Theory and Practice in Quantitative Genetics

With the rapid advances in molecular biology, the near completion of the human genome, the development of appropriate statistical genetic methods and the availability of the necessary computing power, the identification of quantitative trait loci has now become a realistic prospect for quantitative geneticists. We briefly describe the theoretical biometrical foundations underlying quantitative genetics. These theoretical underpinnings are translated into mathematical equations that allow the assessment of the contribution of observed (using DNA samples) and unobserved (using known genetic relationships) genetic variation to population variance in quantitative traits. Several statistical models for quantitative genetic analyses are described, such as models for the classical twin design, multivariate and longitudinal genetic analyses, extended twin analyses, and linkage and association analyses. For each, we show how the theoretical biometrical model can be translated into algebraic equations that may be used to generate scripts for statistical genetic software packages, such as Mx, Lisrel, SOLAR, or MERLIN. For using the former program a web-library (available from http://www.psy.vu.nl/mxbib) has been developed of freely available scripts that can be used to conduct all genetic analyses described in this paper

How long can humans live? Lower bound for biological limit of human longevity calculated from Danish twin data using correlated frailty model

How long can people live? Opinions of the researchers diverge and debates continue. Is there any systematic way to address this question? In this paper, we suggest an approach to the estimation of the biological limit of human longevity using survival data for twins from different zygocity groups. The approach is based on the genetic model of individual frailty. It combines ideas used in demography and survival analysis with methods of quantitative genetics and genetic epidemiology. The association between the life-spans of related individuals is described by the correlated frailty model of bivariate survival. A version of this model is used in order to estimate heritability of the individual frailty and to calculate the lower bound of human longevity. The limitations of this approach and directions of further research are discussed.</p

Dependent Hazards in Multivariate Survival Problems

AbstractA new class of bivariate survival distributions is constructed from a given family of survival distributions. The properties of these distributions are analyzed. It is shown that the same bivariate survival function can be derived using two radically different concepts: one involves transformation of the well-known bivariate survival function; the other involves correlated stochastic hazards. The new conditions that guarantee negative associations 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 multivariate correlated gamma-frailty model are investigated

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 are analyzed. It is shown that the same bivariate survival function can be derived using two radically different concepts: one involves transformation of the well-known bivariate survival function; the other involves correlated stochastic hazards. The new conditions that guarantee negative associations 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 multivariate correlated gamma-frailty model are investigated.correlated hazards bivariate frailty, bivariate survival, mortality models