  A class of multivariate mixed survival models for continuous and discrete
time with a complex covariance structure is introduced in a context of
quantitative genetic applications. The methods introduced can be used in many
applications in quantitative genetics although the discussion presented
concentrates on longevity studies. The framework presented allows to combine
models based on continuous time with models based on discrete time in a joint
analysis. The continuous time models are approximations of the frailty model in
which the hazard function will be assumed to be piece-wise constant. The
discrete time models used are multivariate variants of the discrete relative
risk models. These models allow for regular parametric likelihood-based
inference by exploring a coincidence of their likelihood functions and the
likelihood functions of suitably defined multivariate generalized linear mixed
models. The models include a dispersion parameter, which is essential for
obtaining a decomposition of the variance of the trait of interest as a sum of
parcels representing the additive genetic effects, environmental effects and
unspecified sources of variability; as required in quantitative genetic
applications. The methods presented are implemented in such a way that large
and complex quantitative genetic data can be analyzed.
