Flexible copula modeling for bivariate survival and semi-competing risks data

Abstract

Copula modeling for the joint distribution of two survival times has been adopted in many fields, such as ecology, econometrics, reliability engineering, finance, and medicine. However, traditional one-parameter copulas may produce biased or inefficient estimates when the true copula is misspecified. In this article, we propose the two-parameter BB1 copula that can more flexibly model the true copula structure than one-parameter copulas. We develop likelihood-based estimation methods for fitting the two-parameter BB1 copula to bivariate censored data and semi-competing risks data. We also implement the proposed methods in the R package Copula.surv, which can handle both bivariate censorings and semi-competing risks. Based on simulation studies, we demonstrate the robustness and efficiency of the proposed methods under the correctly or incorrectly specified model. Finally, an ovarian cancer dataset is analyzed to illustrate the proposed BB1 copula model for a real application.
Keywords: Archimedean copula; Clayton copula; Censoring; Gumbel copula; Multivariate survival model; Weibull regression

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