David M. Evans Sarah E. Medland QTL Linkage Analysis in Mx David M. Evans Sarah E. Medland Wellcome Trust Centre for Human Genetics Oxford United Kingdom Queensland Institute of Medical Research Brisbane Australia Twin Workshop Boulder 2004

Computing IBD probabilities (MERLIN) QTL linkage analysis using pihat QTL linkage analysis using full distribution of IBD probabilities Multivariate QTL linkage analysis

“Pi hat” method ^ -where π = p2 + 0.5 x p1 -compare against ACE model Q1 e c a q C2 A2 Q2 P2 E2 1 / 0.5 1 / π ^ -where π = p2 + 0.5 x p1 -compare against ACE model (50:50 χ02 χ12) ^

“Pi hat” method -The likelihood for each pedigree (i) is calculated as: L(θ) = (2π-k)|Σi|-1/2exp[-1/2(yi - μ)’Σi-1(yi - μ)] -where Σi q12 + a12 + e12 πiq12 + a12 ^ = -Easy to specify, especially in large pedigrees, but… -Computationally intensive -Bias in selected samples

Computing pi hat within the Mx script F matrix 0 0.5 1 K matrix pIBD0 (Definition Variables) pIBD1 pIBD2 F*K = 0*pIBD0 + 0.5*pIBD1 + 1*pIBD2 = π ^

“Full IBD” method 1 A1 C1 E1 P1 Q1 e c a q C2 A2 Q2 P2 E2 0.5 1 0.5 1 0.5 0.5 E1 C1 A1 Q1 Q2 A2 C2 E2 e c a q q a c e P1 P2 1 A1 C1 E1 P1 Q1 e c a q C2 A2 Q2 P2 E2 0.5

“Full IBD Method” -The likelihood for each pedigree (i) is calculated as: P(IBD = 0)(2π-k)|Σ0|-1/2exp[-1/2(yi - μ)’Σ0-1(yi - μ)] P(IBD = 1)(2π-k)|Σ1|-1/2exp[-1/2(yi - μ)’Σ1-1(yi - μ)] P(IBD = 2)(2π-k)|Σ2|-1/2exp[-1/2(yi - μ)’Σ2-1(yi - μ)] + Σ0 q2 + a2 + e2 a2 = q2 + a2 + e2 Σ1 0.5q2 + a2 = q2 + a2 + e2 Σ2 q2 + a2 = q2 + a2 + e2 -Computationally efficient -More power? (e.g. π = 0.5; p0 = 0.25, p1 = 0.5, p2 = 0.25) p0 = 0.5, p1 = 0, p2 = 0.5) -Difficult to specify in large sibships/pedigrees ^