Abstract
BackgroundMultiple imputation is a popular approach to handling missing data in medical research, yet little is known about its applicability for estimating the relative risk. Standard methods for imputing incomplete binary outcomes involve logistic regression or an assumption of multivariate normality, whereas relative risks are typically estimated using log binomial models. It is unclear whether misspecification of the imputation model in this setting could lead to biased parameter estimates.MethodsUsing simulated data, we evaluated the performance of multiple imputation for handling missing data prior to estimating adjusted relative risks from a correctly specified multivariable log binomial model. We considered an arbitrary pattern of missing data in both outcome and exposure variables, with missing data induced under missing at random mechanisms. Focusing on standard model-based methods of multiple imputation, missing data were imputed using multivariate normal imputation or fully conditional specification with a logistic imputation model for the outcome.ResultsMultivariate normal imputation performed poorly in the simulation study, consistently producing estimates of the relative risk that were biased towards the null. Despite outperforming multivariate normal imputation, fully conditional specification also produced somewhat biased estimates, with greater bias observed for higher outcome prevalences and larger relative risks. Deleting imputed outcomes from analysis datasets did not improve the performance of fully conditional specification.ConclusionsBoth multivariate normal imputation and fully conditional specification produced biased estimates of the relative risk, presumably since both use a misspecified imputation model. Based on simulation results, we recommend researchers use fully conditional specification rather than multivariate normal imputation and retain imputed outcomes in the analysis when estimating relative risks. However fully conditional specification is not without its shortcomings, and so further research is needed to identify optimal approaches for relative risk estimation within the multiple imputation framework.
Highlights
Multiple imputation is a popular approach to handling missing data in medical research, yet little is known about its applicability for estimating the relative risk
Conditional specification fully conditional specification (FCS) involves specifying a series of univariate imputation models, one for each variable with missing data [12,13,14], with models tailored according to the distribution of the variable being imputed
The bias of −0.32 shown in Table 1 for an outcome prevalence of 0.30 under the coordinated mechanism equates to a relative risk estimate of 2.19 compared with the true value of 3; coverage was just 0.55 in this scenario
Summary
Multiple imputation is a popular approach to handling missing data in medical research, yet little is known about its applicability for estimating the relative risk. Standard methods for imputing incomplete binary outcomes involve logistic regression or an assumption of multivariate normality, whereas relative risks are typically estimated using log binomial models. It is unclear whether misspecification of the imputation model in this setting could lead to biased parameter estimates. Several alternative approaches to relative risk estimation have been proposed to address failed convergence with the log binomial model, with modified Poisson regression using a log link and a robust error variance [8] one of the more commonly used methods
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