  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.
