A copula-based approach for estimating the survival functions of two alternating recurrent events

Modelling alternately recurring events using subject specific hazard estimation approach

The motivation for this paper is to account for subject specific variations in a Cox proportional hazard model for alternating recurrent events. This is done through two sets of frailty components, whose marginal distributions are bound together by a copula function. The likelihood function involves unobservable variables, which requires the use of the EM algorithm. This leads to intractable integrals, which after some approximations, are solved using computationally intensive techniques. The results are applied to a real-life data. A simulation study is also carried out to check for consistency.

Effects of covariates on alternating recurrent events in accelerated failure time models

In this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency.

Bayesian Autoregressive Frailty Models for Inference in Recurrent Events

We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.