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Modeling heterogeneity for bivariate survival data by shared gamma frailty regression model

机译：通过共享伽玛脆弱回归模型为双变量生存数据建模异质性

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摘要

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling survival data where the hazard rate is non-monotonic. For such cases, where hazard rates are bathtub-shaped or unimodal (or hump-shaped), log-logistic, lognormal, Birnbaun-Saunders, and inverse Gaussian models are used for the computational simplicity and popularity among users. When models are inadequate and inappropriate, compound Rayleigh, arctangent, generalized Weibull, and Weibull-Pareto composite models are also used. Out of these models log-logistic (LL) model is frequently used. The log-logistic distribution (LLD) has the advantage of having simple algebraic expressions for its survivor and hazard functions and a closed form for its distribution function. In this paper, we consider gamma distribution as frailty distribution and LLD as baseline distribution for bivariate survival times. The problem of analyzing and estimating parameters of bivariate LLD with shared gamma frailty is of interest and the focus of this paper. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model. We present a simulation study and two real data examples to compute Bayesian estimates of the parameters and their standard errors and then compare the true values of the parameters with the estimated values for different sample sizes. A search of the literature suggests there is currently no work has been done for bivariate log-logistic regression model with shared gamma frailty using Bayesian approach.
机译：在使用参数模型分析生存数据时，众所周知，Weibull模型不适用于风险率非单调的生存数据建模。对于此类情况，在危险率是浴缸形或单峰（或驼峰形）的情况下，使用对数逻辑，对数正态，Birnbaun-Saunders和反高斯模型可简化计算并在用户中广受欢迎。当模型不适当且不合适时，还将使用复合瑞利，反正切，广义威布尔和威布尔-帕累托复合模型。在这些模型中，经常使用对数逻辑（LL）模型。对数逻辑分布（LLD）的优势在于，其幸存函数和危险函数具有简单的代数表达式，而其分布函数具有封闭形式。在本文中，我们将γ分布视为脆弱分布，将LLD视为双变量生存时间的基线分布。具有共享伽玛脆弱性的双变量LLD参数的分析和估计问题是研究的重点，也是本文的重点。我们介绍了使用马尔可夫链蒙特卡洛（MCMC）技术的贝叶斯估计程序，以估计所提出的模型中涉及的参数。我们提供了一个仿真研究和两个真实的数据示例，以计算参数及其标准误差的贝叶斯估计，然后将参数的真实值与不同样本大小的估计值进行比较。文献检索表明，目前尚无使用贝叶斯方法对共享伽玛脆弱的双变量对数逻辑回归模型进行研究。

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