The Yang and Prentice (YP) regression models have garnered interest from the scientific community due to their ability to analyze data whose survival curves exhibit intersection. These models include proportional hazards (PH) and proportional odds (PO) models as specific cases. However, they encounter limitations when dealing with multivariate survival data due to potential dependencies between the times-to-event. A solution is introducing a frailty term into the hazard functions, making it possible for the times-to-event to be considered independent, given the frailty term. In this study, we propose a new class of YP models that incorporate frailty. We use the exponential distribution, the piecewise exponential distribution (PE), and Bernstein polynomials (BP) as baseline functions. Our approach adopts a Bayesian methodology. The proposed models are evaluated through a simulation study, which shows that the YP frailty models with BP and PE baselines perform similarly to the generator parametric model of the data. We apply the models in two real data sets.

翻译：杨和普伦斯（YP）回归模型因其能够分析生存曲线存在交叉的数据而受到科学界的关注。这些模型将比例风险（PH）模型和比例优势（PO）模型作为特例。然而，在处理多元生存数据时，由于事件时间之间可能存在相关性，这些模型面临局限性。一种解决方案是在风险函数中引入一个脆弱项，使得在给定脆弱项的条件下，事件时间可以被视为独立。在本研究中，我们提出了一类包含脆弱项的新型YP模型。我们采用指数分布、分段指数分布（PE）和伯恩斯坦多项式（BP）作为基线函数。我们的方法采用贝叶斯方法论。通过模拟研究对提出的模型进行评估，结果表明，采用BP和PE基线的YP脆弱模型在性能上与数据的生成参数模型相近。我们将这些模型应用于两个真实数据集。