! Sib pair ACE data #define nvar 1 #define nvarx2 2 #define nallele 2 #ngroups 2 ACE data Data NInput=13 ! 13 input variables missing=-99.989998 Rectangular File=marker5.dat ! read data from file Labels locus pednum id1 id2 pibd0 pibd1 pibd2 ace1 ace2 a1s1 a2s1 a1s2 a2s2 ! aisj is allele i of sibling j ! select only those sib pairs with no missing marker genotypes select if a1s1 ^= 0 select if a2s1 ^= 0 select if a1s2 ^= 0 select if a2s2 ^= 0 ! Phenotype sib 1, phenotype sib 2, probabilities of sharing 0, 1, and 2 ! alleles ibd, genotype of sib 1, genotype of sib 2 Select ace1 ace2 pibd0 pibd1 pibd2 a1s1 a2s1 a1s2 a2s2 ; ! use the genotypic information to define the mean and covariance models Definition_variables pibd0 pibd1 pibd2 a1s1 a2s1 a1s2 a2s2 ; Begin Matrices; A Lower nvar nvar Free ! Polygenic component z lower nvar nvar Free ! Unique environmental component q lower nvar nvar free ! Linkage component b full 3 1 ! IBD probabilities (from Genehunter or ! Mapmaker/SIBS) d full 1 3 ! will contain 0, .5, 1 c fu 1 1 ! constant to contain .5 ! association specification E Full 1 4 ! First allele of sib 1 F Full 1 4 ! Second allele of sib 1 G Full 1 4 ! First allele of sib 2 H Full 1 4 ! Second allele of sib 2 L Full 1 4 ! 0 1 0 1 - matrix to offset to a_w column m fu 1 1 free ! grand mean U Unit 4 1 ! Unit matrix W Full nallele 2 Free ! a_b and a_w parameters, rows are alleles, ! a_b is first column, a_w second column End Matrices; ! fix the constants matrix d 0 .5 1 matrix c .5 ! starting values for matrices used in linkage component of model Matrix A .5 Matrix z .7 Matrix q .1 ! matrices used for association component of model ! which take genotypes in columns 1 and 3, with columns 2 and 4 ! fixed to 1. Matrix E 1 1 1 1 Matrix F 1 1 1 1 Matrix G 1 1 1 1 Matrix H 1 1 1 1 ! L is a constant Matrix L 0 1 0 1 matrix m 0 ! starting value for estimate of the overall mean ! put ibd probabilities in b Specify b pibd0 pibd1 pibd2 ! put sib genotypes into matrices Specify E a1s1 0 a1s1 0 Specify F a2s1 0 a2s1 0 Specify G a1s2 0 a1s2 0 Specify H a2s2 0 a2s2 0 Begin Algebra; ! compute the between effects, which are the sum of all the alleles ! in the sibship, obtained by pulling out the appropriate row of ! the first column of the W matrix, which contains the between ! effects for alleles 1 and 2, and summing those effects I = \part(W,E) + \part(W,F) + \part(W,G) + \part(W,H) ; ! compute the within effects, which use the second column of the W ! matrix. This is the difference between sib 1 and sib 2's ! genotypic scores. J = \part(W,(E+L)) + \part(W,(F+L)) - \part(W,(G+L)) - \part(W,(H+L)) ; ! compute pihat from ibd probabilities p = d*b; End Algebra; ! sib 1's mean is composed of the grand mean plus the between effect ! plus the within effect, sib 2's mean is composed of the grand mean, the ! between effect minus the within effect Means (M + I + J | M + I - J); ! the expected covariance matrix contains a polygenic component (A), ! a unique environmental component (z) and the QTL component (Q) Covariance A*A' + z*z' + q*q' | c@a*a' + p@q*q' _ c@a*a' + p@q*q' | a*a' + z*z' + q*q' ; Option nd=4 ! request 4 decimal places in output OPtion RS Multiple ! request residuals, multiple fit Option issat ! this is saturated model for submodel comparison End Constrain sum of weights on diffs to equal 0 ! this is done because a separate parameter was fitted for each ! of the two possible alleles, while it is only possible to estimate ! one parameter less than the number of alleles Constraint NI=2 Begin Matrices = Group 1; O Zero 1 2 P Unit 1 nallele End Matrices; ! a_b_1 + a_b_2 = 0 ! a_w_1 + a_w_2 = 0 Constrain P*W = O ; Option multiple option issat ! define the full model End ! equate a_b to a_w Specify 1 w 5 5 6 6 option df=-1 ! necessary to get a single df test End save combined.mxs option issat ! a_b = a_w is the new base model end ! drop both a_b and a_w against a_b = a_w - overall test of association Drop w 1 1 1 to w 2 2 2 option df=-2 End ! get the a_b = a_w result ! and then drop the linkage parameter get combined.mxs drop q 1 1 1 ! test for linkage in the presence of association end