Cox’s proportional hazards regression model is the standard method for modelling censored life-time data with covariates. In its standard form, this method relies on a semiparametric proportional hazards structure, leaving the baseline unspecified. Naturally, specifying a parametric model also for the baseline hazard, leading to fully parametric Cox models, will be more efficient when the parametric model is correct, or close to correct. The aim of this paper is two-fold. (a) We compare parametric and semiparametric models in terms of their asymptotic relative efficiencies when estimating different quantities. We find that for some quantities the gain of restricting the model space is substantial, while it is negligible for others. (b) To deal with such selection in practice we develop certain focused and averaged focused information criteria (FIC and AFIC). These aim at selecting the most appropriate proportional hazards models for given purposes. Our methodology applies also to the simpler case without covariates, when comparing Kaplan–Meier and Nelson–Aalen estimators to parametric counterparts. Applications to real data are also provided, along with analyses of theoretical behavioural aspects of our methods.

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什么价格半参数Cox回归？

Cox比例风险回归模型是使用协变量对审查的生命周期数据进行建模的标准方法。以其标准形式，此方法依赖于半参数比例风险结构，而未指定基线。自然地，当参数模型正确或接近正确时，也为基线危害指定参数模型，从而导致完全参数化的Cox模型将更加有效。本文的目的是双重的。（a）在估计不同数量时，我们根据参数和半参数模型的渐近相对效率对其进行比较。我们发现，对于某些数量而言，限制模型空间的收益是可观的，而对于其他数量则可忽略不计。（b）为了在实践中应对这种选择，我们制定了某些集中和平均集中的信息标准（FIC和AFIC）。这些旨在针对给定的目的选择最合适的比例风险模型。当将Kaplan–Meier和Nelson–Aalen估计量与参数对应量进行比较时，我们的方法也适用于没有协变量的简单情况。还提供了对实际数据的应用，以及对我们方法的理论行为方面的分析。