scanone {qtl} | R Documentation |
Genome scan with a single QTL model, with possible allowance for covariates, using any of several possible models for the phenotype and any of several possible numerical methods.
scanone(cross, chr, pheno.col=1, model=c("normal","binary","2part","np"), method=c("em","imp","hk","mr","mr-imp","mr-argmax"), addcovar=NULL, intcovar=NULL, weights=NULL, upper=FALSE, ties.random=FALSE, start=NULL, maxit=4000, tol=1e-4, n.perm, trace=TRUE)
cross |
An object of class cross . See
read.cross for details. |
chr |
Vector indicating the chromosomes for which LOD scores should be calculated. |
pheno.col |
Column number in the phenotype matrix which should be used as the phenotype. |
model |
The phenotypic model: the usual normal model, a model for binary traits, a two-part model or non-parametric. |
method |
Indicates whether to use the EM algorithm,
imputation, Haley-Knott regression, or marker regression. Not all
methods are available for all models. Marker regression is performed
either by dropping individuals with missing genotypes ("mr" ),
or by first filling in missing data using a single imputation
("mr-imp" ) or by the Viterbi algorithm ("mr-argmax" ). |
addcovar |
Additive covariates; allowed only for the normal model. |
intcovar |
Interactive covariates (interact with QTL genotype); allowed only for the normal model. |
weights |
Optional weights of individuals. Should be either NULL
or a vector of length n.ind containing positive weights. Used only
in the case model="normal" |
upper |
Used only for the two-part model; if true, the ``undefined'' phenotype is the maximum observed phenotype; otherwise, it is the smallest observed phenotype. |
ties.random |
Used only for the non-parametric ``model;'' if TRUE, ties in the phenotypes are ranked at random. If FALSE, average ranks are used and a corrected LOD score is calculated. |
start |
Used only for the EM algorithm with the normal model and
no covariates. If NULL , use the usual starting values; if
length 1, use random initial weights for EM; otherwise, this should
be a vector of length n+1 (where n is the number of possible
genotypes for the cross), giving the initial values for EM. |
maxit |
Maximum number of iterations in the EM algorithm; used only in interval mapping. |
tol |
Tolerance value for determining convergence in the EM algorithm; used only in interval mapping. |
n.perm |
If specified, a permutation test is performed rather than an analysis of the observed data. This argument defines the number of permutation replicates. |
trace |
In the case n.perm is specified, display
information about the progress of the permutation tests. |
Use of the EM algorithm or Haley-Knott regression require that
multipoint genotype probabilities are first calculated using
calc.genoprob
. The imputation method uses the
results of sim.geno
.
Individuals with missing phenotypes are dropped.
In the case that n.perm
is not missing, so that a permutation
test is performed, the R function scanone
is called repeatedly.
See further details on the models, the methods and the use of covariates below.
If n.perm
is missing, the function returns a data.frame whose
first two columns contain the chromosome IDs and cM positions. The
third column contains the LOD score. In the case of the two-part
model, the third column is LOD(p,mu), while the fourth
and fifth columns are LOD(p) and LOD(mu). In the
case of no covariates, further columns specify the parameter
estimates. The data frame is given class "scanone"
and
attributes "model"
, "method"
and "type"
(the
latter is the type of cross analyzed).
If n.perm
is specified, the function returns either a vector of
length n.perm
, containing the maximum LOD scores, genome-wide,
for the permutation replicates. In the case of the two-part model, the
return value is a matrix of size n.perm x 3
, with columns
corresponding to the three different LOD scores.
The normal model is the standard model for QTL mapping. The residual phenotypic variation is assumed to follow a normal distribution, and analysis is analogous to linear regression.
The binary model is for the case of a binary phenotype, which
must have values 0 and 1. The proportions of 1's in the different
genotype groups are compared. Currently only methods em
and
mr
are available for this model.
