Applications of misspecified models in the field of survival analysis particularly frailty models may result in poor generalization and biases. Since gamma and inverse Gaussian distributions are often used interchangeably as frailty distributions for heterogeneous survival data, clear distinction between them is necessary. Based on closed form expressions of unconditional hazards and survival functions, in this paper we compare the effectiveness of gamma and inverse Gaussian distributions for frailty term in modeling survival data for heterogeneous populations. Different baseline hazards were considered including exponential, Weibull and Gompertz. We derived the closed form expressions for unconditional hazards and survival functions under each baseline distribution for both gamma and inverse Gaussian frailty models. Both graphical and extensive statistical simulation approaches are applied to compare the models. For the inference purpose, real data concerning the East Coast Fever (ECF) transmission dynamics is applied. General overview from the graphical analysis and results from both real and synthetic data indicate that gamma distribution under the Gompertz and Weibull baseline hazards is better compared to inverse Gaussian in modeling survival data for a heterogeneous population. Simulation, graphical and inferential analyses were done using appropriate packages in R language.

在生存分析领域中应用不正确的模型，特别是脆弱的模型可能会导致泛化和偏差。由于伽马分布和高斯逆分布经常作为脆弱分布用于异质生存数据，因此必须对它们进行明确区分。基于无条件危险和生存函数的封闭形式表达式，在本文中，我们比较了脆弱性项的gamma和逆高斯分布在建模异质种群生存数据中的有效性。考虑了不同的基准危害，包括指数风险，威布尔风险和Gompertz风险。对于伽玛模型和逆高斯脆弱模型，我们在每个基线分布下得出了无条件危险和生存函数的封闭形式表达式。图形和广泛的统计模拟方法都可以用来比较模型。出于推理目的，应用了有关东海岸热（ECF）传输动力学的真实数据。图形分析的总体概述以及实际数据和综合数据的结果均表明，在建模异质种群的生存数据时，与逆高斯方法相比，Gompertz和Weibull基准风险下的伽马分布更好。使用R语言的适当软件包进行了仿真，图形和推论分析。图形分析的总体概述以及实际数据和综合数据的结果均表明，在建模异质种群的生存数据时，与逆高斯方法相比，Gompertz和Weibull基准风险下的伽马分布更好。使用R语言的适当软件包进行了仿真，图形和推论分析。图形分析的总体概述以及实际数据和综合数据的结果均表明，在建模异质种群的生存数据时，与逆高斯方法相比，Gompertz和Weibull基准风险下的伽马分布更好。使用R语言的适当软件包进行了仿真，图形和推论分析。