Familial aggregation of a disease consequent upon correlation between relatives in a risk factor measured on a continuous scale

Abstract

Correlation between relatives in one or more risk factors for a disease will contribute to the risk in relatives of an affected individual, irrespective of the cause(s) of the correlation. In this paper, a model is proposed to quantify the relation between 1) the correlation (rho) between a random pair of relatives in a quantitative risk factor, 2) the dependence of the probability of being affected on a risk factor, assumed to be a logistic function and summarized by a risk ratio (RR) between upper and lower quartiles, and 3) the resultant disease association between relatives, represented as an odds ratio. For one risk factor, the odds ratio is almost independent of disease frequency across the range 0.001-0.1, and is approximately linearly related to rho on a logarithmic scale. An odds ratio between relatives of about 2 occurs if rho = 1 and RR = 9, if rho = 0.6 and RR = 20, or if rho = 0.3 and RR = 100. For two independent risk factors with the same risk ratio and rho, the resultant odds ratio exceeds unity by about twice as much as when there is one risk factor. That is, even moderate familial aggregation of a disease is consistent with there being one or more strong familial (genetic and/or environmental) risk factors. Illustrations of the model are discussed.