JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (4): 108-116.doi: 10.6040/j.issn.1671-9352.0.2022.465

Previous Articles    

Model averaging study with a cured group right-censored data

WANG Shuying, ZHANG Yanan, CHENG Yunfei, ZHOU Lifang*   

  1. School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, Jilin, China
  • Published:2024-04-12

PDF (PC)

16

Abstract: In the existing survival analysis studies, most of them directly assume the model form of response variables and specified covariates, and then estimate the covariate effect. However, when the assumption of the model is wrong, the corresponding conclusion may be wrong. Under the right-censored data with a cured group, in order to avoid the inaccuracy caused by the construction of the model with specified covariates, an accelerated failure time model(AFT model)based on the model averaging method is proposed. In the framework of maximum likelihood estimation, model selection and model averaging based on information criteria are used for statistical inference. The numerical simulation results show that under the right-censored data with a cured group, the estimation and prediction accuracy of the AFT model based on the model averaging method is higher than that of model selection method. Finally, the feasibility and practicability of the proposed method are verified by analysis of trial data on melanoma clinical.

Key words: right-censored data, model averaging, mixture cure model, accelerated failure time model, maximum likelihood estimation

CLC Number: 

  • O212
[1] BOAG J W. Maximum likelihood estimates of the proportion of patients cured by cancer therapy[J]. Journal of the Royal Statistical Society: Series B(Methodological), 1949, 11(1):15-44.
[2] BERKSON J, GAGE R P. Survival curve for cancer patients following treatment[J]. Journal of the American Statistical Association, 1952, 47(259):501-515.
[3] PENG Y, DEAR K B G, DENHAM J W. A generalized F mixture model for cure rate estimation[J]. Statistics in Medicine, 1998, 17(8):813-830.
[4] SY J P, TAYLOR J M G. Estimation in a Cox proportional hazards cure model[J]. Biometrics, 2000, 56(1):227-236.
[5] PENG Y W, DEAR K B G. A nonparametric mixture model for cure rate estimation[J]. Biometrics, 2000, 56(1):237-243.
[6] LI C S, TAYLOR J M G. A semi-parametric accelerated failure time cure model[J]. Statistics in Medicine, 2002, 21(21):3235-3247.
[7] ZHANG J J, PENG Y W. A new estimation method for the semiparametric accelerated failure time mixture cure model[J]. Statistics in Medicine, 2007, 26(16):3157-3171.
[8] BATES J M, GRANGER C W J. The combination of forecasts[J]. Journal of the Operational Research Society, 1969, 20(4):451-468.
[9] BUCKLAND S, BURNHAM K, AUGUSTIN N. Model selection: an integral part of inference[J]. Biometrics, 1997, 53(2):603-618.
[10] CLAESKENS G, HJORT N L. The focused information criterion[J]. Journal of the American Statistical Association, 2003, 98(464):900-916.
[11] HANSEN B E. Least squares model averaging[J]. Econometrica, 2007, 75(4):1175-1189.
[12] ZHANG X Y, LIANG H. Focused information criterion and model averaging for generalized additive partial linear models[J]. The Annals of Statistics, 2011, 39(1):174-200.
[13] ZHANG X Y, ZOU G H, LIANG H. Model averaging and weight choice in linear mixed-effects models[J]. Biometrika, 2014, 101(1):205-218.
[14] 张翊,王秀丽. 响应变量缺失下线性模型的模型平均[J]. 山东师范大学学报(自然科学版), 2020, 35(2):178-182. ZHANG Yi, WANG Xiuli. Model averaging procedure for linear model with missing responses[J]. Journal of Shandong Normal University(Natural Science), 2020, 35(2):178-182.
[15] 胡国治,程维虎,曾婕. 协变量缺失下部分线性模型的模型选择和模型平均[J]. 应用数学学报, 2020, 43(3):535-554. HU Guozhi, CHENG Weihu, ZENG Jie. Model selection and model averaging for partially linear models with missing covariates[J]. Acta Mathematicae Applicatae Sinica, 2020, 43(3):535-554.
[16] DING X W, XIE J H, YAN X D. Model averaging for multiple quantile regression with covariates missing at random[J]. Journal of Statistical Computation and Simulation, 2021, 91(11):2249-2275.
[17] 祝恒坤,张海丽. 基于逆概率加权和插补的Mallows模型平均方法[J]. 系统科学与数学, 2022, 42(4):1032-1059. ZHU Hengkun, ZHANG Haili. Mallows model averaging based on inverse probability weighting and imputation[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(4):1032-1059.
[18] 王苗苗. 基于线性模型平均估计的置信区间[J]. 系统科学与数学, 2020, 40(10):1866-1881. WANG Miaomiao. Confidence interval based on model average estimator for linear regression[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(10):1866-1881.
[19] 尹潇潇,鲁筠,石磊. Meta分析中的频率模型平均估计[J]. 数理统计与管理, 2021, 40(2):233-241. YIN Xiaoxiao, LU Jun, SHI Lei. Frequentist model averaging in Meta-analysis[J]. Journal of Applied Statistics and Management, 2021, 40(2):233-241.
[20] FENG Y, LIU Q, YAO Q, et al. Model averaging for nonlinear regression models[J]. Journal of Business & Economic Statistics, 2022, 40(2):785-798.
[21] LI J, YU T H, LYU J, et al. Semiparametric model averaging prediction for lifetime data via hazards regression[J]. Journal of the Royal Statistical Society Series C: Applied Statistics, 2021, 70(5):1187-1209.
[22] SCOLAS S, El GHOUCH A, LEGRAND C, et al. Variable selection in a flexible parametric mixture cure model with interval-censored data[J]. Statistics in Medicine, 2016, 35(7):1210-1225.
[23] HJORT N L, CLAESKENS G. Focused information criteria and model averaging for the Cox hazard regression model[J]. Journal of the American Statistical Association, 2006, 101(476):1449-1464.
[24] HJORT N L, CLAESKENS G. Frequentist model average estimators[J]. Journal of the American Statistical Association, 2003, 98(464):879-899.
[25] 朱容,邹国华. 半参数模型平均估计的渐近理论[J]. 中国科学(数学),2018,48(8):1019-1052. ZHU Rong, ZOU Guohua. The asymptotic theory for model averaging in general semiparametric models[J]. Scientia Sinica(Mathematica), 2018, 48(8):1019-1052.
[26] 朱容,邹国华,张新雨. 部分函数线性模型的模型平均方法[J]. 系统科学与数学, 2018, 38(7):777-800. ZHU Rong, ZOU Guohua, ZHANG Xinyu. Optimal model averaging estimation for partial functional linear models[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(7):777-800.
[27] KIRKWOOD J M, STRAWDERMAN M H, ERNSTOFF M S, et al. Interferon Alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the Eastern Cooperative Oncology Group Trial EST 1684[J]. Journal of Clinical Oncology, 1996, 14(1):7-17.
[28] BRADFORD P T, GOLDSTEIN A M, MCMASTER M L, et al. Acral lentiginous melanoma: incidence and survival patterns in the United States, 1986-2005[J]. Archives of Dermatology, 2009, 145(4):427-434.
[29] OMER M E A M E, ABU BAKAR M R, ADAM M B, et al. Cure models with exponentiated Weibull exponential distribution for the analysis of melanoma patients[J]. Mathematics, 2020, 8(11):1926.
[1] ZHAO Yu-huan, ZHANG Xiao-bin. Maximum likelihood estimation for linear stochastic evolution equations#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 54-60.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd