A visualizing method for investigating individual frailties using frailtyHL R-package

Abstract

Abstract For analysis of clustered survival data, the inferences of parameters in semi-parametricfrailty models have been widely studied. It is also important to investigate the potentialheterogeneity in event times among clusters (e.g. centers, patients). For purpose of thisanalysis, the interval estimation of frailty is useful. In this paper we propose a visual-izing method to present con dence intervals of individual frailties across clusters usingthe frailtyHL R-package, which is implemented from h-likelihood methods for frailtymodels. The proposed method is demonstrated using two practical examples.Keywords: frailtyHL R-package, h-likelihood, interval estimation, multilevel frailty, sharedfrailty. 1. Introduction The frailty models, Cox’s proportional hazards models (Park et al., 2012) allowing frailty(random e ect) terms, have been widely used for the analysis of clustered survival-time data.For the inference, the marginal likelihood often involves analytically intractable integrals,particularly when modelling multilevel or correlated frailties. However, the hierarchical-likelihood (h-likelihood; Lee and Nelder, 1996, 2001) obviates the need for intractable inte-gration over the frailty terms (Ha et al., 2001, 2011; Ha and Cho, 2012). It is also importantto investigate the potential heterogeneity in event times among clusters (e.g. centers, pa-tients) in order to understand and interpret the variability in the data (Vaida and Xu,2000). For example, despite the use of standardized protocols in multicenter randomizedclinical trials, outcome may vary between centers (Rondeau et al., 2008; Ha et al., 2011).Such heterogeneity may alter the interpretation and reporting of the treatment. For pur-pose of this analysis, the interval estimation of frailty is more useful than the inferenceof variance components of frailty (Vaida and Xu, 2000; Lee and Nelder, 2009; Ha et al.,