Semiparametric Efficient Estimation for Incomplete Longitudinal Binary Data, With Application to Smoking Trends

Incomplete longitudinal data often are analyzed with estimating equations for inference on a parameter from a marginal mean regression model. Generalized estimating equations, although commonly used for incomplete longitudinal data, are invalid for data that are not missing completely at random. There exists a class of inverse probability weighted estimating equations that are valid under dropouts missing at random, including an easy-to-implement but inefficient member. A relatively computationally complex semiparametric efficient estimator in this class has been applied to continuous data. A specific form of this estimator is developed for binary data and used as a benchmark for assessing the efficiency of the simpler estimator in a simulation study. Both are applied in the estimation of 15-year cigarette smoking trends in the United States from a cohort of 5077 young adults. The results suggest that declines in smoking from previous reports have been exaggerated.