An Information Ratio-Based Goodness-of-Fit Test for Copula Models on Censored Data

• Activity Number: 417 - Recent advancement on life time data analysis
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
• Sponsor: Lifetime Data Science Section
• Author(s): Tao Sun* and Yu Cheng and Ying Ding
• Companies: Renmin University of China and University of Pittsburgh and University of Pittsburgh
• Keywords: copula; goodness-of-fit; information ratio; interval censoring; right censoring; recurrent events

Abstract

Copula is popular for modeling the dependence between marginal distributions in multivariate censored data, such as interval-, right- censored, and recurrent events. One critical question is whether the fitted copula model is a good fit for the data. However, no formal goodness-of-fit (GOF) test exists for copula specification in interval censoring or recurrent events. To address this critical issue, we develop a novel information ratio (IR)-based goodness-of-fit test for diagnosing copula-based survival models. It is the first method that handles interval-, right-censored and recurrent events. It applies to any copula family with a parametric form, including Archimedean and Gaussian families. The test statistic is simple to calculate, and the test procedure is straightforward to implement. We prove its asymptotic consistency and normality. The simulation results show that our method can control type-I errors well and achieve satisfactory power performance when the dependence strength (in terms of Kendall’s ?) is moderate to high. Finally, we employ our method to test a list of copula models in multiple real datasets and our method exhibits strong differentiating power.