Solution (source code)

= Solution

<Parametric linkage analysis> specifies a disease-transmission model: the mode of inheritance, disease-<allele> frequency and <penetrance> of each <genotype>. Combining these with <Mendelian segregation> and the <recombination fraction> gives a <pedigree likelihood>. One can estimate the <recombination fraction> or compare a linked model, $\theta<1/2$, with the unlinked model, $\theta=1/2$, using a <likelihood-ratio test> or <LOD score>. Incomplete <penetrance> and unobserved <genotypes> are accommodated by summing over the possible underlying inheritance states.

<Nonparametric linkage analysis> instead tests whether relatives with the same disease <phenotype> share marker <alleles> <identical by descent> more often than expected from their <pedigree>. For example, <affected-sib-pair analysis> compares sharing among affected <full siblings> with its Mendelian null distribution. It avoids specifying a complete disease-<penetrance> model and disease-<allele> frequency. “Model-free” still assumes an inheritance model for the marker, correct family relationships and a justified treatment of <genetic-study ascertainment>; it does not <mean> assumption-free.

\b[Parametric analysis models the disease <likelihood>; nonparametric analysis tests departure from the marker's Mendelian sharing distribution.]