MST Sample Cross object

Description

Created with 'SimCrossCausal()'.

Details

'CMSTCross' is created with 'SimCrossCausal()' and used in several examples.

Source

'SimCrossCausal'

Examples

data(CMSTCross)

Perform CMST Tests on cross object

Description

Performs 6 separate CMST tests (3 versions, 2 penalties).

Usage

CMSTtests(
  cross,
  pheno1,
  pheno2,
  Q.chr,
  Q.pos,
  addcov1 = NULL,
  addcov2 = NULL,
  intcov1 = NULL,
  intcov2 = NULL,
  method = c("par", "non.par", "joint", "all"),
  penalty = c("bic", "aic", "both"),
  verbose = FALSE,
  highobj = NULL,
  cand.reg = NULL,
  lod.thr = NULL
)

CMSTtestsList(
  cross,
  pheno1,
  pheno2,
  Q.chr,
  Q.pos,
  addcov1 = NULL,
  addcov2 = NULL,
  intcov1 = NULL,
  intcov2 = NULL,
  method = c("par", "non.par", "joint", "all"),
  penalty = c("bic", "aic", "both"),
  verbose = TRUE
)

GetCisCandReg(highobj, cand.reg, lod.thr = NULL)

Arguments

Details

Explain method and penalty here.

References

Chaibub Neto E, Broman AT, Keller MP, Attie AD, Zhang B, Zhu J, Yandell BS, Causal model selection hypothesis tests in systems genetics. Genetics (in review).

See Also

'CMSTCross', 'PrecTpFpMatrix', 'FitAllTests'

Examples

## Not run: 
# Create CMSTCross object
example(SimCrossCausal)
nms <- names(CMSTCross$pheno)
out1 <- CMSTtests(CMSTCross, 
                  pheno1 = nms[1], 
                  pheno2 = nms[2],
                  Q.chr = 1,
                  Q.pos = 55,
                  addcov1 = NULL, 
                  addcov2 = NULL, 
                  intcov1 = NULL, 
                  intcov2 = NULL, 
                  method = "all",
                  penalty = "both")
out1[1:6]
out1[7]
out1[8:12]
out1[13:17]
## list of phenotypes
out2 <- CMSTtests(CMSTCross, 
                  pheno1 = nms[1], 
                  pheno2 = nms[-1],
                  Q.chr = 1,
                  Q.pos = 55,
                  addcov1 = NULL, 
                  addcov2 = NULL, 
                  intcov1 = NULL, 
                  intcov2 = NULL, 
                  method = "par",
                  penalty = "bic")
out2

## End(Not run)

Determine false positive and true positive rates for known targets.

Description

Determine how well different tests do to predict candidates of regulation.

Usage

FitAllTests(cross, pheno1, pheno2, Q.chr, Q.pos, verbose = TRUE)

CitTests(LL, GG, TT)

CombineTests(comap, file)

JoinTestOutputs(comap, tests, file = NULL)

Arguments

Details

'FitAllTests()' invokes 7 tests. The hidden routine 'CitTests()' is invoked by call to 'FitAllTests()'; this is hidden because we do not recommend its use.

'JoinTestOutputs()' joins results of 'FitAllTests()', either from a list 'tests' or from a collection of files prefixed by 'file'. The joined tests from 'JoinTestOutputs' are summarized with 'PrecTpFpMatrix()' using the biologically validated true positives, false positives and precision, for the inferred causal relations. We define a true positive as a statistically significant causal relation between a gene and a putative target gene when the putative target gene belongs to the known signature of the gene. Similarly, we define a false positive as a statistically significant causal relation between a gene and a putative target gene when the target gene does not belong to the signature. (For the AIC and BIC methods that do not provide a p-value measuring the significance of the causal call, we simply use the detected causal relations in the computation of true and false positives). The validated precision is computed as the ratio of true positives by the sum of true and false positives. The 'PrecTpFpMatrix' computes these measures to both all genes, and to cis genes only. Simulations suggest only non-parametric tests need to be adjusted using Benjamini-Hochberg via 'p.adjust.np()'.

