Assessment of Dependence In the Life Times of Twins

On the basis of data on the like-sexed twins born 1881–1930 in Denmark, and known to be alive by the age of 15 (8985 pairs) various approaches to the analysis of bivariate survival data are discussed. A simple approach is to calculate a nonparametric measure of dependence, e.g. Kendall’s coefficient of concordance. This is useful as a general measure of dependence, but cannot be applied for making individual prognoses. A natural approach is to model the life times as conditionally independent given some common unobserved risk factors. Some choices for this, so called frailty distribution, are positive stable, gamma and inverse Gaussian distributions. These are markedly different, with stable and gamma being extreme cases implying a very high dependence at low ages and high ages, respectively. The other models examined are intermediate. Another approach is a multi-state model analyzed by the procedure of Cox with time-dependent covariates describing the status of the partner. This offers larger flexibility and is more directed towards conditional distributions, but at the price of loosing a part of the bivariate interpretation. It can further throw some light on the various frailty distributions. According to the Cox model the risk is high immediately after death of the partner, but the risk decreases so fast that it cannot be described by a frailty distribution.

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