Multiple imputation is particularly well suited to deal with missing data in large epidemiologic studies, because typically these studies support a wide range of analyses by many data users. Some of these analyses may involve complex modeling, including interactions and nonlinear relations. Identifying such relations and encoding them in imputation models, for example, in the conditional regressions for multiple imputation via chained equations, can be daunting tasks with large numbers of categorical and continuous variables. The authors present a nonparametric approach for implementing multiple imputation via chained equations by using sequential regression trees as the conditional models. This has the potential to capture complex relations with minimal tuning by the data imputer. Using simulations, the authors demonstrate that the method can result in more plausible imputations, and hence more reliable inferences, in complex settings than the naive application of standard sequential regression imputation techniques. They apply the approach to impute missing values in data on adverse birth outcomes with more than 100 clinical and survey variables. They evaluate the imputations using posterior predictive checks with several epidemiologic analyses of interest.

In many observational studies, analysts estimate treatment effects using propensity scores, e.g. by matching or sub-classifying on the scores. When some values of the covariates are missing, analysts can use multiple imputation to fill in the missing data, estimate propensity scores based on the m completed datasets, and use the propensity scores to estimate treatment effects. We compare two approaches to implement this process. In the first, the analyst estimates the treatment effect using propensity score matching within each completed data set, and averages the m treatment effect estimates. In the second approach, the analyst averages the m propensity scores for each record across the completed datasets, and performs propensity score matching with these averaged scores to estimate the treatment effect. We compare properties of both methods via simulation studies using artificial and real data. The simulations suggest that the second method has greater potential to produce substantial bias reductions than the first, particularly when the missing values are predictive of treatment assignment.

Multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large sample, public use surveys. In the last two decades, the multiple imputation framework has been adapted for other statistical contexts. As examples, individual researchers use multiple imputation to handle missing data in small samples; statistical agencies disseminate multiply-imputed datasets for purposes of protecting data confidentiality; and, survey methodologists and epidemiologists use multiple imputation to correct for measurement errors. In some of these settings, Rubin's original rules for combining the point and variance estimates from the multiply-imputed datasets are not appropriate, because what is known-and therefore in the conditional expectations and variances used to derive inferential methods-differs from the missing data context. These applications require new combining rules and methods of inference. In fact, more than ten combining rules exist in the * Jerome P. Reiter is Assistant Professor,

The paper presents an illustration and empirical study of releasing multiply imputed, fully synthetic public use microdata. Simulations based on data from the US Current Population Survey are used to evaluate the potential validity of inferences based on fully synthetic data for a variety of descriptive and analytic estimands, to assess the degree of protection of confidentiality that is afforded by fully synthetic data and to illustrate the specification of synthetic data imputation models. Benefits and limitations of releasing fully synthetic data sets are discussed. Copyright 2005 Royal Statistical Society.