Value

List containing

Author(s)

Elias Chaibub Neto

See Also

p.adjust

Examples

## Not run: 
example(GetCandReg)
## Suppose y1 is causal with targets y2 and y3.
targets <- list(y1 = c("y2","y3"))

tests <- list()
for(k in seq(names(comap.targets))) {
  tests[[k]] <- FitAllTests(CMSTCross, pheno1 = names(comap.targets)[k],
                      pheno2 = comap.targets[[k]],
                      Q.chr = cand.reg[k, 4],
                      Q.pos = cand.reg[k, 5])
}
names(tests) <- names(comap.targets)
tests <- JoinTestOutputs(comap.targets, tests)

PrecTpFpMatrix(alpha = seq(0.01, 0.10, by = 0.01),
  val.targets = targets, all.orfs = CMSThigh$names, tests = tests,
  cand.reg = cand.reg, cis.cand.reg = cis.cand.reg)

## End(Not run)

Get genetic information on candidate regulators and co-mapping traits.

Description

Get chromosome (phys.chr) and physical position in cM (phys.pos), along with the LOD score (peak.lod) at the peak position (peak.pos), and the chromosome where the peak is located (peak.chr). Some candidates may map to the same chromosome where they are physically located.

Usage

GetCandReg(highobj, annot, traits)

GetCoMappingTraits(highobj, cand.reg)

Arguments

Details

Traits that map to positions close to their physical locations are said to map in cis (local linkages). Traits that map to positions away from their physical locations are said to map in trans (distal linkages). There is no unambiguous way to determine how close a trait needs to map to its physical location in order to be classified as cis. Our choice is to classify a trait as cis if the 1.5-LOD support interval (Manichaikul et al. 2006) around the LOD peak contains the trait's physical location, and if the LOD score at its physical location is higher the the LOD threshold. The function 'GetCisCandReg' determines which of the candidate regulators map in cis. The function 'GetCoMappingTraits' returns a list with the putative targets of each trait. A trait is included in the putative target list of a trait when its LOD peak is greater than 'lod.thr' and the 'drop' LOD support interval around the peak contains the location of the trait's QTL. The function 'JoinTestOutputs' currently relies on external files that contain results of 'FitAllTests'. It needs to be rewritten to save space.

Value

'GetCoMappingTraits' returns a list with each element being the names of co-mapping traits for a particular name in 'traits'. 'GetCandReg' returns a data frame while 'GetCisCandReg' returns a list with a similar candidate regulator data frame as the element 'cis.reg', and the index of trait names as the element 'cis.index'. The elements of the candidate regulator data frame are as follows ('peak.pos.lower' and 'peak.pos.upper' only for 'GetCisCandReg'):

Author(s)

Elias Chaibub Neto

References

Manichaikul et al. (2006) Genetics

See Also

'highlod', 'FitAllTests', scanone

Examples

## Not run: 
# Create CMSTCross object
example(SimCrossCausal)
# data(CMSTCross) loaded lazily
CMSTscan <- scanone(CMSTCross, pheno.col = 1:3, method = "hk")
CMSThigh <- highlod(CMSTscan)
traits <- names(CMSTCross$pheno)
annot <- data.frame(name = traits, traits = traits, chr = rep(1, 3),
 Mb.pos = c(55,10,100))
annot$cM.pos <- annot$Mb.pos
cand.reg <- GetCandReg(CMSThigh, annot, traits)
cis.cand.reg <- GetCisCandReg(CMSThigh, cand.reg)
comap.targets <- GetCoMappingTraits(CMSThigh, cand.reg)

## End(Not run)

Get common QTLs for phenotypes

Description

Perform joint QTL mapping for phenotypes with marginal LOD peak positions higher than LOD threshold and within set distance of each other

Usage

GetCommonQtls(
  cross,
  pheno1,
  pheno2,
  thr = 3,
  peak.dist = 5,
  addcov1 = NULL,
  addcov2 = NULL,
  intcov1 = NULL,
  intcov2 = NULL
)

Arguments

References

Chaibub Neto E, Broman AT, Keller MP, Attie AD, Zhang B, Zhu J, Yandell BS, Causal model selection hypothesis tests in systems genetics. Genetics (in review).

