Abstract
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 baseline 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. Some key model control techniques are discussed in a supplementary online material.
Highlights
Longevity is an important trait often considered in animal breeding programs [31, 30, 33, 37, 27, 35, 17, 9, 6, 32, 1]
We will present a model framework here that allows to overcome these challenges. These models will have a structure of means and covariances similar to the gaussian linear mixed models classically used in quantitative genetics
The quantitative genetic theory behind the models considered here requires a special decomposition of the phenotypic variance in terms of the variance of the random components and a scale parameter present in the models. This will be necessary for the calculation of the so called heritability, which is crucial in quantitative genetic applications
Summary
Longevity is an important trait often considered in animal breeding programs [31, 30, 33, 37, 27, 35, 17, 9, 6, 32, 1]. The aim of this article is to introduce, characterize and discuss a class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure in a context of quantitative genetics applications. There, a suitable multivariate version of the proportional hazard model is introduced in general terms Those models will encompass models for competing risks possibly defined with different types of time scale (continuous and discrete time). The quantitative genetic theory behind the models considered here requires a special decomposition of the phenotypic variance in terms of the variance of the random components and a scale parameter present in the models This will be necessary for the calculation of the so called heritability, which is crucial in quantitative genetic applications.
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