Recurrent Gap Time Research Articles

A model checking method for the proportional hazards model with recurrent gap time data

Recurrent events are the natural outcome in many medical and epidemiology studies. To assess covariate effects on the gaps between consecutive recurrent events, the Cox proportional hazards model is frequently employed in data analysis. The validity of statistical inference, however, depends on the appropriateness of the Cox model. In this paper, we propose a class of graphical techniques and formal tests for checking the Cox model with recurrent gap time data. The building block of our model checking method is an averaged martingale-like process, based on which a class of multiparameter stochastic processes is proposed. This maneuver is very general and can be used to assess different aspects of model fit. Numerical simulations are conducted to examine finite-sample performance, and the proposed model checking techniques are illustrated with data from the Danish Psychiatric Central Register.

Analysis of recurrent gap time data using the weighted risk‐set method and the modified within‐cluster resampling method

The gap times between recurrent events are often of primary interest in medical and epidemiology studies. The observed gap times cannot be naively treated as clustered survival data in analysis because of the sequential structure of recurrent events. This paper introduces two important building blocks, the averaged counting process and the averaged at-risk process, for the development of the weighted risk-set (WRS) estimation methods. We demonstrate that with the use of these two empirical processes, existing risk-set based methods for univariate survival time data can be easily extended to analyze recurrent gap times. Additionally, we propose a modified within-cluster resampling (MWCR) method that can be easily implemented in standard software. We show that the MWCR estimators are asymptotically equivalent to the WRS estimators. An analysis of hospitalization data from the Danish Psychiatric Central Register is presented to illustrate the proposed methods.

Semiparametric regression analysis on longitudinal pattern of recurrent gap times.

In longitudinal studies, individual subject may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of gaps between successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the stratified proportional reverse-time hazards models with unspecified baseline functions to accommodate individual heterogeneity, when the longitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The proposed methodology is demonstrated by the Monte Carlo simulations and an application to a well-known Denmark schizophrenia cohort study data set.