Copula models of joint last survivor analysis
copula function, joint survival function, Weibull distribution, Stable (Gumbel–Hougaard) copula, Bayesian estimation, Metropolis–Hastings algorithm
Copula models are becoming increasingly popular for modelling dependencies between random variables. The range of their recent applications includes such fields as analysis of extremes in financial assets and returns; failure of paired organs in health science; reliability studies; and human mortality in insurance. This paper gives a brief overview of the principles of construction of such copula models as Gaussian, student, and Archimedean. The latter includes Frank, Clayton, and St.able (Gumbel–Hougaard) families. The emphasis is on application of copula models to joint last survivor analysis. The main example discussed in this paper deals with the mortality of spouses, known to be associated through such factors as common disaster, common lifestyle, or the broken-heart syndrome. These factors suggest modelling dependence of spouses' lives on both calendar date scale and age-at-death scale. This dependence structure suggests a different treatment than that for problems of survival analysis such as paired organ failure or twins' mortality. Construction of a conditional Bayesian copula model is further generalized in view of the relationship between the joint first life and last surviror probabilities. A numerical example is considered, involving the implementation of Markov chain Monte Carlo algorithms using WinBUGs.
Applied Statistics Methods in Business and Industry