Population Health Sciences, Bristol Medical School, University of Bristol, Bristol, UK.
Medical Research Council Integrative Epidemiology Unit, Bristol Medical School, University of Bristol, Bristol, UK.
Biom J. 2023 Dec;65(8):e2200116. doi: 10.1002/bimj.202200116. Epub 2023 Sep 20.
Randomized controlled trials (RCTs) are vulnerable to bias from missing data. When outcomes are missing not at random (MNAR), estimates from complete case analysis (CCA) and multiple imputation (MI) may be biased. There is no statistical test for distinguishing between outcomes missing at random (MAR) and MNAR. Current strategies rely on comparing dropout proportions and covariate distributions, and using auxiliary information to assess the likelihood of dropout being associated with the outcome. We propose using the observed variance difference across trial arms as a tool for assessing the risk of dropout being MNAR in RCTs with continuous outcomes. In an RCT, at randomization, the distributions of all covariates should be equal in the populations randomized to the intervention and control arms. Under the assumption of homogeneous treatment effects and homoskedastic outcome errors, the variance of the outcome will also be equal in the two populations over the course of follow-up. We show that under MAR dropout, the observed outcome variances, conditional on the variables included in the model, are equal across trial arms, whereas MNAR dropout may result in unequal variances. Consequently, unequal observed conditional trial arm variances are an indicator of MNAR dropout and possible bias of the estimated treatment effect. Heterogeneous treatment effects or heteroskedastic outcome errors are another potential cause of observing different outcome variances. We show that for longitudinal data, we can isolate the effect of MNAR outcome-dependent dropout by considering the variance difference at baseline in the same set of patients who are observed at final follow-up. We illustrate our method in simulation for CCA and MI, and in applications using individual-level data and summary data.
随机对照试验（RCT）容易受到缺失数据的影响。当结局缺失不是随机的（MNAR）时，完全案例分析（CCA）和多重插补（MI）的估计可能存在偏差。目前没有用于区分随机缺失（MAR）和 MNAR 的统计检验。当前的策略依赖于比较辍学比例和协变量分布，并使用辅助信息来评估辍学与结局相关的可能性。我们提出使用观察到的试验臂之间的方差差异作为评估连续结局 RCT 中辍学存在 MNAR 风险的工具。在 RCT 中，在随机分组时，随机分配到干预组和对照组的人群中所有协变量的分布应该相等。在假定治疗效果同质和结局误差同方差的情况下，在随访过程中，两个人群的结局方差也应该相等。我们表明，在 MAR 辍学的情况下，观察到的结局方差，根据纳入模型的变量，在试验臂之间是相等的，而 MNAR 辍学可能导致方差不等。因此，观察到的条件试验臂方差不等是 MNAR 辍学和估计的治疗效果可能存在偏差的指标。治疗效果异质性或结局误差异方差是观察到不同结局方差的另一个潜在原因。我们表明，对于纵向数据，我们可以通过考虑在最终随访时观察到的同一组患者的基线差异来分离依赖于结局的 MNAR 辍学的影响。我们在 CCA 和 MI 的模拟中以及在使用个体水平数据和汇总数据的应用中说明了我们的方法。
