| scanone {qtl} | R Documentation |
Genome scan with a single QTL model
Description
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.
Usage
scanone(cross, chr, pheno.col=1, model=c("normal","binary","2part","np"),
method=c("em","imp","hk","ehk","mr","mr-imp","mr-argmax"),
addcovar=NULL, intcovar=NULL, weights=NULL,
use=c("all.obs", "complete.obs"), upper=FALSE,
ties.random=FALSE, start=NULL, maxit=4000,
tol=1e-4, n.perm, perm.Xsp=FALSE, perm.strata=NULL, verbose,
batchsize=250, n.cluster=1, ind.noqtl)
Arguments
cross |
An object of class |
chr |
Optional vector indicating the chromosomes for which LOD
scores should be calculated. This should be a vector of character
strings referring to chromosomes by name; numeric values are
converted to strings. Refer to chromosomes with a preceding |
pheno.col |
Column number in the phenotype matrix which should be
used as the phenotype. This can be a vector of integers; for methods
|
model |
The phenotype model: the usual normal model, a model for binary traits, a two-part model or non-parametric analysis |
method |
Indicates whether to use the EM algorithm,
imputation, Haley-Knott regression, the extended Haley-Knott method,
or marker regression. Not all methods are available for all models.
Marker regression is performed either by dropping individuals with
missing genotypes ( |
addcovar |
Additive covariates; allowed only for the normal and binary models. |
intcovar |
Interactive covariates (interact with QTL genotype); allowed only for the normal and binary models. |
weights |
Optional weights of individuals. Should be either NULL
or a vector of length n.ind containing positive weights. Used only
in the case |
use |
In the case that multiple phenotypes are selected to be scanned, this argument indicates whether to use all individuals, including those missing some phenotypes, or just those individuals that have data on all selected phenotypes. |
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 |
maxit |
Maximum number of iterations for methods |
tol |
Tolerance value for determining convergence for methods
|
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. |
perm.Xsp |
If |
perm.strata |
If |
verbose |
In the case |
batchsize |
The number of phenotypes (or permutations) to be run
as a batch; used only for methods |
n.cluster |
If the package |
ind.noqtl |
Indicates individuals who should not be allowed a QTL effect (used rarely, if at all); this is a logical vector of same length as there are individuals in the cross. |
Details
Use of the EM algorithm, Haley-Knott regression, and the extended
Haley-Knott method 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>0, so that a permutation
test is performed, the R function scanone is called repeatedly.
If perm.Xsp=TRUE, separate permutations are performed for the
autosomes and the X chromosome, so that an X-chromosome-specific
threshold may be calculated. In this case, n.perm specifies
the number of permutations used for the autosomes; for the X
chromosome, n.perm \times \, L_A/L_X permutations
will be run, where L_A and L_X are the total genetic
lengths of the autosomes and X chromosome, respectively. More
permutations are needed for the X chromosome in order to obtain
thresholds of similar accuracy.
For further details on the models, the methods and the use of covariates, see below.
Value
If n.perm is missing, the function returns a data.frame whose
first two columns contain the chromosome IDs and cM positions.
Subsequent columns contain the LOD scores for each phenotype.
In the case of the two-part model, there are three LOD score columns
for each phenotype: LOD(p,\mu), LOD(p) and
LOD(\mu). The result is given class "scanone" and
has attributes "model", "method", and
"type" (the latter is the type of cross analyzed).
If n.perm is specified, the function returns the results of a
permutation test and the output has class "scanoneperm". If
perm.Xsp=FALSE, the function returns a matrix with
n.perm rows, each row containing the genome-wide
maximum LOD score for each of the phenotypes. In the case of the
two-part model, there are three columns for each phenotype,
corresponding to the three different LOD scores. If
perm.Xsp=TRUE, the result contains separate permutation results
for the autosomes and the X chromosome respectively, and an attribute
indicates the lengths of the chromosomes and an indicator of which
chromosome is X.
Models
The normal model is the standard model for QTL mapping (see Lander and Botstein 1989). The residual phenotypic variation is assumed to follow a normal distribution, and analysis is analogous to analysis of variance.
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, hk, and
mr are available for this model. See Xu and Atchley (1996) and
Broman (2003).
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
Boyartchuk et al. (2001) and Broman (2003). 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 \sigma. 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, analogous 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.
Methods
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).
ehk: the extended Haley-Knott method is used (like H-K,
but taking account of the variances), as described in Feenstra et
al. (2006).
mr: Marker regression is used. Analysis is performed
only at the genetic markers, and individuals with missing genotypes
are discarded. See Soller et al. (1976).
Covariates
Covariates are allowed only for the normal and binary models. The
normal model is y = \beta_q + A \gamma + Z \delta_q + \epsilon 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 binary model is
the logistic regression analog.
The LOD score is calculated comparing the likelihood of the above
model to that of the null model y = \mu + A \gamma + \epsilon.
Covariates must be numeric matrices. Individuals with any missing covariates are discarded.
X chromosome
The X chromosome must be treated specially in QTL mapping. See Broman et al. (2006).
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.
