Pseudo-likelihood Methods for the Analysis of Longitudinal Binary Data Subject to Nonignorable Non-monotone Missingness

For longitudinal binary data with non-monotone non-ignorable missing outcomes over time, a full likelihood approach is complicated algebraically, and maximum likelihood estimation can be computationally prohibitive with many times of follow-up. We propose pseudo-likelihoods to estimate the covariate effects on the marginal probabilities of the outcomes, in addition to the association parameters and missingness parameters. The pseudo-likelihood requires specification of the distribution for the data at all pairs of times on the same subject, but makes no assumptions about the joint distribution of the data at three or more times on the same subject, so the method can be considered semi-parametric. If using maximum likelihood, the full likelihood must be correctly specified in order to obtain consistent estimates. We show in simulations that our proposed pseudolikelihood produces a more efficient estimate of the regression parameters than the pseudo-likelihood for non-ignorable missingness proposed by Troxel et al. (1998). Application to data from the Six Cities study (Ware, et.al, 1984), a longitudinal study of the health effects of air pollution, is discussed.