= Allele-sharing sufficiency for recessive linkage
For independent affected sib pairs with IBD counts $n_0,n_1,n_2$, the <likelihood function> of the <recombination fraction> is proportional to $s^{2n_0+n_1}(1-s)^{2n_2+n_1}$, with $s=2\theta(1-\theta)$. At fixed sample size, the total shared-copy count $2n_2+n_1$ is a <sufficient statistic> by the <Fisher-Neyman factorization theorem>. Thus a one-sided <likelihood-ratio test> has the same ordering as a test for excess mean IBD sharing. This equivalence depends on the stated fully penetrant recessive model and does not extend to arbitrary disease models.
// Target: biology.bigb
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