Liu Hao, Shen Yu
Division of Biostatistics, Dan L. Duncan Cancer Center, BCM 305, Baylor College of Medicine, Houston, TX 77030, U.S.A. (E-mail:
J Am Stat Assoc. 2009 Dec 1;104(487):1168-1178. doi: 10.1198/jasa.2009.tm07494.
Motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring, we presents a semiparametric non-mixture cure model for the regression analysis of interval-censored time-to-event datxa. We develop semiparametric maximum likelihood estimation for the model using the expectation-maximization method for interval-censored data. The maximization step for the baseline function is nonparametric and numerically challenging. We develop an efficient and numerically stable algorithm via modern convex optimization techniques, yielding a self-consistency algorithm for the maximization step. We prove the strong consistency of the maximum likelihood estimators under the Hellinger distance, which is an appropriate metric for the asymptotic property of the estimators for interval-censored data. We assess the performance of the estimators in a simulation study with small to moderate sample sizes. To illustrate the method, we also analyze a real data set from a medical study for the biochemical recurrence of prostate cancer among patients who have undergone radical prostatectomy. Supplemental materials for the computational algorithm are available online.
受医学研究的启发，在这些研究中患者的疾病可以治愈，但疾病发生时间可能受到区间删失的影响，我们提出了一种半参数非混合治愈模型，用于对区间删失的事件发生时间数据进行回归分析。我们使用针对区间删失数据的期望最大化方法为该模型开发了半参数最大似然估计。基线函数的最大化步骤是非参数的，并且在数值上具有挑战性。我们通过现代凸优化技术开发了一种高效且数值稳定的算法，从而得到了用于最大化步骤的自一致性算法。我们证明了在Hellinger距离下最大似然估计量的强一致性，Hellinger距离是用于区间删失数据估计量渐近性质的合适度量。我们在一个小到中等样本量的模拟研究中评估了估计量的性能。为了说明该方法，我们还分析了一项医学研究中的真实数据集，该数据集涉及接受根治性前列腺切除术后患者前列腺癌的生化复发情况。计算算法的补充材料可在线获取。
