Estimation of Distribution Function in Bivariate Competing Risk Models

Abstract

We consider lifetime data involving pairs of study individuals with more than one possible cause of failure for each individual. Non-parametric estimation of cause-specific distribution functions is considered under independent censoring. Properties of the estimators are discussed and an illustration of their application is given.

An improved nonparametric estimator of sub-distribution function for bivariate competing risk models

“…Note that nonparametric estimation under bivariate competing risks is much more challenging than its univariate counterpart. Especially in small sample sizes, the estimator of Sankaran et al [19] will generally be a crude step function and will have a large mean squared error (MSE). In light of this problem, the main objective of this paper is to propose a new nonparametric estimator that aims to improve upon the existing estimator.…”

“…Section 2 introduces basic notations and the estimator of Sankaran et al [19]. Section 3 proposes a new estimator for the bivariate sub-distribution function.…”

“…This paper considers nonparametric estimation of the bivariate sub-distribution functions under right censoring as in [4,19]. Note that nonparametric estimation under bivariate competing risks is much more challenging than its univariate counterpart.…”

“…The bivariate competing risk models have been recently considered by many authors [4,19,17,18,20]. Under the bivariate competing risks models, the target of estimation is the bivariate sub-distribution function (formally defined in Section 2).…”

“…Several nonparametric estimators have been proposed under various censoring and truncation schemes. Antony and Sankaran [4] and Sankaran et al [19] developed nonparametric estimators under right-censoring. Sankaran and Antony [18] considered a similar problem where the censoring times are missing.…”