Analysis Of Clustered Survival Data Research Articles

MEGH: A parametric class of general hazard models for clustered survival data.

In many applications of survival data analysis, the individuals are treated in different medical centres or belong to different clusters defined by geographical or administrative regions. The analysis of such data requires accounting for between-cluster variability. Ignoring such variability would impose unrealistic assumptions in the analysis and could affect the inference on the statistical models. We develop a novel parametric mixed-effects general hazard (MEGH) model that is particularly suitable for the analysis of clustered survival data. The proposed structure generalises the mixed-effects proportional hazards and mixed-effects accelerated failure time structures, among other structures, which are obtained as special cases of the MEGH structure. We develop a likelihood-based algorithm for parameter estimation in general subclasses of the MEGH model, which is implemented in our R package MEGH. We propose diagnostic tools for assessing the random effects and their distributional assumption in the proposed MEGH model. We investigate the performance of the MEGH model using theoretical and simulation studies, as well as a real data application on leukaemia.

An approach to model clustered survival data with dependent censoring.

In this study we introduce a likelihood-based method, via the Weibull and piecewise exponential distributions, capable of accommodating the dependence between failure and censoring times. The methodology is developed for the analysis of clustered survival data and it assumes that failure and censoring times are mutually independent conditional on a latent frailty. The dependent censoring mechanism is accounted through the frailty effect and this is accomplished by means of a key parameter accommodating the correlation between failure and censored observations. The full specification of the likelihood in our work simplifies the inference procedures with respect to Huang and Wolfe since it reduces the computation burden of working with the profile likelihood. In addition, the assumptions made for the baseline distributions lead to models with continuous survival functions. In order to carry out inferences, we devise a Monte Carlo EM algorithm. The performance of the proposed models is investigated through a simulation study. Finally, we explore a real application involving patients from the Dialysis Outcomes and Practice Patterns Study observed between 1996 and2015.

The Generalized Gamma Shared Frailty Model under Different Baseline Distributions

In the analysis of clustered survival data, shared frailty models are often used when observations in the same group share common unknown risk factors or frailty. There is dependence in the event times belonging to the same group, while event times from different groups are conditionally independent given their covariates. In such models, the known effect on survival time is described using the baseline distribution and regression coefficients while the unknown effect is described through a frailty distribution. In this paper, the Gompertz, log-logistic, and generalized exponential distributions are studied as baseline distributions, under a shared frailty effect described by the generalized gamma distribution. Their hazard functions have been compared and their applicability under different settings and performance with generalized gamma frailty has been explored. These models are fitted to three real life datasets using Bayesian estimation methods and compared using the Bayesian Information Criteria (AIC, BIC, and DIC) and the Bayes Factor.

Semiparametric regression analysis of clustered survival data with semi-competing risks

Analysis of semi-competing risks data is becoming increasingly important in medical research in which a subject may experience both nonterminal and terminal events, and the time to the intermediate nonterminal event (e.g. onset of a disease) is subject to dependent censoring by the terminal event (e.g. death) but not vice versa. Typically, both two types of events are dependent. In many applications, subjects may also be nested within clusters, such as patients in a multi-center study, leading to possible association among event times due to unobserved shared factors across subjects. To incorporate dependency within clusters and association between two types of event times, we propose a new flexible semiparametric modeling framework where a copula model is employed for the joint distribution of the nonterminal and terminal events, and their marginal distributions are modeled by Cox proportional hazards models with random effects. A nonparametric maximum likelihood estimation procedure is developed and implemented through a Monte Carlo EM algorithm. The proposed estimator is also shown to enjoy desirable asymptotic properties. Results from extensive simulation studies indicate that the proposed method performs very well in finite samples and is especially robust against misspecification of the random effects distribution. We further illustrate the practical utility of the method by analyzing data from a multi-institutional study of breast cancer.

Log-normal frailty models fitted as Poisson generalized linear mixed models

Background and objectivesThe equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to “explode” the data set by the number of pieces. MethodsIn this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. ResultsThe simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. ConclusionsThe suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters.

Extending the Archimedean Copula Methodology to Model Multivariate Survival Data Grouped in Clusters of Variable Size

Summary For the analysis of clustered survival data, two different types of model that take the association into account are commonly used: frailty models and copula models. Frailty models assume that, conditionally on a frailty term for each cluster, the hazard functions of individuals within that cluster are independent. These unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster. Copula models in contrast assume that the joint survival function of the individuals within a cluster is given by a copula function, evaluated in the marginal survival function of each individual. It is the copula function which describes the association between the lifetimes within a cluster. A major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal to set up manageable estimation procedures for the different model parameters. We describe a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of Archimedean copulas with completely monotone generator. We develop both one- and two-stage estimators for the copula parameters. Furthermore we show the consistency and asymptotic normality of these estimators. Finally, we perform a simulation study to investigate the finite sample properties of the estimators. We illustrate the method on a data set containing the time to first insemination in cows, with cows clustered in herds.

Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis.

Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta-analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log-cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non-PH (time-dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss-Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta-analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta-analysis of prognostic factor studies in patients with breast cancer. User-friendly Stata software is provided to implement the methods.

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

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.,

Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Model

In this article, we consider shared frailty model with inverse Gaussian distribution as frailty distribution and log-logistic distribution (LLD) as baseline distribution for bivariate survival times. We fit this model to three real-life bivariate survival data sets. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty is the interest of this article and then compare the results with shared gamma frailty model under the same baseline for considered three data sets. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. We carried out a test for frailty (or heterogeneity) using Bayes factor. Model comparison is made using information criteria and Bayes factor. We observed that the shared inverse Gaussian frailty model with LLD as baseline is the better fit for all three bivariate data sets.

Analysis of diabetic retinopathy data using shared inverse Gaussian frailty model

The dependence between individuals in a group is modeled by the group specific quantity, which can be interpreted as an unobserved covariates or “frailties” common to the individuals in the group and assumed to follow some distribution. We consider the shared frailty model in the frame work of parametric Cox proportional hazard model. The Cox regression model with the shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing life time data. In this paper, we consider shared inverse Gaussian frailty model with bivariate exponential of Marshall-Olkin [20] distribution as baseline hazard for bivariate survival times. We fit the model to the real life bivariate survival data set of diabetic retinopathy data. Data are analyzed using Bayesian approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same group. The variance component estimation provides the estimated dispersion of the random effects. The problem of analyzing and estimating parameters of shared inverse Gaussian frailty for diabetic retinopathy data is the interest of this paper. Also, we carried out a test for independence using information criteria.

Non-parametric Bayesian analysis of clustered survival data

Clustered survival data are often modelled with frailty models which incorporate frailties to model the cluster specific heterogeneity and the dependence between observations in the same cluster. For the analysis of the frailty models, we propose Bayesian modelling with beta process prior on the cumulative hazard function and describe the details of the posterior computation. We demonstrate the method with two data sets using three different frailty distributions: gamma, log-normal and log-logistic distributions. We also empirically demonstrate the difficulty in checking the assumed frailty distribution with the posterior sample of the frailties.

Using survival methodologies in demonstrating caries efficacy.

Exploiting recent advances in statistical methods, particularly for correlated intra-subject data, could increase the efficiency of caries clinical trials. Methods of analysis using the tooth surface as the unit should be investigated. Whole-mouth measures such as the DMFS increment ignore the variation in the number of surfaces at risk between subjects and within a subject over time. The use of "survival time" for each surface as the outcome measure--i.e., the time from the start of the trial to when a surface is recorded as decayed or filled--is proposed. Data from caries clinical trials could be described as clustered survival data, where clustering of tooth surfaces exists such that survival times within the same cluster or subject are correlated. Advances in the analysis of clustered survival data, such as the use of marginal models with robust variance estimators, have recently been exploited in the analysis of caries clinical trials. The analysis produced results similar to those achieved by conventional DMFS-based analysis. The results using survival analysis are easily interpreted-for example, the median survival time of tooth surfaces in female subjects using a toothpaste with a higher level of fluoride (1500 ppm F) is 1.07 times the median survival time of surfaces in female subjects using toothpaste with less fluoride (1000 ppm F). Further research is required to investigate if survival analysis is a more sensitive method of analysis, i.e., whether causative factors can be identified with fewer subjects than with the conventional method of analysis.

Use of Generalised Linear Mixed Models for the Analysis of Clustered Survival Data

AbstractData from a litter matched tumorigenesis experiment are analysed using a generalised linear mixed model (GLMM) approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same litter. Maximum likelihood (ML) and residual maximum likelihood (REML) estimates of risk variable parameters, variance component parameters and the prediction of random effects are given. Estimation of treatment effect parameter (carcinogen effect) has good agreement with previous analyses obtained in the literature though the dependence structure within a litter is modelled in different ways. The variance component estimation provides the estimated dispersion of the random effects. The prediction of random effects, is useful, for instance, in identifying high risk litters and individuals. The present analysis illustrates its wider application to detecting increased risk of occurrence of disease in particular families of a study population.

Simulation study of the glmm method applied to the analysis of clustered survival data

A simulation study is carried out for the analysis of clustered survival data based on the generalised linear mixed model (GLMM) methodology. Data are simulated for a proportional hazards model containing random components corresponding to a cluster effect and a subject effect. The performance of approximate maximum likelihood (ML) and residual maximum likelihood (REML) estimation of the regression parameter and variance components are evaluated. For a range of true parameter values,average biases of estimators, standard error of average bias and standard error of estimates over simulations are reported. A discussion of the use of random effects predictions is also given.