Simple test of the Multifactorial-Polygenic Model with sex dependent thresholds

Under the Multifactorial-Polygenic Model, a sex difference in population incidence implies higher risk in relatives of low risk sex probands than in those of high risk sex probands. The relationship between sex ratio in population incidence and expected relative risk (RR) to first-degree relatives of probands of the low risk sex vs the high risk sex under the Multifactorial-Polygenic Model was examined. Five observations were made from this analysis: (1) as the sex ratio increases, the expected RR increases for each combination of incidence and r, the liability correlation between relatives. (2) RRs are higher for low risk sex relatives than for high risk sex relatives at each combination of incidence, r. and sex ratio. (3) the expected RR increases as r increases at each incidence and sex ratio, and (4) variation in population incidence has little effect on RR at a given sex ratio and r, and (5) the expected RRs are small, rarely exceeding two-fold. The quantitative relationship between sex ratio and RR provides the basis for a simple test of the Multifactorial-Polygenic Model when two different sex or severity thresholds can be identified.