Combining rules for F- and Beta-statistics from multiply-imputed data

Missing values in data impede the task of inference for population parameters of interest. Multiple Imputation (MI) is a popular method for handling missing data since it accounts for the uncertainty of missing values. Inference in MI involves combining point and variance estimates from each imputed dataset via Rubin’s rules. A sufficient condition for these rules is that the estimator is approximately (multivariate) normally distributed. However, these traditional combining rules get computationally cumbersome for multicomponent parameters of interest, and unreliable at high rates of missingness (due to an unstable variance matrix). New combining rules for univariate F- and Beta-statistics from multiply-imputed data are proposed for decisions about multicomponent parameters. The proposed combining rules have the advantage of being computationally convenient since they only involve univariate F- and Beta-statistics, while providing the same inferential reliability as the traditional multivariate combining rules. Simulation study is conducted to demonstrate that the proposed method has good statistical properties of maintaining low type I and type II error rates at relatively large proportions of missingness. The general applicability of the proposed method is demonstrated within a lead exposure study to assess the association between lead exposure and neurological motor function.