Dependent competing risks: Cause elimination and its impact on survival

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Dimitrova, D. S. ; Haberman, S. ; Kaishev, V. K. (2013)

The dependent competing risks model of human mortality is considered, assuming that the dependence between lifetimes is modelled by a multivariate copula function. The effect on the overall survival of removing one or more causes of death is explored under two alternative definitions of removal, ignoring the causes and eliminating them. Under the two definitions of removal, expressions for the overall survival functions in terms of the specified copula (density) and the net (marginal) survival functions are given. The net survival functions are obtained as a solution to a system of non-linear differential equations, which relates them through the specified copula (derivatives) to the crude (sub-) survival functions, estimated from data. The overall survival functions in a model with four competing risks, cancer, cardiovascular diseases, respiratory diseases and all other causes grouped together, have been implemented and evaluated, based on cause-specific mortality data for England and Wales published by the Office for National Statistics, for the year 2007. We show that the two alternative definitions of removal of a cause of death have different effects on the overall survival and in particular on the life expectancy at birth and at age 65, when one, two or three of the competing causes are removed. An important conclusion is that the eliminating definition is better suited for practical use in competing risks’ applications, since it is more intuitive, and it suffices to consider only positive dependence between the lifetimes which is not the case under the alternative ignoring definition.
  • References (17)
    17 references, page 1 of 2

    Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., and Nesbitt, C.J. (1997). Actuarial Mathematics. Itasca, III: Society of Actuaries.

    Bryant, J. and Dignam, J.J. (2004). Semiparametric Models for Cumulative Incidence Functions. Biometrics, 60, 182-190.

    Buettner, T. (2004). Approaches and experiences in projecting mortality patterns for oldest-old. North American Actuarial Journal, 6 (3), 14-29.

    Carriere, J. (1994). Dependent Decrement Theory. Transactions, Society of Actuaries, v. XLVI, 45-65.

    Carriere, J. (1995). Removing Cancer when it is Correlated with other Causes of Death. Biometrical Journal, 3, 339-350.

    Chen, Y. (2010). Semiparametric marginal regression analysis for dependent competing risks under an assumed copula. J. R. Statist. Soc. B, 72, Part 2, 235-251.

    Cherubini, U., Luciano, E. and Vecchiato, W. (2004). Copula methods in nance. John Wiley and Sons Ltd.

    Gaynor, J.J., Feuer, E.J., Tan, C.C., Wu, D.H., Little, C.R., Straus, D.J., Clarkson, B.D., Brennan, M.F. (1993). On the use of cause-specific failure time and conditional failure probabilities: examples from clinical oncology data. J. Am. Stat. Assoc., 88, 400-409.

    Gooley, T.A., Leisenring, W., Crowley, J., Storer, B. (1999). Estimation of failure probabilities in the presence of competing risks: new representation of old estimators. Stat Med, 18, 695-706.

    Honor´e, B. E. and Lleras-Muney, A. (2006). Bounds in competing risks models and the war on cancer. Econometrica, 74, 4 , 1675-1698.

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