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基于指数分布混合治愈模型的客观贝叶斯分析

肖翔 吴懿祺 古晞

肖翔, 吴懿祺, 古晞. 基于指数分布混合治愈模型的客观贝叶斯分析[J]. 上海工程技术大学学报, 2021, 35(4): 395-400.
引用本文: 肖翔, 吴懿祺, 古晞. 基于指数分布混合治愈模型的客观贝叶斯分析[J]. 上海工程技术大学学报, 2021, 35(4): 395-400.
XIAO Xiang, WU Yiqi, GU Xi. Objective Bayesian analysis of mixture cure model based on exponential distribution[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 395-400.
Citation: XIAO Xiang, WU Yiqi, GU Xi. Objective Bayesian analysis of mixture cure model based on exponential distribution[J]. Journal of Shanghai University of Engineering Science, 2021, 35(4): 395-400.

基于指数分布混合治愈模型的客观贝叶斯分析

基金项目: 全国统计科学研究项目(2020LY080)
详细信息
    作者简介:

    肖翔:肖 翔(1980−),男,讲师,硕士,研究方向为统计学. E-mail: xiaoxiang@sues.edu.cn

  • 中图分类号: O212.1

Objective Bayesian analysis of mixture cure model based on exponential distribution

  • 摘要: 提出基于指数分布的混合治愈模型,通过引入隐变量,利用完全似然函数比较容易计算Fisher信息矩阵,推导出参数的Jeffreys先验和reference先验,并验证后验分布的恰当性. 研究结果表明,客观贝叶斯方法对参数的估计效果很好,特别是在样本量小时比较明显.
  • 表  1  客观贝叶斯估计下的估计偏差

    Table  1.   Bias under objective Bayesian estimation

    $n$先验$p = 0.3$$\lambda = 3$$p = 0.3$$\lambda = 4$$p = 0.4$$\lambda = 4$
    20 ${\pi _J}$ −0.025 0.141 −0.024 0.154 −0.008 0.085
    ${\pi _R}$ 0.016 −0.095 −0.018 0.137 0.006 0.065
    50 ${\pi _J}$ −0.018 0.134 −0.022 0.144 −0.005 0.078
    ${\pi _R}$ 0.015 0.087 −0.016 0.135 0.004 0.064
    下载: 导出CSV

    表  2  客观贝叶斯估计下均方误差

    Table  2.   RMSE under objective Bayesian estimation

    $n$先验$p = 0.3$$\lambda = 3$$p = 0.3$$\lambda = 4$$p = 0.4$$\lambda = 4$
    20 $ {\pi _J} $ 0.031 0.059 0.019 0.075 0.022 0.051
    $ {\pi _R} $ 0.028 0.044 0.016 0.072 0.015 0.032
    50 $ {\pi _J} $ 0.027 0.056 0.018 0.071 0.022 0.048
    $ {\pi _R} $ 0.024 0.047 0.015 0.068 0.014 0.030
    下载: 导出CSV

    表  3  客观贝叶斯估计的95%覆盖率

    Table  3.   95% coverage probabilities under objective Bayesian estimation

    $n$先验$p = 0.3$$\lambda = 3$$p = 0.3$$\lambda = 4$$p = 0.4$$\lambda = 4$
    20$ {\pi _J} $0.9450.9570.9560.9540.9610.958
    $ {\pi _R} $0.9470.9550.9540.9530.9550.946
    50$ {\pi _J} $0.9460.9560.9550.9530.9580.957
    $ {\pi _R} $0.9470.9540.9520.9520.9530.947
    下载: 导出CSV
  • [1] 肖翔. 0−1膨胀几何分布回归模型及其应用[J] . 系统科学与数学,2019,39(9):1486 − 1499. doi: 10.12341/jssms13723
    [2] 肖翔, 刘福窑. 零膨胀几何分布的参数估计[J] . 上海工程技术大学学报,2018,32(3):267 − 271. doi: 10.3969/j.issn.1009-444X.2018.03.013
    [3] 肖翔, 古晞. 0−1膨胀几何分布的客观贝叶斯分析[J] . 上海工程技术大学报,2021,35(3):202 − 207.
    [4] 张良超, 周金亮, 温利民. 零膨胀泊松模型中风险参数的贝叶斯估计[J] . 江西师范大学学报(自然科学版),2020(3):269 − 274.
    [5] 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 − 53. doi: 10.1111/j.2517-6161.1949.tb00020.x
    [6] FAREWELL V T. The use of mixture models for the analysis of survival data with long-term survivors[J] . Biometrics,1982:1041 − 1046.
    [7] GHITANY M, MALLER R A, ZHOU S. Exponential mixture models with long-term survivors and covariates[J] . Journal of Multivariate Analysis,1994,49(2):218 − 241. doi: 10.1006/jmva.1994.1023
    [8] TAYLOR J M. Semi-parametric estimation in failure time mixture models[J] . Biometrics,1995:899 − 907.
    [9] PENG Y W, DEAR K B. A nonparametric mixture model for cure rate estimation[J] . Biometrics,2000,56(1):237 − 243. doi: 10.1111/j.0006-341X.2000.00237.x
    [10] ZHOU J, ZHANG J J, MCLAIN A C, et al. A multiple imputation approach for semiparametric cure model with interval censored data[J] . Computational Statistics & Data Analysis,2016,99:105 − 114.
    [11] DIAO G, YUAN A. A class of semiparametric cure models with current status data[J] . Lifetime Data Analysis,2019,25:26 − 51. doi: 10.1007/s10985-018-9420-0
    [12] LAM K F, LEE C Y, WONG K Y, et al. Marginal analysis of current status data with informative cluster size using a class of semiparametric transformation cure models[J] . Statistics in Medicine,2021,40(10):2400 − 2412. doi: 10.1002/sim.8910
    [13] 茆诗松, 汤银才. 贝叶斯统计[M]. 2版. 北京: 中国统计出版社, 2012.
    [14] BERGER J O, BERNARDO J M. On the development of the reference prior method[J] . Bayesian Statistics,1992a,4(4):35 − 60.
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出版历程
  • 收稿日期:  2021-05-17
  • 刊出日期:  2022-02-23

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