frailtyEM: An R Package for Estimating Semiparametric Shared Frailty Models

Abstract

When analyzing correlated time to event data, shared frailty (random effect) models are particularly attractive. However, the estimation of such models has proved challenging. In semiparametric models, this is further complicated by the presence of the nonparametric baseline hazard. Although recent years have seen an increased availability of software for fitting frailty models, most software packages focus either on a small number of distributions of the random effect, or support only on a few data scenarios. frailtyEM is an R package that provides maximum likelihood estimation of semiparametric shared frailty models using the expectation-maximization algorithm. The implementation is consistent across several scenarios, including possibly left truncated clustered failures and recurrent events in both calendar time and gap time formulation. A large number of frailty distributions belonging to the power variance function family are supported. Several methods facilitate access to predicted survival and cumulative hazard curves, both for an individual and on a population level. An extensive number of summary measures and statistical tests are also provided.

A tutorial on frailty models

“…38 , 40 It can be extended in a straightforward way to the class of infinitely divisible distributions described in section 2.3.2. 9 , 41 This involves iterating between two steps: The “E” step, which involves calculating the expected log-likelihood …”

“… 12 , 57 Semi-parametric frailty models with the infinitely divisible class of frailty distributions discussed in section 2.3.2 may be estimated via the profile EM algorithm with the frailtyEM package. 58 Log-normal frailty models (including correlated frailties, discussed in section 5) may be estimated with the coxme package. 59 Similar models may be fitted with the Monte Carlo EM algorithm with the phmm R package.…”

Non-parametric frailty Cox models for hierarchical time-to-event data

“…The black curves represent the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\hat{\pi}_2 = 0.53 \%$\end{document} of healthcare providers in latent population \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$2$\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\hat{w}_2$\end{document} = 1.40 times the hazard of readmission relative to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\hat{w}_1$\end{document} . All estimates for this reduced cohort are reported in Table 1 , together with the estimates from a standard Cox model and a Cox model with a Gamma frailty, fitted with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\texttt{frailtyEM}$\end{document} ( Balan and Putter, 2017 ). The discrete frailty model describes the data best, as judged by the maximized likelihood values.…”

“…The most common distributions for the frailty term are Gamma and Log-Normal, probably due their analytical tractability and software availability [see package \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\texttt{coxph in survival}$\end{document} by Therneau and Grambsch (2000) and Therneau (2014) ]. Positive stable and power variance distributions have also become accessible through the package \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\texttt{frailtyEM}$\end{document} ( Balan and Putter, 2017 ). All the mentioned packages are developed in R ( R Development Core Team, 2016 ).…”

Investigating hospital heterogeneity with a competing risks frailty model

“…The model can be estimated similarly to the classical competing risks model, by using coxph() together with the frailty() function from the R package survival or the emfrail() function from the frailtyEM package. The results of the estimated model with independent gamma frailties are shown in Table .…”