Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA.
Stat Med. 2023 Dec 10;42(28):5113-5134. doi: 10.1002/sim.9904. Epub 2023 Sep 14.
In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval-censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log-likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study.
本文考虑了一种竞争风险生存模型，其中初始风险数假定服从负二项分布，并受到破坏机制的影响。假设感兴趣的人群有治愈因素，数据形式为区间删失，并考虑初始风险数和破坏后仍处于活动状态的风险数均为缺失数据，我们为该模型开发了两种不同的估计算法。利用缺失数据的条件分布，我们开发了一种期望最大化（EM）算法，其中将缺失数据的条件期望完全对数似然函数分解为更简单的函数，然后独立最大化这些函数。还开发了 EM 算法的一种变体，称为随机 EM（SEM）算法，其目的是避免计算复杂的期望并提高参数恢复的性能。通过计算偏差、均方根误差和渐近置信区间的覆盖率，进行了蒙特卡罗模拟研究，以评估这两种估计方法的性能。我们通过模拟证明了 SEM 算法是首选的估计方法，并进一步说明了 SEM 算法的优势，以及破坏模型的使用，使用的是儿童死亡率研究的数据。
