Department of Biostatistics and Epidemiology, 48463Kerman University of Medical Sciences, Kerman, Islamic Republic of Iran.
Modeling in Health Research Center, Institute for Futures Studies in Health, 48463Kerman University of Medical Sciences, Kerman, Islamic Republic of Iran.
Stat Methods Med Res. 2021 Mar;30(3):731-746. doi: 10.1177/0962280220974699. Epub 2020 Nov 26.
Mixture cure rate models are commonly used to analyze lifetime data with long-term survivors. On the other hand, frailty models also lead to accurate estimation of coefficients by controlling the heterogeneity in survival data. Gamma frailty models are the most common models of frailty. Usually, the gamma distribution is used in the frailty random variable models. However, for survival data which are suitable for populations with a cure rate, it may be better to use a discrete distribution for the frailty random variable than a continuous distribution. Therefore, we proposed two models in this study. In the first model, continuous gamma as the distribution is used, and in the second model, discrete hyper-Poisson distribution is applied for the frailty random variable. Also, Bayesian inference with Weibull distribution and generalized modified Weibull distribution as the baseline distribution were used in the two proposed models, respectively. In this study, we used data of patients with gastric cancer to show the application of these models in real data analysis. The parameters and regression coefficients were estimated using the Metropolis with Gibbs sampling algorithm, so that this algorithm is one of the crucial techniques in Markov chain Monte Carlo simulation. A simulation study was also used to evaluate the performance of the Bayesian estimates to confirm the proposed models. Based on the results of the Bayesian inference, it was found that the model with generalized modified Weibull and hyper-Poisson distributions is a suitable model in practical study and also this model fits better than the model with Weibull and Gamma distributions.
混合治愈率模型通常用于分析具有长期幸存者的寿命数据。另一方面，脆弱性模型通过控制生存数据中的异质性也可以准确估计系数。伽马脆弱性模型是最常见的脆弱性模型。通常，在脆弱性随机变量模型中使用伽马分布。然而，对于适合具有治愈率的人群的生存数据，使用脆弱性随机变量的离散分布可能比连续分布更好。因此，我们在本研究中提出了两种模型。在第一种模型中，连续伽马分布用于分布，在第二种模型中，离散超泊松分布用于脆弱性随机变量。此外，在这两种提出的模型中，分别使用威布尔分布和广义修正威布尔分布作为基线分布进行贝叶斯推断。在本研究中，我们使用胃癌患者的数据来展示这些模型在实际数据分析中的应用。使用 Metropolis with Gibbs 抽样算法估计参数和回归系数，因此该算法是马尔可夫链蒙特卡罗模拟的关键技术之一。还进行了模拟研究来评估贝叶斯估计的性能，以确认所提出的模型。基于贝叶斯推断的结果，发现广义修正威布尔和超泊松分布的模型是实际研究中合适的模型，并且该模型比具有威布尔和伽马分布的模型更合适。