The two-part model is appropriate for the case of a spike in the phenotype distribution (for example, metastatic density when many individuals show no metastasis, or survival time following an infection when individuals may recover from the infection and fail to die). The two-part model was described by Broman et al. (2000) and Boyartchuk et al. (2001). Individuals with QTL genotype g have probability p[g] of having an undefined phenotype (the spike), while if their phenotype is defined, it comes from a normal distribution with mean mu[g] and common standard deviation s. Three LOD scores are calculated: LOD(p,mu) is for the test of the hypothesis that p[g] = p and mu[g] = mu. LOD(p) is for the test that p[g] = p while the mu[g] may vary. LOD(mu) is for the test that mu[g] = mu while the p[g] may vary.
With the non-parametric ``model'', an extension of the
Kruskal-Wallis test is used; this is similar to the method described
by Kruglyak and Lander (1995). In the case of incomplete genotype
information (such as at locations between genetic markers), the
Kruskal-Wallis statistic is modified so that the rank for each
individual is weighted by the genotype probabilities, analgous to
Haley-Knott regression. For this method, if the argument
ties.random
is TRUE, ties in the phenotypes are assigned random
ranks; if it is FALSE, average ranks are used and a corrected LOD
score is calculate. Currently the method
argument is ignored
for this model.
em
: maximum likelihood is performed via the
EM algorithm (Dempster et al. 1977), first used in this context by
Lander and Botstein (1989).
imp
: multiple imputation is used, as described by Sen
and Churchill (2001).
hk
: Haley-Knott regression is used (regression of the
phenotypes on the multipoint QTL genotype probabilities), as described
by Haley and Knott (1992).
mr
: Marker regression is used. Analysis is performed
only at the genetic markers, and individuals with missing genotypes
are discarded.
Covariates are allowed only for the normal model, in which case the model is y = b[q] + A g + Z d[q] + e where q is the unknown QTL genotype, A is a matrix of additive covariates, and Z is a matrix of covariates that interact with the QTL genotype. The columns of z are forced to be contained in the matrix A.
The LOD score is calculated comparing the likelihood of the above model to that of the null model y = m + A g + e.
Covariates must be numeric matrices. Individuals with any missing covariates are discarded.
The X chromosome must be treated specially in QTL mapping.
If both males and females are included, male hemizygotes are allowed to be different from female homozygotes. Thus, in a backcross, we will fit separate means for the genotype classes AA, AB, AY, and BY. In such cases, sex differences in the phenotype could cause spurious linkage to the X chromosome, and so the null hypothesis must be changed to allow for a sex difference in the phenotype.
BC | Sexes | Null | Alternative | df | |
both sexes | sex | AA/AB/AY/BY | 2 | ||
all female | grand mean | AA/AB | 1 | ||
all male | grand mean | AY/BY | 1 | ||
F2 | Direction | Sexes | Null | Alternative | df |
Both | both sexes | femaleF/femaleR/male | AA/ABf/ABr/BB/AY/BY | 3 | |
all female | pgm | AA/ABf/ABr/BB | 2 | ||
all male | grand mean | AY/BY | 1 | ||
Forward | both sexes | sex | AA/AB/AY/BY | 2 | |
all female | grand mean | AA/AB | 1 | ||
all male | grand mean | AY/BY | 1 | ||
Backward | both sexes | sex | AB/BB/AY/BY | 2 | |
all female | grand mean | AB/BB | 1 | ||
all male | grand mean | AY/BY | 1 |
Karl W Broman, kbroman@jhsph.edu; Hao Wu, hao@jax.org
Boyartchuk V. L., Broman, K. W., Mosher, R. E., D'Orazio S. E. F., Starnbach, M. N. and Dietrich, W. F. (2001) Multigenic control of Listeria monocytogenes susceptibility in mice. Nature Genetics 27, 259–260.
Broman, K. W., Boyartchuk, V. L. and Dietrich, W. F. (2000) Mapping time-to-death quantitative trait loci in a mouse cross with high survival rates. Technical Report MS00-04, Department of Biostatistics, Johns Hopkins University, Baltimore, MD.
