Outcome-sensitive multiple imputation: a simulation study

Abstract

Background: Multiple imputation is frequently used to deal with missing data in healthcare research. Although it is known that the outcome should be included in the imputation model when imputing missing covariate values, it is not known whether it should be imputed. Similarly no clear recommendations exist on: the utility of incorporating a secondary outcome, if available, in the imputation model; the level of protection offered when data are missing not-at-random; the implications of the dataset size and missingness levels.

Methods: We used realistic assumptions to generate thousands of datasets across a broad spectrum of contexts: three mechanisms of missingness (completely at random; at random; not at random); varying extents of missingness (20-80% missing data); and different sample sizes (1,000 or 10,000 cases). For each context we quantified the performance of a complete case analysis and seven multiple imputation methods which deleted cases with missing outcome before imputation, after imputation or not at all; included or did not include the outcome in the imputation models; and included or did not include a secondary outcome in the imputation models. Methods were compared on mean absolute error, bias, coverage and power over 1,000 datasets for each scenario.

Results: Overall, there was very little to separate multiple imputation methods which included the outcome in the imputation model. Even when missingness was quite extensive, all multiple imputation approaches performed well. Incorporating a secondary outcome, moderately correlated with the outcome of interest, made very little difference. The dataset size and the extent of missingness affected performance, as expected. Multiple imputation methods protected less well against missingness not at random, but did offer some protection.

Conclusions: As long as the outcome is included in the imputation model, there are very small performance differences between the possible multiple imputation approaches: no outcome imputation, imputation or imputation and deletion. All informative covariates, even with very high levels of missingness, should be included in the multiple imputation model. Multiple imputation offers some protection against a simple missing not at random mechanism.

Keywords: Imputed outcome; Missing data; Missingness; Multiple imputation.

Fig. 1

Data structure

Fig. 2

Mean Bias and 95% Confidence Intervals for exposure E in datasets of 1000 (top) and 10,000 observations (bottom)

Fig. 3

Mean absolute Error and 95% Confidence Intervals for exposure E in datasets of 1000 (top) and 10,000 observations (bottom)

Fig. 4

Coverage and 95% Confidence Intervals for exposure E in datasets of 1000 (top) and 10,000 observations (bottom)

Fig. 5

Power and 95% Confidence Intervals for exposure E in datasets of 1000 (top) and 10,000 observations (bottom)