The University of Adelaide, School of Public Health, Adelaide, SA, Australia.
Clinical Epidemiology and Biostatistics Unit, Murdoch Childrens Research Institute, Melville, VIC, Australia.
BMC Med Res Methodol. 2017 Sep 6;17(1):134. doi: 10.1186/s12874-017-0414-5.
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.
Using 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.
Multivariate 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.
Both 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.
在医学研究中，多重插补是一种常用的处理缺失数据的方法，但对于估计相对风险的适用性知之甚少。标准的用于插补不完全二分类结局的方法包括逻辑回归或多元正态性假设，而相对风险通常使用对数二项式模型进行估计。在这种情况下，插补模型的指定不当是否会导致参数估计有偏差尚不清楚。
使用模拟数据，我们评估了在使用正确指定的多变量对数二项式模型估计校正相对风险之前，多重插补处理缺失数据的性能。我们考虑了结局和暴露变量中任意缺失模式的情况，缺失数据是在随机缺失机制下产生的。重点关注多重插补的标准基于模型的方法，使用多元正态插补或完全条件指定进行缺失数据插补，对数插补模型用于结局。
多元正态插补在模拟研究中表现不佳，一致地产生了偏向于零的相对风险估计值。尽管全条件指定表现优于多元正态插补，但也产生了有些偏倚的估计值，较高的结局发生率和较大的相对风险观察到更大的偏倚。从分析数据集删除插补结局并不能改善全条件指定的性能。
多元正态插补和全条件指定都产生了相对风险的偏倚估计值，可能是因为它们都使用了指定不当的插补模型。基于模拟结果，我们建议研究人员在估计相对风险时使用全条件指定而不是多元正态插补，并在分析中保留插补结局。然而，全条件指定也并非没有缺点，因此需要进一步研究以确定多重插补框架内相对风险估计的最佳方法。
