Pattern-mixture and selection models for analysing longitudinal data with monotone missing patterns

We examine three pattern-mixture models for making inference about parameters of the distribution of an outcome of interest Y that is to be measured at the end of a longitudinal study when this outcome is missing in some subjects. We show that these pattern-mixture models also have an interpretation as selection models., Because these models make unverifiable assumptions, we recommend that inference about the distribution of Y be repeated under a range of plausible assumptions. We argue that, of the three models considered, only one admits a parameterization that facilitates the examination of departures from the assumption of sequential ignorability The three models are nonparametric in the sense that they do not impose restrictions on the class of observed data distributions. Owing to the curse of dimensionality, the assumptions that are encoded in these models are sufficient for identification but not for inference. We describe additional flexible and easily interpretable assumptions under which it is possible to construct estimators that are well behaved with moderate sample sizes. These assumptions define semiparametric models for the distribution of the observed data. We describe a class of estimators which, up to asymptotic equivalence, comprise all the consistent and asymptotically normal estimators of the parameters of interest under the postulated semiparametric models. We illustrate our methods with the analysis of data from a randomized clinical trial of contracepting women.