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Special Communication |

Missing Data and Multiple Imputation

Peter Cummings, MD, MPH1
[+] Author Affiliations
1Department of Epidemiology and Harborview Injury Prevention and Research Center, University of Washington, Seattle.
JAMA Pediatr. 2013;167(7):656-661. doi:10.1001/jamapediatrics.2013.1329.
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Missing data can result in biased estimates of the association between an exposure X and an outcome Y. Even in the absence of bias, missing data can hurt precision, resulting in wider confidence intervals. Analysts should examine the missing data pattern and try to determine the causes of the missingness. Modern software has simplified multiple imputation of missing data and the analysis of multiply imputed data to the point where this method should be part of any analyst’s toolkit. Multiple imputation will often, but not always, reduce bias and increase precision compared with complete-case analysis. Some exceptions to this rule are noted in this review. When describing study results, authors should disclose the amount of missing data and other details. Investigators should consider how to minimize missing data when planning a study.

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Figure 1.
Distribution of Risk Ratio Estimates From Complete-Case Analyses (Solid Line) and After Multiple Imputation (Dashed Line) in 2000 Simulations Using Data From Table 1

Data sets were created with data missing at random for 50% of speed data and 20% of seat belt use data among drivers who survived, data missing completely at random for 25% of speed data and 20% of seat belt data among all drivers, and data missing not at random for both seat belt use and death among 30 drivers who used seat belts and died. The true adjusted risk ratio for death among belted vs unbelted drivers was 0.500, shown by a vertical line. The distributions of the risk ratio estimates were smoothed by using a kernel density method.

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Figure 2.
Scatterplot From 2000 Simulations of Table 1 Data

Data for speed were missing completely at random (MCAR) in 25% of the records, and data about seat belt use were MCAR for 20%. Vertical and horizontal lines indicate the true risk ratio of 0.500. The solid diagonal line indicates identical values for both risk ratios, and the dashed diagonal line is from linear regression, with complete-case risk ratios as the explanatory variable and multiple-imputation risk ratios as the outcome. This regression line and the 2000 plotted points both show that the risk ratios produced by multiple imputation are usually closer to 0.500 than those produced by complete-case analysis.

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