Monographie

Bivariate quadratic hazard model: results of analysis of the Danish twins survival data

Abstract

In this paper we investigate the properties of the bivariate quadratic hazard (QH) frailty model appropriate for genetic analysis of twin survival data and apply it to the analysis of survival data on Danish twins. Two estimation procedures are used in the analysis. One is based on a version of the EM-algorithm for the quadratic hazard model. The other procedure is a new one. It is based on a numerical inversion method combined with aparametric specification of the univariate survival functions. Since this method is parametric, the asymptotic properties of the estimates are available from the classical MLE theory. We compare the results of analysis of the Danish twin data by the two methods for the QH-model with those obtained in our earlier studies using the correlated gamma-frailty model. The results indicate that the QH-model can be successfully used in the analysis of genetic effects in duration studies. We also address the questions of analysis of data on pedigrees and families and show how the QH-model may be used to combine traditional methods of genetic analysis based on liability models with multivariate survival models. We present some ideas behind an extended version of the QH-model appropriate for modeling of effects of gene-environment interaction. The limitations of this approach and directions of further research are discussed.