Examples

## Not run: 
# Create CMSTCross object
example(SimCrossCausal)
# data(CMSTCross) loaded lazily
commqtls <- GetCommonQtls(CMSTCross, 
                          pheno1 = "y1", 
                          pheno2 = "y3",
                          thr = 3,
                          peak.dist = 5,
                          addcov1 = NULL, 
                          addcov2 = NULL, 
                          intcov1 = NULL, 
                          intcov2 = NULL)
commqtls

## End(Not run)

Compute Precision, True Positives, and False Positives

Description

The 'PrecTpFpMatrix' function calculates precision, true positives, and false positives for various tests. It is used to evaluate the performance of QTL mapping methods.

Usage

PrecTpFpMatrix(alpha, val.targets, all.orfs, tests, cand.reg, cis.cand.reg)

Arguments

Value

A list of matrices containing precision, true positives, and false positives for each method and significance level.

Examples

## Not run: 
results <- PrecTpFpMatrix(alpha = seq(0.01, 0.1, by = 0.01),
                          val.targets = validated_genes,
                          all.orfs = all_genes,
                          tests = test_results,
                          cand.reg = candidate_regions,
                          cis.cand.reg = cis_regions)

## End(Not run)

Simulate Cross for Causal Tests

Description

Creates cross with certain pattern of dependence across phenotypes.

Usage

SimCrossCausal(
  n.ind,
  len,
  n.mar,
  beta,
  add.eff,
  dom.eff,
  sig2.1 = 1,
  sig2.2 = 1,
  eq.spacing = FALSE,
  cross.type = c("bc", "f2"),
  normalize = FALSE
)

Arguments

References

Chaibub Neto E, Broman AT, Keller MP, Attie AD, Zhang B, Zhu J, Yandell BS, Causal model selection hypothesis tests in systems genetics. Genetics (in review).

Examples

## Not run: 
set.seed(987654321)
CMSTCross <- SimCrossCausal(n.ind = 100, 
  len = rep(100, 3), n.mar = 101,
  beta = rep(0.5, 2), add.eff = 1, dom.eff = 0, 
  sig2.1 = 0.4, sig2.2 = 0.1, eq.spacing = FALSE, 
  cross.type = "bc", normalize = TRUE)
CMSTCross <- calc.genoprob(CMSTCross, step = 1)
save(CMSTCross, file = "CMSTCross.RData", compress = TRUE)
class(CMSTCross)

## End(Not run)

Add phenotypes to cross object.

Description

Add phenotypes to cross object by checking index.

Usage

add.phenos(cross, newdata = NULL, index = NULL)

Arguments

Details

The name index must be a phenotype in the cross object. The row names of newdata are matched with values of index.

Value

object of class cross with added phenotypes

Author(s)

Brian S. Yandell, byandell@wisc.edu

See Also

read.cross

Examples

## Not run: 
data(hyper)
x <- data.frame(x = rnorm(nind(hyper)))
hyperx <- add.phenos(hyper, x)

## End(Not run)

Summary of threshold results

Description

Summary of threshold results.

Usage

filter.threshold(
  cross,
  pheno.col,
  latent.eff,
  res.var,
  lod.thrs,
  drop.lod = 1.5,
  s.quant,
  n.perm,
  alpha.levels,
  qh.thrs = summary(hotperm(cross, max(s.quant), n.perm, alpha.levels, lod.thrs, verbose
    = verbose)),
  ww.thrs = summary(ww.perm(highobj, n.perm, lod.thrs, alpha.levels)),
  addcovar = NULL,
  intcovar = NULL,
  verbose = FALSE,
  ...
)

Arguments

Value

List with items

References

Manichaikul A, Dupuis J, Sen S, Broman KW (2006) Poor performance of bootstrap confidence intervals for the location of a quantitative trait locus. Genetics 174: 481-489.

See Also

hotperm, ww.perm, scanone

Pull high LOD values with chr and pos.

Description

Pull high LOD values with chr and pos.

Usage

highlod(
  scans,
  lod.thr = 0,
  drop.lod = 1.5,
  extend = TRUE,
  restrict.lod = FALSE,
  ...
)

## S3 method for class 'highlod'
print(x, ...)

## S3 method for class 'highlod'
summary(object, ...)

## S3 method for class 'highlod'
plot(x, ..., quant.level = NULL, sliding = FALSE)

pull.highlod(object, chr, pos, ...)

