Approximate score test for association in related people

grammar {GenABEL}R Documentation

Approximate score test for association in related people


Fast approximate score test for association between a trait and genetic polymorphism, in samples of related individuals. When used with argument "times=1", it is equivalent to running qtscore on "environmental residuals" from polygenic. However, it does not produce correct results with permutations, because the raw trait values, which are not exchangeable, are permuted. Use qtscore on "environmental residuals" when you want to have empirical GW significance with GRAMMAR method.




h2object An object returned by polygenic polygenic mixed model analysis routine. The sub-objects used are measuredIDs, residualY, h2an\$estimates (last element, total variance, only), and InvSigma. One can supply grammar with a fake h2object, containing these list elements.
data An object of
snpsubset Index, character or logical vector with subset of SNPs to run analysis on. If missing, all SNPs from data are used for analysis.
idsubset Index, character or logical vector with subset of IDs to run analysis on. If missing, all people from data/cc are used for analysis.
strata Stratification variable. If provieded, scores are computed within strata and then added up.
times If more then one, the number of replicas to be used in derivation of empirical genome-wide significance. NOTE: do not use times > 1 unless you are really sure you understand what you are doing!
quiet do not print warning messages
bcast If the argument times > 1, progress is reported once in bcast replicas
clambda If inflation facor Lambda is estimated as lower then one, this parameter controls if the original P1df (clambda=TRUE) to be reported in Pc1df, or the original 1df statistics is to be multiplied onto this "deflation" factor (clambda=FALSE). With GRAMMAR, Lambda is expected ot be less than 1. If a numeric value is provided, it is used as a correction factor.
propPs proportion of non-corrected P-values used to estimate the inflation factor Lambda, passed directly to the estlambda


Approximate score test is performed using the formula

sigma^4 (((G-E[G]) V^(-1) residualY)^2)/((G-E[G]) (G-E[G]))

where $sigma^4$ is the square of the residual variance, $G$ is the vector of genotypes (coded 0, 1, 2) and $E[G]$ is a vector of (strata-specific) mean genotypic values; V^(-1) is the InvSigma and $residualY$ are residuals from the trait analysis with polygenic procedure.

Compared to score test implemented in mmscore, grammar test is faster and computation time grows only linearly with the number of subjects (with mmscore this relation is quadratic). While raw P1df from grammar are not quite correct, the GC p-values correspond very closely to these from the mmscore.


Object of class scan.gwaa-class; only 1 d.f. test is implemented currently.


Yurii Aulchenko


Aulchenko YS, de Koning DJ, Haley C. Genomewide rapid association using mixed model and regression: a fast and simple method for genome-wide pedigree-based quantitative trait loci association analysis. Genetics. 2007 177(1):577-85.

Amin N, van Duijn CM, Aulchenko YS. A genomic background based method for association analysis in related individuals. PLoS ONE. 2007 Dec 5;2(12):e1274.

See Also

grammar, qtscore, plot.scan.gwaa, scan.gwaa-class


# ge03d2.clean is rather bad data set to demonstrate grammar, 
# because this is a population-based study
#take half for speed
ge03d2.clean <- ge03d2.clean[1:100,]
gkin <- ibs(ge03d2.clean,w="freq")
h2ht <- polygenic(height ~ sex + age,kin=gkin,ge03d2.clean)
# can use "grammar", but ...
a <- grammar(h2ht,data=ge03d2.clean)
# ... use rather qtscore (note clam=FALSE), which is a better alternative for the same thing
a <- qtscore(h2ht$pgres,data=ge03d2.clean,clam=FALSE)
# compare to GC:
b <- qtscore(height ~ sex + age,data=ge03d2.clean)
# relatively large difference is due to high heritability
# note that locus at chromosome 2 should indeed be there...

[Package GenABEL version 1.6-7 Index]