Research For The Saturated Model On Exchangeable Missing Binary Data

In many statistic applications, we always encounter the exchangeable binary data. It is reasonable to expect that the data from the same cluster is exchangeability. In real life, the exchangeable binary data are frequently founded in cluster sample survey, ophthalmological and otolaryngologic studies teratological studies and other clinical trials. In this paper we aim to research the problem of the exchangeable binary data with missing data by the approach of saturated models.In order to solve the statistic problem of exchangeable binary missing data, we first present a general form of optimal unbiased estimating equations and some theory results for the consistency and the asymptotic normality of the solutions to general estimating equations. Then we construct estimating equations with the ap-proach of saturated models. For the estimating equations with missing data, we adopt the AU algorithm:at first, the equations with missing data are replaced by the conditional expectation or the approximating values of the conditional expecta-tions; Then we get the explicit expression by putting the results into the estimating equations. This algorithm has its advantages because it makes the computation very feasible and simple. Moreover, it provides the approximating form for the conditional expectation.For the data from a reproductive toxicity study, we apply the algorithm above to analysis and compute. From the result of the simulation, it is proved that our algorithm is effective and performs better than the case excluding the missing data.