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Generating survival times to simulate Cox proportional hazards models with time-varying covariates

机译：生成生存时间以模拟具有时变协变量的Cox比例风险模型

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Simulations and Monte Carlo methods serve an important role in modern statistical research. They allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible. A key element in any statistical simulation is the existence of an appropriate data-generating process: one must be able to simulate data from a specified statistical model. We describe data-generating processes for the Cox proportional hazards model with time-varying covariates when event times follow an exponential, Weibull, or Gompertz distribution. We consider three types of time-varying covariates: first, a dichotomous time-varying covariate that can change at most once from untreated to treated (e.g., organ transplant); second, a continuous time-varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition; third, a dichotomous time-varying covariate with a subject being able to move repeatedly between treatment states (e.g., current compliance or use of a medication). In each setting, we derive closed-form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time-invariant covariates and to a single time-varying covariate. We illustrate the utility of our closed-form expressions for simulating event times by using Monte Carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time-varying covariates. This is compared with the statistical power to detect as statistically significant a binary time-invariant covariate. Copyright © 2012 John Wiley & Sons, Ltd.
机译：模拟和蒙特卡洛方法在现代统计研究中起着重要作用。它们允许检查在分析和数学推导可能不可行的情况下统计程序的性能。任何统计模拟中的一个关键要素是是否存在适当的数据生成过程：必须能够模拟来自指定统计模型的数据。当事件时间遵循指数，Weibull或Gompertz分布时，我们将描述时变协变量的Cox比例风险模型的数据生成过程。我们考虑了三种时变协变量：首先，二分时变协变量最多可以在未经处理的情况下变化为经过处理的（例如，器官移植）。第二，连续的时变协变量，例如恒定剂量的放射线或用于慢性病的药剂的累积暴露；第三，二分时变协变量，受试者能够在治疗状态（例如，当前的依从性或药物的使用）之间重复移动。在每种情况下，我们导出封闭形式的表达式，这些表达式可以模拟生存时间，从而使生存时间与固定或时不变协变量的向量以及单个时变协变量有关。我们通过使用蒙特卡洛模拟来估计统计能力，以检测不同类型的二进制时变协变量的影响，以统计显着性的方式说明闭合形式的效用，用于模拟事件时间。将此与统计能力进行比较，以检测具有统计意义的二进制时不变协变量。版权所有©2012 John Wiley＆Sons，Ltd.

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