Some Topics in Missing Data and Adaptive Confidence Intervals. Some Topics in Missing Data and Adaptive Confidence Intervals.

[摘要] When data are missing at random, the missing-data mechanism can be ignored but this assumption is not always intuitive for general patterns of missing data. In part I, we consider maximum likelihood (ML) estimation for a non-ignorable mechanism which is called almost missing at random (AMAR). We examine in some detail the case of two multinomially distributed categorical variables. Although ML can be fitted using the EM algorithm, we find non-iterative ML estimates sometimes exist, with some data being excluded for estimating the parameters of interest. A variation of this type of mechanism is also discussed. We apply the AMAR models to data from the Muscatine Coronary Risk Factor Study (Woolson and Clark, 1984).In part II, we consider one extension of AMAR with an additional fully observed covariate. Specifically, we consider randomized clinical trials with non-compliance to the treatment assignments and subsequent non-response. We build a connection between AMAR and latent ignorability (Frangakis and Rubin, 1999). To identify the model, we further specify two assumptions for principal compliance and two assumptions for missing outcome. We show that the models of principal compliance determine which type of analysis is used to estimate treatment efficacy, while the assumptions for missing outcome determine whether non-iterative ML estimates exist. We apply our methods to data from a double-blinded randomized clinical trial with clozapine vs. haloperidol (Rosenheck et al, 1997).In part III, we consider the combination of bootstrap and Bayes inferences. In the case of independent identically distributed samples, the simple bootstrap yields confidence limits that are asymptotically correct to the first order but have less reliable confidence coverage in small samples. Bayesian credibility intervals based on the posterior distribution of the model parameters tend to perform better for small samples, but are more dependent on modeling assumptions than the bootstrap. A discrepancy statistic based on the difference of model and bootstrap estimates of variance is developed to combine bootstrap and Bayesian inferences. Our goal is to yield intervals that combine robustness with good small-sample confidence coverage. We assess properties of our method by some simple simulation experiments.

[发布机构] University of Michigan

[效力级别] EM Algorithm

[关键词] Missing Data;EM Algorithm;Clinical Trials;Noncompliance;Bootstrap;Bayesian;Statistics and Numeric Data;Science;Biostatistics