Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B-spline function. For those "semi-parametric" proposals, different prior scenarios ranging from prior independence to particular correlated structures are discussed in a real study with microvirulence data and in an extensive simulation scenario that includes different data sample and time axis partition sizes in order to capture risk variations. The posterior distribution of the parameters was approximated using Markov chain Monte Carlo methods. Model selection was performed in accordance with the deviance information criteria and the log pseudo-marginal likelihood. The results obtained reveal that, in general, Cox models present great robustness in covariate effects and survival estimates independent of the baseline hazard specification. In relation to the "semi-parametric" baseline hazard specification, the B-splines hazard function is less dependent on the regularization process than the piecewise specification because it demands a smaller time axis partition to estimate a similar behavior of the risk.

中文翻译：

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Cox生存模型中灵活基线危险函数的贝叶斯正则化

Cox 模型的完全贝叶斯方法指定了基线风险函数的模型。参数方法通常提供单调估计。半参数选择允许更灵活的模式，但它们可能会受到过度拟合和不稳定的影响。通过具有相关结构的先验分布的正则化方法通常会对这些类型的情况给出合理的答案。我们讨论了 Cox 生存模型的贝叶斯正则化，该模型通过由分段常数函数和三次 B 样条函数的混合指定的灵活基线风险定义。对于那些“半参数”提案，在使用微毒力数据的真实研究和包括不同数据样本和时间轴分区大小以捕捉风险变化的广泛模拟场景中，讨论了从先验独立性到特定相关结构的不同先验情景。使用马尔可夫链蒙特卡罗方法来近似参数的后验分布。根据偏差信息标准和对数伪边际似然进行模型选择。获得的结果表明，总的来说，Cox 模型在独立于基线风险规范的协变量效应和生存估计方面表现出很大的稳健性。关于“半参数”基线危险规范，