Churchill, G. A. and Doerge, R. W. (1994) Empirical threshold values for quantitative trait mapping. Genetics 138, 963–971.
Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B, 39, 1–38.
Haley, C. S. and Knott, S. A. (1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, 315–324.
Kruklyak, L. and Lander, E. S. (1995) A nonparametric approach for mapping quantitative trait loci. Genetics 139, 1421–1428.
Lander, E. S. and Botstein, D. (1989) Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121, 185–199.
Sen, S. and Churchill, G. A. (2001) A statistical framework for quantitative trait mapping. Genetics 159, 371–387.
Soller, M., Brody, T. and Genizi, A. (1976) On the power of experimental designs for the detection of linkage between marker loci and quantitative loci in crosses between inbred lines. Theor. Appl. Genet. 47, 35–39.
plot.scanone
,
summary.scanone
, scantwo
,
calc.genoprob
, sim.geno
,
max.scanone
################### # Normal Model ################### data(hyper) # Genotype probabilities for EM and H-K hyper <- calc.genoprob(hyper, step=2.5) out.em <- scanone(hyper, method="em") out.hk <- scanone(hyper, method="hk") # Summarize results: peaks above 3 summary(out.em, 3) summary(out.hk, 3) # Plot the results plot(out.hk, out.em) plot(out.hk, out.em, chr=c(1,4), lty=1, col=c("blue","black")) # Imputation; first need to run sim.geno # Do just chromosomes 1 and 4, to save time hyper.c1n4 <- sim.geno(subset(hyper, chr=c(1,4)), step=2.5, n.draws=8) out.imp <- scanone(hyper.c1n4, method="imp") summary(out.imp, 3) # Plot all three results plot(out.imp, out.hk, out.em, chr=c(1,4), lty=1, col=c("red","blue","black")) # Permutation tests ## Not run: permo <- scanone(hyper, method="hk", n.perm=1000) ## End(Not run)quantile(permo, 0.95) ################### # Non-parametric ################### out.np <- scanone(hyper, model="np") summary(out.np, 3) # Plot with previous results plot(out.np, chr=c(1,4), lty=1, col="green") plot(out.imp, out.hk, out.em, chr=c(1,4), lty=1, col=c("red","blue","black"), add=TRUE) ################### # Two-part Model ################### data(listeria) listeria <- calc.genoprob(listeria,step=2.5) out.2p <- scanone(listeria, model="2part", upper=TRUE) summary(out.2p, 5) # Plot all three LOD scores together plot(out.2p, out.2p, out.2p, lodcolumn=c(4,5,3), lty=1, chr=c(1,5,13), col=c("red","blue","black")) # Permutation test ## Not run: permo <- scanone(listeria, model="2part", upper=TRUE, n.perm=1000) ## End(Not run)apply(permo, 2, quantile, 0.95) ################### # Binary model ################### listeria <- subset(listeria, ind=!is.na(listeria$pheno[,1])) listeria$pheno[,2] <- rep(0,nind(listeria)) listeria$pheno[listeria$pheno[,1]==264,2] <- 1 out.bin <- scanone(listeria, pheno.col=2, model="binary") summary(out.bin, 3) # Plot LOD for binary model with LOD(p) from 2-part model plot(out.bin, out.2p, lodcolumn=c(3,4), lty=1, col=c("black", "red"), chr=c(1,5,13)) # Permutation test ## Not run: permo <- scanone(listeria, pheno.col=2, model="binary", n.perm=1000) ## End(Not run)quantile(permo, 0.95) ################### # Covariates ################### data(fake.bc) plot(fake.bc) fake.bc <- calc.genoprob(fake.bc, step=2.5) # genome scans without covariates out.nocovar <- scanone(fake.bc) # genome scans with covariates ac <- fake.bc$pheno[,c("sex","age")] ic <- fake.bc$pheno[,"sex"] out.covar <- scanone(fake.bc, pheno.col=1, addcovar=ac, intcovar=ic) summary(out.nocovar,3) summary(out.covar,3) plot(out.covar,out.nocovar,chr=c(2,5,10))