An Empirical Study on Bias of Kendall’s tau estimators for Gap Times under Right Censoring

An Empirical Study on Bias of Kendall’s tau estimators for Gap Times under Right Censoring


2021-10-29 - 14:00

Cecília Castro and Ana Paula Amorim

CMAT - University of Minho


Abstract ::  In several clinical and epidemiology studies, recurrent event data frequently arise, where each subject may experience multiple failures of the same type over the course of follow-up.Examples include repeated hospitalization of patients, recurrences of tumor or recurrent infections among others. In this work the interest is to study the correlation between times of that successive recurrent events – gap times.Correlations between gap times are of interest in themselves, when investigating whether the first gap time is predictive of the occurrence of the second event. Measuring correlation can be challenging in the presence of right censoring where some data values are not observed due to an upper detection limit, dropout or due to the end of the study. Right censoring is present in a wide range of survival data, so it is natural that one or both of the gap times may not be observed. When looking at correlation between times to event in a single subject, the censoring time may be the same time for both outcomes.Several different methods have been proposed to measure and test the correlation between two right-censored time-to-event variables. It is usual to use nonparametric estimators like Kendall’s  coefficient because it has good properties, like invariance to monotone transformations and robustness in the presence of outliers.

In this presentation we follow the Wang and Wells work to define estimators of  tau that accounts for joint information of the random pair of gap times. In fact, a natural way to estimate  is to incorporate a suitable bivariate estimator of the survival function, or of the distribution function, into the integral that defines  tau. However this approach leads to biased estimators because the Kaplan-Meier integrals are biased. Our main objective is to present such estimators, using a nonparametric and a semi-parametric Kaplan-Meier estimator of the bivariate function under right censoring, and study the bias distribution of the proposed estimators under different scenarios. 

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