This paper compares six different parameter estimation methods for shared frailty models via a series of simulation studies. A shared frailty model is a survival model that incorporates a random effect term, where the frailties are common or shared among individuals within specific groups. Several parameter estimation methods are available for fitting shared frailty models, such as penalized partial likelihood (PPL), expectation-maximization (EM), pseudo full likelihood (PFL), hierarchical likelihood (HL), maximum marginal likelihood (MML), and maximization penalized likelihood (MPL) algorithms. These estimation methods are implemented in various R packages, providing researchers with various options for analyzing clustered survival data using shared frailty models. However, there is a limited amount of research comparing the performance of these parameter estimation methods for fitting shared frailty models. Consequently, it can be challenging for users to determine the most appropriate method for analyzing clustered survival data. To address this gap, this paper aims to conduct a series of simulation studies to compare the performance of different parameter estimation methods implemented in R packages. We will evaluate several key aspects, including parameter estimation, bias and variance of the parameter estimates, rate of convergence, and computational time required by each package. Through this systematic evaluation, our goal is to provide a comprehensive understanding of the advantages and limitations associated with each estimation method.

翻译：本文通过一系列模拟研究，比较了共享脆弱模型的六种不同参数估计方法。共享脆弱模型是一种包含随机效应项的生存模型，其中脆弱性在特定组内的个体间是共同或共享的。现有多种参数估计方法可用于拟合共享脆弱模型，包括惩罚偏似然（PPL）、期望最大化（EM）、伪全似然（PFL）、分层似然（HL）、最大边际似然（MML）和最大化惩罚似然（MPL）算法。这些估计方法已在多个R软件包中实现，为研究人员使用共享脆弱模型分析聚类生存数据提供了多种选择。然而，目前比较这些参数估计方法在拟合共享脆弱模型时性能的研究仍然有限。因此，用户可能难以确定分析聚类生存数据的最适方法。为弥补这一不足，本文旨在开展一系列模拟研究，比较R软件包中不同参数估计方法的性能。我们将从参数估计结果、估计值的偏倚与方差、收敛速度以及各软件包的计算时间等关键维度进行评估。通过这一系统评价，我们旨在全面理解每种估计方法的优势与局限。