Dependent hazards in multivariate survival problems

A new class of bivariate survival distributions is constructed from a given family of survival distributions. The properties of these distributions ar e analyzed. It is shown that the same bivariate survival function can be de rived using two radically different concepts: one involves transformation o f the well-known bivariate survival function; the other involves correlated stochastic hazards. The new conditions that guarantee negative association s of life spans are derived. An exponential representation of the survival function for two related individuals is derived in terms of the conditional distribution of the stochastic hazards among survivors. Versions of the mu ltivariate correlated gamma-frailty model are investigated. (C) 1999 Academ ic Press AMS 1991 subject classifications: 62P10.