A vine copula approach for regression analysis of bivariate current status data with informative censoring

Abstract

ABSTRACTBivariate current status data occur in many areas and many authors have discussed their analysis and proposed many inference procedures [Jewell, N.P., van der Laan, M.J., and Lei, X. (2005), ‘Bivariate Current Status Data with Univariate Monitoring Times’, Biometrika, 92, 847–862; Wang, N., Wang, L., and McMahan, C.S. (2015), ‘Regression Analysis of Bivariate Current Status Data Under the Gammafrailty Proportional Hazards Model Using the Em Algorithm’, Computational Statistics & Data Analysis, 83, 140–150; Hu, T., Zhou, Q., and Sun, J. (2017), ‘Regression Analysis of Bivariate Current Status Data Under the Proportional Hazards Model’, The Canadian Journal of Statistics, 45, 410–424]. However, most of these methods are for the situation where the observation or censoring is non-informative and sometimes one may face informative censoring [Zhang, Z., Sun, J., and Sun, L. (2005), ‘Statistical Analysis of Current Data with Informative Observation Times’, Statistics in Medicine, 24, 1399–1407; Chen, C.M., Lu, T.F.C., Chen, M.H., and Hsu, C.M. (2012), ‘Semiparametric Transformation Models for Current Status Data with Informative Censoring’, Biometrical Journal, 19, 641–656; Ma, L., Hu, T., and Sun, J. (2015), ‘Sieve Maximum Likelihood Regression Analysis of Dependent Current Status Data’, Biometrika, 85, 649–658], where one has to deal with three correlated random variables. In this paper, a vine copula approach is developed for regression analysis of bivariate current status data in the presence of informative censoring. The proposed estimators are shown to be strongly consistent and the asymptotic normality and efficiency of the estimated regression parameter are also established. Numerical results suggest that the proposed method works well in practice.