The goals in clinical and cohort studies often include evaluation of the association of a time-dependent binary treatment or exposure with a survival outcome. Recently, several impactful studies targeted the association between initiation of aspirin and survival following colorectal cancer (CRC) diagnosis. The value of this exposure is zero at baseline and may change its value to one at some time point. Estimating this association is complicated by having only intermittent measurements on aspirin-taking. Commonly used methods can lead to substantial bias. We present a class of calibration models for the distribution of the time of status change of the binary covariate. Estimates obtained from these models are then incorporated into the proportional hazard partial likelihood in a natural way. We develop non-parametric, semiparametric, and parametric calibration models, and derive asymptotic theory for the methods that we implement in the aspirin and CRC study. We further develop a risk-set calibration approach that is more useful in settings in which the association between the binary covariate and survival is strong.

中文翻译：

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当在稀疏时间点测量二进制协变量时，用于生存分析的新型校准框架。

临床和队列研究的目标通常包括评估时间依赖性二元治疗或暴露与生存结局的关联。最近，一些有影响力的研究针对阿司匹林的起始与大肠癌（CRC）诊断后的生存之间的关联。此风险暴露的值在基线为零，并且可能在某个时间点将其值更改为一。由于仅对阿司匹林服用进行间歇性测量，因此估计这种关联非常复杂。常用的方法可能会导致重大偏差。我们提供了一类用于二进制协变量状态变化时间分布的校准模型。然后将从这些模型中获得的估计值自然地合并到比例风险部分可能性中。我们开发非参数，半参数，和参数校正模型，并为我们在阿司匹林和CRC研究中实施的方法推导渐近理论。我们进一步开发了一种风险设置校准方法，该方法在二进制协变量与生存之间的关联较强的设置中更有用。