Hazard Estimation With Bivariate Survival Data and Copula Density Estimation

• Published in: Journal of computational and graphical statistics Vol. 24; no. 4; pp. 1053 - 1073
• Main Author: Gu, Chong
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.10.2015; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Copularization; Cross-validation; Density; Estimating techniques; Mathematical functions; Nonparametric and High Dimensional Problems; Open source software; Parameter estimation; Penalized likelihood; Simulation; Smoothing parameter; Studies
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2014.964356

Bivariate survival function can be expressed as the composition of marginal survival functions and a bivariate copula and, consequently, one may estimate bivariate hazard functions via marginal hazard estimation and copula density estimation. Leveraging on earlier developments on penalized likelihood density and hazard estimation, a nonparametric approach to bivariate hazard estimation is being explored in this article. The new ingredient here is the nonparametric estimation of copula density, a subject of interest by itself, and to accommodate survival data one needs to allow for censoring and truncation in the setting. A simple copularization process is implemented to convert density estimates into copula densities, and a cross-validation scheme is devised for density estimation under censoring and truncation. Empirical performances of the techniques are investigated through simulation studies, and potential applications are illustrated using real-data examples and open-source software.