Numerous special cases must be considered, as detailed in the following table.
| 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 | ||
In the case that the number of degrees of freedom for the linkage test
for the X chromosome is different from that for autosomes, a separate
X-chromosome LOD threshold is recommended. Autosome- and
X-chromosome-specific LOD thresholds may be estimated by permutation
tests with scanone by setting n.perm>0 and using
perm.Xsp=TRUE.
Author(s)
Karl W Broman, broman@wisc.edu; Hao Wu
References
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. (2003) Mapping quantitative trait loci in the case of a spike in the phenotype distribution. Genetics 163, 1169–1175.
Broman, K. W., Sen, Ś, Owens, S. E., Manichaikul, A., Southard-Smith, E. M. and Churchill G. A. (2006) The X chromosome in quantitative trait locus mapping. Genetics, 174, 2151–2158.
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.
Feenstra, B., Skovgaard, I. M. and Broman, K. W. (2006) Mapping quantitative trait loci by an extension of the Haley-Knott regression method using estimating equations. Genetics, 173, 2111–2119.
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.
Kruglyak, 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, Ś. 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.
Xu, S., and Atchley, W.R. (1996) Mapping quantitative trait loci for complex binary diseases using line crosses. Genetics 143, 1417–1424.
See Also
plot.scanone,
summary.scanone, scantwo,
calc.genoprob, sim.geno,
max.scanone,
summary.scanoneperm,
-.scanone, +.scanone
Examples
###################
# Normal Model
###################
data(hyper)
# Genotype probabilities for EM and H-K
## Not run: 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, thr=3)
summary(out.hk, thr=3)
# An alternate method of summarizing:
# patch them together and then summarize
out <- c(out.em, out.hk)
summary(out, thr=3, format="allpeaks")
# 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
## Not run: hyper.c1n4 <- sim.geno(subset(hyper, chr=c(1,4)),
step=2.5, n.draws=8)
## End(Not run)
out.imp <- scanone(hyper.c1n4, method="imp")
summary(out.imp, thr=3)
# Plot all three results
plot(out.imp, out.hk, out.em, chr=c(1,4), lty=1,
col=c("red","blue","black"))
# extended Haley-Knott
out.ehk <- scanone(hyper, method="ehk")
plot(out.hk, out.em, out.ehk, chr=c(1,4))
# Permutation tests
## Not run: permo <- scanone(hyper, method="hk", n.perm=1000)
# Threshold from the permutation test
summary(permo, alpha=c(0.05, 0.10))
# Results above the 0.05 threshold
summary(out.hk, perms=permo, alpha=0.05)
####################
# scan with square-root of phenotype
# (Note that pheno.col can be a vector of phenotype values)
####################
out.sqrt <- scanone(hyper, pheno.col=sqrt(pull.pheno(hyper, 1)))
plot(out.em - out.sqrt, ylim=c(-0.1,0.1),
ylab="Difference in LOD")
abline(h=0, lty=2, col="gray")
####################
# Stratified permutations
####################
extremes <- (nmissing(hyper)/totmar(hyper) < 0.5)
## Not run: operm.strat <- scanone(hyper, method="hk", n.perm=1000,
perm.strata=extremes)
## End(Not run)
summary(operm.strat)
####################
# X-specific permutations
####################
data(fake.f2)
## Not run: fake.f2 <- calc.genoprob(fake.f2, step=2.5)
# genome scan
out <- scanone(fake.f2, method="hk")
# X-chr-specific permutations
## Not run: operm <- scanone(fake.f2, method="hk", n.perm=1000, perm.Xsp=TRUE)
# thresholds
summary(operm)
# scanone summary with p-values
summary(out, perms=operm, alpha=0.05, pvalues=TRUE)
###################
# Non-parametric
###################
out.np <- scanone(hyper, model="np")
summary(out.np, thr=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)
## Not run: listeria <- calc.genoprob(listeria,step=2.5)
out.2p <- scanone(listeria, model="2part", upper=TRUE)
summary(out.2p, thr=c(5,3,3), format="allpeaks")
# Plot all three LOD scores together
plot(out.2p, out.2p, out.2p, lodcolumn=c(2,3,1), 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)
# Thresholds
summary(permo)
###################
# Binary model
###################
binphe <- as.numeric(pull.pheno(listeria,1)==264)
out.bin <- scanone(listeria, pheno.col=binphe, model="binary")
summary(out.bin, thr=3)
# Plot LOD for binary model with LOD(p) from 2-part model
plot(out.bin, out.2p, lodcolumn=c(1,2), lty=1, col=c("black", "red"),
chr=c(1,5,13))
# Permutation test
## Not run: permo <- scanone(listeria, pheno.col=binphe, model="binary",
n.perm=1000)
## End(Not run)
# Thresholds
summary(permo)
###################
# Covariates
###################
data(fake.bc)
## Not run: fake.bc <- calc.genoprob(fake.bc, step=2.5)
# genome scans without covariates
out.nocovar <- scanone(fake.bc)
# genome scans with covariates
ac <- pull.pheno(fake.bc, c("sex","age"))
ic <- pull.pheno(fake.bc, "sex")
out.covar <- scanone(fake.bc, pheno.col=1,
addcovar=ac, intcovar=ic)
summary(out.nocovar, thr=3)
summary(out.covar, thr=3)
plot(out.covar, out.nocovar, chr=c(2,5,10))