Copulas and measures of dependence under length-biased sampling and informative censoring
Length-biased data are often encountered in cross-sectional surveys and prevalent-cohort studies on disease durations.
Under length-biased sampling subjects with longer disease durations have greater chance to be observed. As a result, covariate values linked to the longer survivors are favoured by the sampling mechanism. When the sampled durations are also subject to right censoring, the censoring is informative. Modelling dependence structure without adjusting for these issues leads to biased results.
In this talk, Dr Rabhi will present a study on copulas for modelling dependence when the collected data are length-biased and account for both informative censoring and covariate bias. He will address the nonparametric estimation of the bivariate distribution, copula function and its density, and Kendall and Spearman measures for right-censored length-biased data.
The proposed estimator of the bivariate CDF is a Hadamard-differentiable functional of two MLEs, Kaplan-Meier and empirical CDF, and inherits their efficiencies. Based on this estimator, we devise estimators for copula function and a local-polynomial estimator for copula density that accounts for boundary bias. In addition, Dr Rabhi will introduce estimators for Kendall and Spearman measures. The weak convergence of the estimators will also be discussed. The proposed method is then applied to analyse a set of right-censored length-biased data on survival with dementia, collected as part of a nationwide study in Canada.
Speaker
Dr Yassir Rabhi, University of Essex
How to attend
If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Osama Mahmoud.
