1. 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

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

4. “Pi hat” method ^ -where π = p2 + 0.5 x p1 -compare against ACE modelQ1 e c a q C2 A2 Q2 P2 E2
1 / 0.5
1 / π ^
-where π = p x p1
-compare against ACE model
(50:50 χ02 χ12) ^

5. “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

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

7. “Full IBD” method 1 A1 C1 E1 P1 Q1 e c a q C2 A2 Q2 P2 E2 0.5 1 0.51
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

8. “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 ^