Estimation of the Association for Bivariate Interval‐censored Failure Time Data

Abstract

Multivariate failure time data frequently occur in medical studies and the dependence or association among survival variables is often of interest ("Biometrics", 51 , 1995, 1384; "Stat. Med.", 18 , 1999, 3101; "Biometrika", 87 , 2000, 879; "J. Roy. Statist. Soc. Ser. B", 65 , 2003, 257). We study the problem of estimating the association between two related survival variables when they follow a copula model and only bivariate interval-censored failure time data are available. For the problem, a two-stage estimation procedure is proposed and the asymptotic properties of the proposed estimator are established. Simulation studies are conducted to assess the finite sample properties of the presented estimate and the results suggest that the method works well for practical situations. An example from an acquired immunodeficiency syndrome clinical trial is discussed. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

Testing independence of bivariate interval‐censored data using modified Kendall's tau statistic

“…In the study, following Sun et al. (), we assume for , and set the bivariate dependence parameter as , and 1/3. The bivariate data are simulated sequentially as (i) we first sample Y 1 from , and (ii) sample Y 2 from the conditional distribution of Y 2 given : …”

“…The estimators , and denote the estimates from our proposed nonparametric score method, the two‐stage estimation method by Sun et al. (), and the multiple imputation method, respectively.…”

Regression analysis of bivariate current status data under the proportional hazards model

“…Various procedures have also been proposed for the regression analysis of bivariate interval‐censored data (Goggins & Finkelstein, ; Wang, Sun, & Tong, ; Chen, Tong, & Sun, ; Cook & Tolusso, ; Wen & Chen, ; Zhou, Hu, & Sun, ). In this case a commonly used idea is to employ a frailty or copula model to characterize the joint cumulative distribution or survival function (Hougaard, ; Wang & Ding, ; Jewell, Van der Laarn, & Lei, ; Sun, Wang, & Sun, ; Li, Prentice, & Lin, ). However, most of the existing methods either have no theoretical justification (Goggins & Finkelstein, ; Chen, Tong, & Sun, ) or rely on parametric or specified frailty or copula models, and thus apply only to limited situations (Wang & Ding, ; Sun, Wang, & Sun, ; Wang, Sun, & Tong, ; Cook & Tolusso, ; Wen & Chen, ; Zhou, Hu, & Sun, ).…”

“…In this case a commonly used idea is to employ a frailty or copula model to characterize the joint cumulative distribution or survival function (Hougaard, ; Wang & Ding, ; Jewell, Van der Laarn, & Lei, ; Sun, Wang, & Sun, ; Li, Prentice, & Lin, ). However, most of the existing methods either have no theoretical justification (Goggins & Finkelstein, ; Chen, Tong, & Sun, ) or rely on parametric or specified frailty or copula models, and thus apply only to limited situations (Wang & Ding, ; Sun, Wang, & Sun, ; Wang, Sun, & Tong, ; Cook & Tolusso, ; Wen & Chen, ; Zhou, Hu, & Sun, ). For example Wen & Chen () and Zhou, Hu, & Sun () recently described gamma‐frailty model‐based approaches.…”

Accelerated failure time model for multivariate two-stage current-status data with parallel and longitudinal correlated random effects

“…Under the bivariate copula model setting, Wang and Ding (2000) proposed an inference procedure to estimate the association between two correlated survival events when current status data of a common monitoring time is observed. Sun et al (2006) developed such an estimation under the interval censoring scheme and the monitoring times for two events are allowed to be different. But the nonparametric estimation of the survival functions involved in the inference will again make the application almost impossible for our data.…”