Atkinson Andrew, Kenward Michael G, Clayton Tim, Carpenter James R
Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, UK.
Department of Infectious Diseases, Bern University Hospital, University of Bern, Bern, Switzerland.
Pharm Stat. 2019 Nov;18(6):645-658. doi: 10.1002/pst.1954. Epub 2019 Jul 15.
The analysis of time-to-event data typically makes the censoring at random assumption, ie, that-conditional on covariates in the model-the distribution of event times is the same, whether they are observed or unobserved (ie, right censored). When patients who remain in follow-up stay on their assigned treatment, then analysis under this assumption broadly addresses the de jure, or "while on treatment strategy" estimand. In such cases, we may well wish to explore the robustness of our inference to more pragmatic, de facto or "treatment policy strategy," assumptions about the behaviour of patients post-censoring. This is particularly the case when censoring occurs because patients change, or revert, to the usual (ie, reference) standard of care. Recent work has shown how such questions can be addressed for trials with continuous outcome data and longitudinal follow-up, using reference-based multiple imputation. For example, patients in the active arm may have their missing data imputed assuming they reverted to the control (ie, reference) intervention on withdrawal. Reference-based imputation has two advantages: (a) it avoids the user specifying numerous parameters describing the distribution of patients' postwithdrawal data and (b) it is, to a good approximation, information anchored, so that the proportion of information lost due to missing data under the primary analysis is held constant across the sensitivity analyses. In this article, we build on recent work in the survival context, proposing a class of reference-based assumptions appropriate for time-to-event data. We report a simulation study exploring the extent to which the multiple imputation estimator (using Rubin's variance formula) is information anchored in this setting and then illustrate the approach by reanalysing data from a randomized trial, which compared medical therapy with angioplasty for patients presenting with angina.
对事件发生时间数据的分析通常基于随机删失假设，即，在模型中的协变量条件下，无论事件时间是被观察到还是未被观察到（即右删失），其分布都是相同的。当仍在随访中的患者继续接受其分配的治疗时，在这个假设下进行的分析大致针对的是法律上的，或“治疗期间策略”的估计量。在这种情况下，我们很可能希望探究我们的推断对于删失后患者行为的更务实、实际的或“治疗策略”假设的稳健性。当删失发生是因为患者改变或恢复到常规（即参照）护理标准时，情况尤其如此。最近的研究表明，对于具有连续结局数据和纵向随访的试验，如何使用基于参照的多重填补来解决此类问题。例如，试验组中的患者在退出试验后假设恢复到对照组（即参照）干预，从而对其缺失数据进行填补。基于参照的填补有两个优点：（a）它避免了用户指定大量描述患者退出后数据分布的参数；（b）在很好的近似程度上，它以信息为锚定，因此在敏感性分析中，主要分析下由于缺失数据而损失的信息比例保持不变。在本文中，我们以生存背景下的最新研究为基础，提出一类适用于事件发生时间数据的基于参照的假设。我们报告了一项模拟研究，探究多重填补估计量（使用鲁宾方差公式）在这种情况下以信息为锚定的程度，然后通过重新分析一项随机试验的数据来说明该方法，该试验比较了药物治疗与血管成形术对心绞痛患者的疗效。
