TABLE 1.

Quantifying the effect of sampling siblings of affected individuals^*

M	F	P	Population Pr[MF]	Population Pr[offspring I MF]	Pr[MFP triad]	Exposure factor	Pr[Sibling has 0 copies, given the parents]	Pr[Sibling has 1 copy, given the parents]	Pr[Sibling has 2 copies, given the parents]
2	2	2	p4	1	R2p4B	1 - r + rTU2	0	0	1
2	1	2	2p3(1 - p)	1/2	R2p3(1 - p)B	1 - r + rTU2	0	1/2	1/2
2	1	1	2p3(1 - p)	1/2	R1p3(1 - p)B	1 - r + rTU1	0	1/2	1/2
1	2	2	2p3(1 - p)	1/2	R2p3(1 - p)B	1 - r + rTU2	0	1/2	1/2
1	2	1	2p3(1 - p)	1/2	R1p3(1 - p)B	1 - r + rTU1	0	1/2	1/2
1	1	0	4p2(1 - p)2	1/4	p2(1 - p)2B	1 - r + rT	1/4	1/2	1/4
1	1	1	4p2(1 - p)2	1/2	2 R1p2(1 - p)2B	1 - r + rTU1	1/4	1/2	1/4
1	1	2	4p2(1 - p)2	1/4	R2p2(1 - p)2B	1 - r + rTU2	1/4	1/2	1/4
1	0	0	2p(1 - p)3	1/2	p(1 - p)3B	1 - r + rT	1/2	1/2	0
1	0	1	2p(1 - p)3	1/2	R1p(1 - p)3B	1 - r + rTU1	1/2	1/2	0
0	1	0	2p(1 - p)3	1/2	p(1 - p)3B	1 - r + rT	1/2	1/2	0
0	1	1	2p(1 - p)3	1/2	R1p(1 - p)3B	1 - r + rTU1	1/2	1/2	0
2	0	1	p2(1 - p)2	1	R1p2(1 - p)2B	1 - r + rTU1	0	1	0
0	2	1	p2(1 - p)2	1	R1p2(1 - p)2B	1 - r + rTU1	0	1	0
0	0	0	(1 - p)4	1	(1 - p)4B	1 - r + rT	1	0	0

^*For a diallelic gene, genetic enrichment when siblings are studied can be calculated from factors given here. Simplifying assumptions are that the gene is in Hardy-Weinberg equilibrium and that exposure and gene occur independently in the population. Probabilities are based on a multiplicative model; R₁ and R₂ are the relative risks for those with one and two copies, respectively. Allele prevalence is p, exposure prevalence is r, the main effect of the exposure is T, and the two interaction parameters are U₁ and U₂. B is simply a normalizing constant, ensuring that probabilities sum to 1.0. M, mother; F, father; P, affected proband.