposed that use minimal parametric assumptions. One formulation requires specification of the marginal distributions of the outcome and missing data mechanism at each time point, but uses an 'independence working assumption,' i.e. an assumption that observations are independent over time. Another method avoids having to estimate the missing data mechanism by formulating a 'protective estimator.' In simulations, these two estimators can be very inefficient, both for estimating time trends in the first case and for estimating both time-varying and time-stationary effects in the second. In this paper, we propose the use of the optimal weighted combination of these two estimators, and in simulations we show that the optimal weighted combination can be much more efficient than either estimator alone. Finally, the proposed method is used to analyze data from two longitudinal clinical trials of HIV-infected patients.