Relative risks for general phenotypes and genetic models

Azra Kurbasic and Ola Hössjer

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Many common diseases are known to have genetic components but since they are non-Mendelian, i.e. a large number of genetic factors effect the phenotype, these components are difficult to localize. These traits are often called complex and analysis of siblings is a valuable tool for mapping. It has been shown that the power of affected relative pairs method to detect linkage of a disease susceptibility locus depends on the locus contribution to increased risk of relatives compared with population prevalence [Risch, 1990a and 1990b]. In this paper we generalize calculation of relative risk to arbitrary phenotypes and genetic models but also show that the relative risk can be split into the relative risk at the main locus and the relative risk due to interaction between the main locus and loci at other chromosomes. In order to achieve power to detect linkage a certain number of relative pairs has to be collected. To be able to quantify the amount of information of the relative pair we use the effective number of meioses introduced in Hössjer [2004], which is closely related to power to detect linkage. Relative risks and effective number of meioses are computed for several genetic models with binary or quantitative phenotypes, with or without polygenic effects.
Key words:
Complex diseases, relative risk, linkage analysis, effective number of meioses.