How genes affect longevity in heterogeneous populations: binomial frailty models and applications
150 pages. Odense, University of Southern Denmark, Faculty of Social Sciences, Institute of Public Health (2000)
A great interest in studying genes and longevity has developed over the past few decades. Two kinds of data are generally being collected: data on related individuals including twin and genealogy data, and data on unrelated individuals but with information on gene markers. As new centenarian studies emerge, more data on individual genotypes will be available. Efficient and powerful statistical models that combine quantitative genetics and survival analysis are needed. This PhD project is aimed at developing new models for data analysis, replacing the conventional statistics used heretofore.
In this presentation, the binomial frailty model derived upon the Cox’s proportional hazard assumption and the binomial distribution of gene alleles is introduced. Characterized by its direct incorporation of polygenic influence on individual survival, the model has been applied at the beginning to describe the genetic influence on life span from one observed gene or genotype given the existence of influences from other genetic and environmental heterogeneity. Some interesting insights on topics such as risk compensation are obtained. The model is extended to study family correlation on life span. Through simulation, correlation of life span and correlation of frailty between relatives are compared and the age-patterns of life span correlation and of frailty correlation are explored. The analysis indicates the following: 1. Behind the modest life span correlation there is a considerably strong correlation of frailty; 2. The life span correlation among related individuals decreases as age increases as a result of influences from environmental heterogeneity. The binomial frailty model is further engaged to estimate the number of longevity genes in human beings. The estimation has been done incorporating various assumptions on the genetic and heterogeneity parameters so that the results presented represent a range from normal to extreme situations. A comparison of the results obtained from Danish twin data, Quebec genealogy data and European noble family genealogy data showed relatively stable estimates from the model. The practice of applying the binomial frailty model to related individuals, serves as a bridge linking molecular genetics with demography in aid of promoting better understanding of the mechanisms of aging and longevity.
A binomial frailty model for gene marker data is specified and this is applied to empirical data in the last part of the thesis. The model combines both the genetic and demographic information together for determining the relative risk of a gene allele or genotype and in estimating the corresponding frequencies. A Two-step MLE has also been introduced, to obtain a non-parametric form of the baseline hazard function. The model has been derived to incorporate gene-environment, gene-sex interactions as well as individual heterogeneity. Detailed studies have been done to examine the sensitivity of the model to the parameter values, data size and data structure. Various aspects of problems arising from sampling bias and confounding as well as problems from introducing period life table survival in the analysis are discussed. The model is then applied to Danish centenarian data to measure the influence on longevity from apolipoprotein genes, genes related to cardiovascular diseases and p450 genes; and to data from Italian centenarian studies used to show the effects of gene-environment and gene-sex interactions. The application of the model to data on cardiovascular disease associated genes and apolipoprotein B gene from the Danish centenarian study reveals genes that manifest significant influences on human life span: the conclusions are supported by previous clinical studies. Inferences on gene-sex and/or gene-environment interactions are supportable for genes examined in both the Danish and the Italian studies. A comparative study has shown remarkable influences from individual heterogeneity in unobserved frailty with risk of genes or genotypes underestimated when ignoring these differences. In addition, the likelihood of the estimation is substantially improved with application of the heterogeneity model.