Time-varying coefficient Cox model has been widely studied and popularly used in survival data analysis due to its flexibility for modeling covariate effects. It is of great practical interest to accurately identify the structure of covariate effects in a time-varying coefficient Cox model, i.e. covariates with null effect, constant effect and truly time-varying effect, and estimate the corresponding regression coefficients. Combining the ideas of local polynomial smoothing and group nonnegative garrote, we develop a new penalization approach to achieve such goals. Our method is able to identify the underlying true model structure with probability tending to one and simultaneously estimate the time-varying coefficients consistently. The asymptotic normalities of the resulting estimators are also established. We demonstrate the performance of our method using simulations and an application to the primary biliary cirrhosis data.

中文翻译：

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时变系数Cox模型中的关节结构选择与估计

时变系数 Cox 模型因其对协变量效应建模的灵活性而被广泛研究并广泛用于生存数据分析。在时变系数Cox模型中准确识别协变量效应的结构，即具有零效应、恒定效应和真正时变效应的协变量，并估计相应的回归系数，具有重要的实际意义。结合局部多项式平滑和组非负绞索的思想，我们开发了一种新的惩罚方法来实现这些目标。我们的方法能够识别潜在的真实模型结构，概率趋于 1，同时一致地估计时变系数。还建立了所得估计量的渐近正态性。