Bivariate linkage analysis for mapping quantitative trait loci in pedigrees: Comparison of methods and assessment of the test statistics distributions in the NEMO study

Authors: A Saint Pierre, B Mangin, M Martinez, Collaborators:JM Kaufman, A Ostertag, M Cohen-Solal, A Boland, I Van Pottelbergh, K Toye, MC de Vernejoul

Multivariate linkage analysis Multiple phenotypes are often correlated with each other to some degree & these correlations may results from common genetic effects Joint analysis uses the correlation structure and thus may have greater power to map QTLs over univariate analysis

Variance Component model

What is the null distribution of the bivariate linkage test ?

(Amos et al, 1994; Almasy et al, 1998)

• Model over-parameterized: (σ2QTL,X, σ2QTL,Y,σQTLXY) not free parameters Three asymptotic distributions proposed: 2 2

• Univariate 2 2 2 Ω f = σQTL , X ×Π f + σ C,Y ×Φ f + σ E , X × Id f Parameters: 2 σ QTL QTL ,X :  2 σ C , X : Polygenic  2 σ E , X : Environment

• Bivariate

Π = Π : Proportions of alleles shared IBD  f ( ij ) f  Φ = Φ : Coefficients of relationship ( )  f ij f

 (σ ,σ , σ Q TL , X Y ) : Q T L  2 2  (σ C , X , σ C ,Y , σ C , X Y ) : P oly ge n ic  2 2  (σ E , X , σ E ,Y , σ E , X Y ) : E n viro nm en t 2 Q TL , X

Parameters:

2 Q T L ,Y

1

2) Almasy et al, 1997 (B)

1

3) Amos et al, 2001 (C)

4

Suggestions: • Reduce the number of df (Almasy et al, 1997) Constraint test: ρQTL,X = ±1 →σQTL, XY = ±σQTL,XσQTL,Y Two asymptotic distributions proposed: 2 1

1) Amos et al, 2001 (D)

4

2) Mangin, pers. com. Wang, 2003 (E)

AIM

χ 0 + 1 2 χ 12 + 1 4 χ 22 1 χ 12 + 1 χ 22 2 2

• Alternative method (Mangin et al, 1998) S_PC test : 1) PCA Analysis of traits X and Y → PC1, PC2 2) Univariate VC analysis of PC1 and PC2 (Uncorrelated) Asymptotic distribution : 1 4 χ 02 + 1 2 χ 12 + 1 4 χ 22

2 2  H 0 : σ QTL , X = σ QTL ,Y = σ QTL, XY = 0  2 2  H 1: σ QTL , X > 0 or σ QTL ,Y > 0 or σ QTL , XY ≠ 0

Linkage test:

χ 1 + 1 2 χ 2 + 1 4 χ 32 χ 2 + 1 2 χ 12 + 1 4 χ 22 4 0 1 χ2 + 1 χ2 + 1 χ2 4 0 2 1 4 3

1) De Andrade et al, 1997 (A)

Asses bivariate tests distributions in NEMO data

N.E.M.O.: NEtwork on Male Osteoporosis in Europe

Simulation Methods:

Families selected through a male (probands) with low BMD values at lumbar spine (LS) or femoral neck (FN) 103 families (821 individuals - 624 have DNA, 597 phenotyped): Mean size: ~ 8 ind/fam Heritability :

Pedigree structure, family information & phenotypes kept as observed in NEMO. 1)Marker genotypes simulated under H0 : No linkage for LS nor FN

h2 (p