Dependence modeling for recurrent event times subject to right-censoring with D-vine copulas.

Publisher: Biometric Society Country of Publication: United States NLM ID: 0370625 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1541-0420 (Electronic) Linking ISSN: 0006341X NLM ISO Abbreviation: Biometrics Subsets: MEDLINE

Publication: Alexandria Va : Biometric Society
Original Publication: Washington.

Data Interpretation, Statistical* ; Likelihood Functions* ; Models, Statistical*; Asthma/pathology ; Child ; Computer Simulation ; Humans ; Recurrence ; Time Factors

In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit correspond to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be right-censored. In contrast to classical analysis, gap times and censoring times cannot be assumed independent, i.e., the sequential nature of the data induces dependent censoring. Also, the number of recurrences typically varies among sample units leading to unbalanced data. To model the association pattern between gap times, so far only parametric margins combined with the restrictive class of Archimedean copulas have been considered. Here, taking the specific data features into account, we extend existing work in several directions: we allow for nonparametric margins and consider the flexible class of D-vine copulas. A global and sequential (one- and two-stage) likelihood approach are suggested. We discuss the computational efficiency of each estimation strategy. Extensive simulations show good finite sample performance of the proposed methodology. It is used to analyze the association of recurrent asthma attacks in children. The analysis reveals that a D-vine copula detects relevant insights, on how dependence changes in strength and type over time.
(© 2019 International Biometric Society.)

Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insur Math Econ 44, 182-198.
Barthel, N., Geerdens, C., Killiches, M., Janssen, P., and Czado, C. (2018). Vine copula based likelihood estimation of dependence patterns in multivariate event time data. Comput Stat Data Anal 117, 109-127.
Cook, R. J. and Lawless, J. (2007). The Statistical Analysis of Recurrent Events. Springer Science & Business Media.
Czado, C. (2010). Pair-copula constructions of multivariate copulas. In Copula Theory and its Applications, 93-109. Springer.
de Uña-Álvarez, J. and Meira-Machado, L. F. (2008). A simple estimator of the bivariate distribution function for censored gap times. Stat Probabil Lett 78, 2440-2445.
Dissmann, J., Brechmann, E. C., Czado, C., and Kurowicka, D. (2013). Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59, 52-69.
Duchateau, L. and Janssen, P. (2008). The Frailty Model. Springer Science & Business Media.
Geerdens, C., Claeskens, G., and Janssen, P. (2016). Copula based flexible modeling of associations between clustered event times. Lifetime Data Anal 22, 363-381.
Hobaek Haff, I. (2013). Parameter estimation for pair-copula constructions. Bernoulli 19, 462-491.
Hobaek Haff, I., Aas, K., and Frigessi, A. (2010). On the simplified pair-copula construction-Simply useful or too simplistic? J Multivariate Anal 101, 1296-1310.
Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman and Hall.
Kraus, D. and Czado, C. (2017). D-vine copula based quantile regression. Comput Stat Data Anal 110, 1-18.
Meyer, R. and Romeo, J. S. (2015). Bayesian semiparametric analysis of recurrent failure time data using copulas. Biom. J. 57, 982-1001.
Nelsen, R. B. (2006). An Introduction to Copulas. Springer Series in Statistics. Springer-Verlag New York Inc.
Prenen, L., Braekers, R., and Duchateau, L. (2017). Extending the Archimedean copula methodology to model multivariate survival data grouped in clusters of variable size. J R Stat Soc Series B 79, 483-505.
Shih, J. H. and Louis, T. A. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51, 1384-1399.
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Stat. Université Paris 8.
Stöber, J. and Schepsmeier, U. (2013). Estimating standard errors in regular vine copula models. Comput Stat 28, 2679-2707.
Stoeber, J., Joe, H., and Czado, C. (2013). Simplified pair copula constructions - Limitations and extensions. J Multivariate Anal 119, 101-118.
Wei, L.-J., Lin, D. Y., and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Am Stat Assoc 84, 1065-1073.

Keywords: D-vine copulas; dependence modeling; induced dependent right-censoring; maximum likelihood estimation; recurrent event time data; unbalanced gap time data

Date Created: 20181215 Date Completed: 20200129 Latest Revision: 20200129

20240829

10.1111/biom.13014

30549012