Abstract
This chapter provides mathematical infrastructures for copula models, focusing on applications to survival analysis involving dependent censoring. After reviewing the concept of copulas, we introduce measures of dependence, including Kendall’s tau and the cross-ratio function. We also introduce the idea of residual dependence that explains how dependence between event times arises and how it can be modeled by copulas. Finally, we apply copulas for modeling the effect of dependent censoring and analyze the bias of the Cox regression analysis owing to dependent censoring.
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References
Clayton DG (1978) A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65(1):141–151
Day R, Bryant J, Lefkopoulou M (1997) Adaptation of bivariate frailty models for prediction, with application to biological markers as prognostic indicators. Biometrika 84(1):45–56
Emura T, Chen YH (2016) Gene selection for survival data under dependent censoring, a copula-based approach. Stat Methods Med Res 25(6):2840–2857
Emura T, Nakatochi M, Murotani K, Rondeau V (2017a) A joint frailty-copula model between tumour progression and death for meta-analysis. Stat Methods Med Res 26(6):2649–2666
Emura T, Nakatochi M, Matsui S, Michimae H, Rondeau V (2017b) Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: meta-analysis with a joint model. Stat Methods Med Res, https://doi.org/10.1177/0962280216688032
Emura T, Pan CH (2017). Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach. Stat Pap, https://doi.org/10.1007/s00362-017-0947-z
Emura T, Wang W, Hung HN (2011) Semi-parametric inference for copula models for dependently truncated data. Stat Sinica 21:349–367
Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New York
Frank MJ (1979) On the simultaneous associativity of f(x, y) and x + y - f(x, y). Aequationes Matbematicae 19:194–226
Gumbel EJ (I960). Distributions de valeurs extremes en plusieurs dimensions. PubL Inst Statist. Parids 9: 171–173
Joe H (1993) Parametric families of multivariate distributions with given margins. J Multivar Anal 46:262–282
Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New York
Morgenstern D (1956) Einfache Beispiele zweidimensionaler Verteilungen. Mitteilungsblatt für Mathematishe Statistik. 8:234–235
Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York
Oakes D (1989) Bivariate survival models induced by frailties. J Am Stat Assoc 84:487–493
Rivest LP, Wells MT (2001) A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. J Multivar Anal 79:138–155
Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris. 8:229–231
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Emura, T., Chen, YH. (2018). Copula Models for Dependent Censoring. In: Analysis of Survival Data with Dependent Censoring. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-10-7164-5_3
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DOI: https://doi.org/10.1007/978-981-10-7164-5_3
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