Correlated gamma frailty models for bivariate survival data

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data) the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this article, we introduce the gamma correlated frailty models with two different baseline distributions namely, the generalized log logistic, and the generalized Weibull. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply these models to a real life bivariate survival dataset related to the kidney infection data and a better model is suggested for the data.     

Robust Poisson likelihood estimation for frailty Cox models: A simulation study

Frailty models can be fit as mixed-effects Poisson models after transforming time-to-event data to the Poisson model framework. We assess, through simulations, the robustness of Poisson likelihood estimation for Cox proportional hazards models with log-normal frailties under misspecified frailty distribution. The log-gamma and Laplace distributions were used as true distributions for frailties on a natural log scale. Factors such as the magnitude of heterogeneity, censoring rate, number and sizes of groups were explored. In the simulations, the Poisson modeling approach that assumes log-normally distributed frailties provided accurate estimates of within- and between-group fixed effects even under a misspecified frailty distribution. Non-robust estimation of variance components was observed in the situations of substantial heterogeneity, large event rates, or high data dimensions.     

Bivariate Birnbaum-Saunders accelerated lifetime model: estimation and diagnostic analysis

In this paper, we discuss the bivariate Birnbaum-Saunders accelerated lifetime model, in which we have modeled the dependence structure of bivariate survival data through the use of frailty models. Specifically, we propose the bivariate model Birnbaum-Saunders with the following frailty distributions: gamma, positive stable and logarithmic series. We present a study of inference and diagnostic analysis for the proposed model, more concisely, are proposed a diagnostic analysis based in local influence and residual analysis to assess the fit model, as well as, to detect influential observations. In this regard, we derived the normal curvatures of local influence under different perturbation schemes and we performed some simulation studies for assessing the potential of residuals to detect misspecification in the systematic component, the presence in the stochastic component of the model and to detect outliers. Finally, we apply the methodology studied to real data set from recurrence in times of infections of 38 kidney patients using a portable dialysis machine, we analyzed these data considering independence within the pairs and using the bivariate Birnbaum-Saunders accelerated lifetime model, so that we could make a comparison and verify the importance of modeling dependence within the times of infection associated with the same patient.     

Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure

The gamma process is a natural model for degradation processes in which deterioration is supposed to take place gradually over time in a sequence of tiny increments. When units or individuals are observed over time it is often apparent that they degrade at different rates, even though no differences in treatment or environment are present. Thus, in applying gamma-process models to such data, it is necessary to allow for such unexplained differences. In the present paper this is accomplished by constructing a tractable gamma-process model incorporating a random effect. The model is fitted to some data on crack growth and corresponding goodness-of-fit tests are carried out. Prediction calculations for failure times defined in terms of degradation level passages are developed and illustrated.     

Acute Middle Ear Infection in Small Children: A Bayesian Analysis Using Multiple Time Scales

The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breast-feeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (Metropolis-Hastings algorithm).     

Flexible modelling of simultaneously interval censored and truncated time‐to‐event data

This paper deals with the analysis of data from a HET‐CAM^VT experiment. From a statistical perspective, such data yield many challenges. First of all, the data are typically time‐to‐event like data, which are at the same time interval censored and right truncated. In addition, one has to cope with overdispersion as well as clustering. Traditional analysis approaches ignore overdispersion and clustering and summarize the data into a continuous score that can be analysed using simple linear models. In this paper, a novel combined frailty model is developed that simultaneously captures all of the aforementioned statistical challenges posed by the data. Copyright © 2015 John Wiley & Sons, Ltd.     

Pseudo Self-Consistent Estimation of a Copula Model with Informative Censoring

Abstract.  We consider the case where a terminal event censors a non-terminal event, but not vice versa. When the events are dependent, estimation of the distribution of the non-terminal event is a competing risks problem, while estimation of the distribution of the terminal event is not. The dependence structure of the event times is formulated with the gamma frailty copula on the upper wedge, with the marginal distributions unspecified. With a consistent estimator of the association parameter, pseudo self-consistency equations are derived and adapted to the semiparametric model. Existence, uniform consistency and weak convergence of the new estimator for the marginal distribution of the non-terminal event is established using theories of empirical processes, U -statistics and Z -estimation. The potential practical utility of the methodology is illustrated with simulated and real data sets.     

Accelerated life regression modelling of dependent bivariate time‐to‐event data

To analyze bivariate time‐to‐event data from matched or naturally paired study designs, researchers frequently use a random effect called frailty to model the dependence between within‐pair response measurements. The authors propose a computational framework for fitting dependent bivariate time‐to‐event data that combines frailty distributions and accelerated life regression models. In this framework users can choose from several parametric options for frailties, as well as the conditional distributions for within‐pair responses. The authors illustrate the flexibility that their framework represents using paired data from a study of laser photocoagulation therapy for retinopathy in diabetic patients.     

Semiparametric Global Cross-ratio Models for Bivariate Censored Data

Abstract.  Multivariate correlated failure time data arise in many medical and scientific settings. In the analysis of such data, it is important to use models where the parameters have simple interpretations. In this paper, we formulate a model for bivariate survival data based on the Plackett distribution. The model is an alternative to the Gamma frailty model proposed by Clayton and Oakes. The parameter in this distribution has a very appealing odds ratio interpretation for dependence between the two failure times; in addition, it allows for negative dependence. We develop novel semiparametric estimation and inference procedures for the model. The asymptotic results of the estimator are developed. The performance of the proposed techniques in finite samples is examined using simulation studies; in addition, the proposed methods are applied to data from an observational study in cancer.     

Operational Slack and Venture Survival

Slack can act as a double‐edged sword. While it can buffer against environmental threats to help ensure business continuity, slack can also be costly and reduce profitability. In this study we focus on operational slack, the form related to the firm's production processes. We investigate the role of operational slack on firm survival during its venture stage when its survival is significantly challenged by environmental threats. Specifically, we explore how change in three types of environmental uncertainty, namely dynamism, complexity, and lack of munificence, affect the relationship between operational slack and venture survival. Results suggest that with an increase in environmental uncertainty, operational slack lowers the likelihood of venture failure.