A class of multivanate failure time distributions

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Abstract
A class of continuous multivariate lifetime distributions is proposed. The dependence between individuals in a group is modelled by a group specific quantity, which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution. It is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account. If the conditional hazards are proportional, then the hazards in the marginal distributions are also proportional, but with different constants of proportionality. Also the hazard for the minimum in a group is proportional to the marginal hazards. If the conditional distributions given the group quantity are Weibull then the marginal distributions are also Weibull. This class can be used to test the hypothesis of independence of litter mates in the proportional hazards model.

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