Yavari Parvin, Abadi Alireza, Amanpour Farzaneh, Bajdik Chris
Department of Health and Community Medicine, School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran.
Asian Pac J Cancer Prev. 2012;13(5):1829-31. doi: 10.7314/apjcp.2012.13.5.1829.
The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates.
We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010.
In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg"are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time.
The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or log- normal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.
广义伽马分布统计构成了一个广泛的族，其中包含几乎所有最常用的分布，包括指数分布、威布尔分布和对数正态分布。该模型的饱和形式允许协变量通过生存时间分布的所有参数产生影响。加速失效时间模型假设分布中只有一个参数依赖于协变量。
我们对传统的GG模型及其每个成员（包括威布尔分布和对数正态分布）的饱和形式进行了拟合；并使用似然比进行比较。为了将选定的参数分布与对数逻辑分布（生存分析中一种著名的分布，不包含在广义伽马族中）进行比较，我们使用了赤池信息准则（AIC；r = l(b) - 2p）。所有模型均使用1990 - 1999年期间在不列颠哥伦比亚省被诊断为IV期乳腺癌且随访至2010年的369名50岁及以上女性的数据进行拟合。
在传统和饱和参数模型中，对数正态分布是GG族成员中最佳的候选分布；此外，对数正态分布的拟合效果优于对数逻辑分布。通过传统的GG模型，变量“手术”“放疗”“激素治疗”“雌激素受体阳性/阴性”以及“激素治疗”与“雌激素受体阳性/阴性”之间的相互作用具有显著性。在加速失效时间模型中，我们估计了这些变量的相对时间。通过饱和GG模型，选择了类似的显著变量。估计扩展模型不同百分位数下的相对时间说明了相对生存时间随时间变化的模式。
使用广义伽马分布的优势在于，与标准的威布尔分布或对数正态分布相比，它有助于估计拟合度更高的模型。或者，可以考虑广义F分布族，广义伽马分布是其中的一个成员，并且还包括常用的对数逻辑分布。
