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On hazard ratio estimators by proportional hazards models in matched-pair cohort studies

机译：配对研究中按比例风险模型估算风险比

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BackgroundIn matched-pair cohort studies with censored events, the hazard ratio (HR) may be of main interest. However, it is lesser known in epidemiologic literature that the partial maximum likelihood estimator of a common HR conditional on matched pairs is written in a simple form, namely, the ratio of the numbers of two pair-types. Moreover, because HR is a noncollapsible measure and its constancy across matched pairs is a restrictive assumption, marginal HR as “average” HR may be targeted more than conditional HR in analysis. MethodsBased on its simple expression, we provided an alternative interpretation of the common HR estimator as the odds of the matched-pair analog of C-statistic for censored time-to-event data. Through simulations assuming proportional hazards within matched pairs, the influence of various censoring patterns on the marginal and common HR estimators of unstratified and stratified proportional hazards models, respectively, was evaluated. The methods were applied to a real propensity-score matched dataset from the Rotterdam tumor bank of primary breast cancer. ResultsWe showed that stratified models unbiasedly estimated a common HR under the proportional hazards within matched pairs. However, the marginal HR estimator with robust variance estimator lacks interpretation as an “average” marginal HR even if censoring is unconditionally independent to event, unless no censoring occurs or no exposure effect is present. Furthermore, the exposure-dependent censoring biased the marginal HR estimator away from both conditional HR and an “average” marginal HR irrespective of whether exposure effect is present. From the matched Rotterdam dataset, we estimated HR for relapse-free survival of absence versus presence of chemotherapy; estimates (95% confidence interval) were 1.47 (1.18–1.83) for common HR and 1.33 (1.13–1.57) for marginal HR. ConclusionThe simple expression of the common HR estimator would be a useful summary of exposure effect, which is less sensitive to censoring patterns than the marginal HR estimator. The common and the marginal HR estimators, both relying on distinct assumptions and interpretations, are complementary alternatives for each other.
机译：背景研究在配对事件队列研究中，事件被审查时，危险比（HR）可能是主要关注对象。然而，在流行病学文献中鲜为人知的是，以匹配对为条件的常见HR的部分最大似然估计是以简单形式写的，即两个对类型的数目之比。此外，由于HR是一项不合条件的度量，并且其在匹配对之间的恒定性是限制性假设，因此在分析中，作为“平均” HR的边际HR可能比条件HR更受关注。方法基于其简单表达，我们提供了一种通用的HR估计量的替代解释，即被删减的事件时间数据的C统计量的配对对类似物的几率。通过假设匹配对中存在比例风险的模拟，分别评估了不同审查模式分别对未分层和分层比例风险模型的边际和通用HR估计量的影响。将该方法应用于来自原发性乳腺癌的鹿特丹肿瘤库的真实倾向评分匹配数据集。结果我们显示，分层模型在匹配对中的比例风险下无偏估计了常见的HR。但是，即使检查没有条件独立于事件，具有稳健方差估计量的边际HR估计器也无法将其解释为“平均”边际HR，除非没有检查发生或没有暴露效应。此外，依赖于暴露的审查会使边际HR估计量偏离条件HR和“平均”边际HR，而与是否存在暴露效应无关。从匹配的鹿特丹数据集中，我们估算了不存在与存在化学疗法之间的无复发生存期的心率;普通HR的估计值（95％置信区间）为1.47（1.18-1.83），边际HR的估计值为1.33（1.13-1.57）。结论普通HR估计量的简单表达将是暴露效果的有用总结，与边缘HR估计量相比，其对检查模式的敏感性较低。共同的和边际的HR估计量都依赖于不同的假设和解释，是彼此互补的选择。

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