Multiple Imputation for Missing Data via Sequential Regression Trees

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Abstract
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.

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