Copula-Based Semiparametric Multivariate Frailty Models for the Multi-Type Recurrent Event Data: Applications on Skin Cancer Data

• Activity Number: 336
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Khaled Bedair*+ and Yili Hong
• Companies: Virginia Tech and Virginia Tech
• Keywords: MCEM algorithm ; copula ; multi-type skin cancer ; recurrent events ; multivariate frailty ; surviaval analysis

Abstract

In this Paper, we generalize the multivariate Gaussian assumption of the frailty terms and allow the frailty distributions to have more features than the symmetric, unimodal properties of the normal density. More flexible approaches to modeling the correlated frailty referred to as copula functions are introduced. Copula functions provide tremendous flexibility especially in allowing to take the advantages of a variety of choices for the marginal distributions and correlation structures. Semiparametric intensity models for multi-type recurrent events based on a combination of the MCEM as a general option to estimate the unknown parameters of high denominational frailty models and copula functions for modeling the multivariate frailty are introduced. Complete estimation procedures for fixed effects, nonparametric baseline intensity functions, and copula parameters are developed. In addition, Louis's formula for variance estimates and predictions of frailties are derived and calculated. Performances of proposed models are evaluated by simulation studies. Applications are illustrated through a dataset collected from a clinical trial of patients with skin cancer.