quantitative trait mapping

Weir BS 2008 Linkage disequilibrium and association mapping. Annu Rev Genom Hum Genet 9:129-142.

• dichotomous traits: case only
• Pr(MM|Case) = p_M² + (1 / μ_G) [p_Mρ_MTσ_AT√(2p_Mp_m) + ρ_MT²σ_DTp_Mp_m]
• Pr(Mm|Case) = 2p_Mp_m + (1 / μ_G) [(p_m − p_M)ρ_MTσ_AT√(2p_Mp_m) − 2ρ_MT²σ_DTp_Mp_m]
• Pr(mm|Case) = p_m² + (1 / μ_G) [−p_mρ_MTσ_AT√(2p_Mp_m) + ρ_MT²σ_DTp_Mp_m]
• these results suggest the use of case-only testing for Hardy-Weinberg equilibrium at marker loci as a way to detect linkage disequilibrium between marker and disease loci

• tests based on a 2 × 2 table of marker allele counts in cases and controls can detect only additive effects at trait loci
• additive and nonadditive effects can be detected jointly with tests based on a 3 × 2 table of marker genotype counts in cases and controls
• the extra df can reduce power
• there may be problems with small expected counts in some cells of the table
• the effects of genotyping errors are especially acute for cells with small expected counts

• it would seem unlikely that the complexity of the human genome could be captured by second-order statistics such as linkage disequilibrium or the correlation of allele frequencies at pairs of loci
• these statistics are indeed very useful