Asymptotic justification of maximum likelihood estimation for the proportional excess hazard model in analysis of cancer registry data
Asymptotic justification of maximum likelihood estimation for the proportional excess hazard model in analysis of cancer registry data
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DOI：
10.1007/s42081-023-00190-6
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发表时间：
2023-03-10
影响因子：
1.3
通讯作者：
Hattori，Satoshi
中科院分区：
文献类型：
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作者：
Komukai，Sho;Hattori，Satoshi
以人群为基础的癌症登记研究旨在调查各种癌症问题，对癌症控制有重要影响。为了根据癌症登记数据调查癌症预后，有必要调整其他原因导致的死亡的影响，因为癌症登记数据包括癌症以外的原因导致的死亡。为了校正其他原因造成的死亡的影响，经常使用超额风险模型。超额风险模型的概念是，癌症登记人群中任何死亡的风险函数是癌症死亡风险（指超额风险）和其他原因死亡风险的总和。已经开发了用于过度风险的考克斯比例风险模型，并且对于该模型，Perme等人（Biostatistics 10：136-146，2009）提出了使用EM算法的技术来计算最大似然估计量的回归系数的推断过程。在这篇文章中，我们提出了大样本性质的最大似然估计。本文利用半参数理论的技巧和估计量的相合性及渐近正态性，给出了回归系数方差的一个相合估计。通过有限样本模拟研究了方差估计的经验性质。我们还将方差估计应用于美国监测、流行病学和最终结果（SEER）数据库中胃癌、肺癌和肝癌患者的癌症登记数据。
Population-based cancer registry studies are conducted to investigate the various cancer question and have important impacts on cancer control. In order to investigate cancer prognosis from cancer registry data, it is necessary to adjust the effect of deaths from other causes, since cancer registry data include deaths from causes other than cancer. To correct for the effect of deaths from other causes, excess hazard models are often used. The concept of the excess hazard model is that the hazard function for any death in a cancer registry population is the sum of the hazard for cancer deaths, refer to the excess hazard, and the hazard for deaths from other causes. The Cox proportional hazard model for the excess hazard has been developed, and for this model, Perme et al. (Biostatistics 10:136–146, 2009) proposed the inference procedure of the regression coefficients using the techniques of the EM algorithm to compute the maximum likelihood estimator. In this article, we present the large sample properties for the maximum likelihood estimator. We introduce a consistent estimator of the variance for the regression coefficients based on the technique of the semiparametric theory and the consistency and the asymptotic normality of the estimator. The empirical property of variance estimator is investigated by the finite sample simulation studies. We also apply the variance estimator to cancer registry data for stomach, lung, and liver cancer patients from the Surveillance, Epidemiology, and End Results (SEER) database in U.S.