Inference on the bivariate L1 median with censored data

Consider two random variables subject to random right censoring, like the time to two different diseases for individuals under study or the survival times of twins. Of interest is the bivariate median of these two random variables. There are various ways that the univariate median has been extended to higher dimensions for completely observed data. We concentrate on the so-called bivariate L1 median and extend this estimator to the censored data situation. The estimator is based on van der Laan (1996)'s estimator of the bivariate distribution of two random variables that are subject to censoring. Asymptotic results for the proposed estimator are established. The obtained results include the asymptotic normality of the estimator, its local power and the construction of a confidence region for the true median. Finally, we consider a data set on kidney dialysis patients and estimate the median time to two different infections for these individuals.