Department of Mathematics, College of Science, Sudan University of Science and Technology, Khartoum, Sudan.
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang, Malaysia.
Asian Pac J Cancer Prev. 2021 Apr 1;22(4):1045-1053. doi: 10.31557/APJCP.2021.22.4.1045.
Cure rate models are survival models, commonly applied to model survival data with a cured fraction. In the existence of a cure rate, if the distribution of survival times for susceptible patients is specified, researchers usually prefer cure models to parametric models. Different distributions can be assumed for the survival times, for instance, generalized modified Weibull (GMW), exponentiated Weibull (EW), and log-beta Weibull. The purpose of this study is to select the best distribution for uncured patients' survival times by comparing the mixture cure models based on the GMW distribution and its particular cases.
A data set of 91 patients with high-risk acute lymphoblastic leukemia (ALL) followed for five years from 1982 to 1987 was chosen for fitting the mixture cure model. We used the maximum likelihood estimation technique via R software 3.6.2 to obtain the estimates for parameters of the proposed model in the existence of cure rate, censored data, and covariates. For the best model choice, the Akaike information criterion (AIC) was implemented.
After comparing different parametric models fitted to the data, including or excluding cure fraction, without covariates, the smallest AIC values were obtained by the EW and the GMW distributions, (953.31/969.35) and (955.84/975.99), respectively. Besides, assuming a mixture cure model based on GMW with covariates, an estimated ratio between cure fractions for allogeneic and autologous bone marrow transplant groups (and its 95% confidence intervals) were 1.42972 (95% CI: 1.18614 - 1.72955).
The results of this study reveal that the EW and the GMW distributions are the best choices for the survival times of Leukemia patients.
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治愈率模型是生存模型，常用于对具有治愈分数的生存数据进行建模。在存在治愈率的情况下，如果指定易感患者的生存时间分布，则研究人员通常更喜欢治愈率模型而不是参数模型。可以为生存时间假设不同的分布，例如广义修正 Weibull（GMW）、指数 Weibull（EW）和对数 beta Weibull。本研究的目的是通过比较基于 GMW 分布及其特例的混合治愈率模型，选择未治愈患者生存时间的最佳分布。
材料与方法：选择了 1982 年至 1987 年随访五年的 91 例高危急性淋巴细胞白血病（ALL）患者的数据，用于拟合混合治愈率模型。我们使用 R 软件 3.6.2 中的最大似然估计技术，在存在治愈率、删失数据和协变量的情况下，获得所提出模型参数的估计值。为了进行最佳模型选择，实施了赤池信息量准则（AIC）。
结果：在比较了包括或不包括治愈率、无协变量的不同参数模型后，EW 和 GMW 分布的 AIC 值最小，分别为（953.31/969.35）和（955.84/975.99）。此外，假设基于 GMW 的混合治愈率模型存在协变量，同种异体和自体骨髓移植组的治愈率比例（及其 95%置信区间）估计值为 1.42972（95%CI：1.18614-1.72955）。
结论：本研究结果表明，EW 和 GMW 分布是白血病患者生存时间的最佳选择。
