Missing Data in Clinical Research: A Tutorial on Multiple Imputation

Abstract

Missing data is a common occurrence in clinical research. Missing data occurs when the value of the variables of interest are not measured or recorded for all subjects in the sample. Common approaches to addressing the presence of missing data include complete-case analyses, where subjects with missing data are excluded, and mean-value imputation, where missing values are replaced with the mean value of that variable in those subjects for whom it is not missing. However, in many settings, these approaches can lead to biased estimates of statistics (eg, of regression coefficients) and/or confidence intervals that are artificially narrow. Multiple imputation (MI) is a popular approach for addressing the presence of missing data. With MI, multiple plausible values of a given variable are imputed or filled in for each subject who has missing data for that variable. This results in the creation of multiple completed data sets. Identical statistical analyses are conducted in each of these complete data sets and the results are pooled across complete data sets. We provide an introduction to MI and discuss issues in its implementation, including developing the imputation model, how many imputed data sets to create, and addressing derived variables. We illustrate the application of MI through an analysis of data on patients hospitalised with heart failure. We focus on developing a model to estimate the probability of 1-year mortality in the presence of missing data. Statistical software code for conducting MI in R, SAS, and Stata are provided.