Inference methods for saturated models in longitudinal clinical trials with incomplete binary data

In the longitudinal studies with binary response, it is often of interest to estimate the percentage of positive responses at each time point and the percentage of having at least one positive response by each time point. When missing data exist, the conventional method based on observed percentages could result in erroneous estimates. This study demonstrates two methods of using expectation-maximization (EM) and data augmentation (DA) algorithms in the estimation of the marginal and cumulative probabilities for incomplete longitudinal binary response data. Both methods provide unbiased estimates when the missingness mechanism is missing at random (MAR) assumption. Sensitivity analyses have been performed for cases when the MAR assumption is in question.