## S3 method for class 'highlod'
max(x, lod.thr = NULL, window = NULL, quant.level = NULL, ...)

Arguments

Details

The highlod condenses a scanone object to the peaks above a lod.thr and/or within drop.lod of such peaks. The pull.highlod pulls out the entries at a particular genomic location or interval of locations. Summary, print, plot, max and quantile methods provide ways to examine a highlod object.

Value

Data frame with

Author(s)

Brian S Yandell and Elias Chaibub Neto

See Also

highlod, hotperm

Examples

ncross1 <- sim.null.cross(chr.len = rep(100, 4),
                          n.mar = 51,
                          n.ind = 100,
                          type = "bc",
                          n.phe = 1000,
                          latent.eff = 3,
                          res.var = 1,
                          init.seed = 123457)
cross1 <- include.hotspots(cross = ncross1,
                           hchr = c(2, 3, 4),
                           hpos = c(25, 75, 50),
                           hsize = c(100, 50, 20),
                           Q.eff = 2,
                           latent.eff = 3,
                           lod.range.1 = c(2.5, 2.5),
                           lod.range.2 = c(5, 8),
                           lod.range.3 = c(10, 15),
                           res.var = 1,
                           n.phe = 1000,
                           init.seed = 12345)
scan1 <- scanone(cross1, pheno.col = 1:1000, method = "hk")
high1 <- highlod(scan1, lod.thr = 2.11, drop.lod = 1.5)
pull.highlod(high1, chr = 2, pos = 24)
summary(high1, lod.thr = 2.44)
max(high1, lod.thr = seq(2.11, 3.11, by = .1))

Conduct NL and N permutation tests

Description

This set of functions compute the permutation LOD thresholds for the NL-method and the permutation hotspot size thresholds for the N-method. The output is a list with two elements: the NL- and the N-method's threshold matrices. The NL-method output is a nN (number of spurious hotspot sizes) by nalpha (number of significance levels) threshold matrix. Note that for the NL-method we have a single "alpha" since we use the same significance level for QTL mapping and permutation significance. The N-method output is a nlod (number of LOD thresholds) by nalpha (number of significance levels) threshold matrix. Note that here we have two "alphas", one for the QTL mapping (the LOD thresholds) and one for the permutation significance (alpha levels).

Usage

hotperm(
  cross,
  n.quant,
  n.perm,
  lod.thrs,
  alpha.levels,
  drop.lod = 1.5,
  window = NULL,
  verbose = FALSE,
  init.seed = 0,
  addcovar = NULL,
  intcovar = NULL,
  ...
)

## S3 method for class 'hotperm'
print(x, ...)

## S3 method for class 'hotperm'
summary(object, quant.levels, ...)

## S3 method for class 'summary.hotperm'
print(x, ...)

## S3 method for class 'hotperm'
plot(x, probs = seq(0.9, 0.99, by = 0.01), level = 0.95, ...)

Arguments

Author(s)

Elias Chaibub Neto and Brian S Yandell

Examples

ncross1 <- sim.null.cross(chr.len = rep(100, 4),
                          n.mar = 51,
                          n.ind = 100,
                          type = "bc",
                          n.phe = 1000,
                          latent.eff = 3,
                          res.var = 1,
                          init.seed = 123457)
cross1 <- include.hotspots(cross = ncross1,
                           hchr = c(2, 3, 4),
                           hpos = c(25, 75, 50),
                           hsize = c(100, 50, 20),
                           Q.eff = 2,
                           latent.eff = 3,
                           lod.range.1 = c(2.5, 2.5),
                           lod.range.2 = c(5, 8),
                           lod.range.3 = c(10, 15),
                           res.var = 1,
                           n.phe = 1000,
                           init.seed = 12345)
pt.scanone <- scanone(ncross1, method = "hk", n.perm = 1000)
alphas <- seq(0.01, 0.10, by=0.01)
lod.thrs <- summary(pt.scanone, alphas)
# This takes awhile, so we save the object.
## Not run: 
hotperm1 <- hotperm(cross = cross1,
                    n.quant = 300,
                    n.perm = 100,
                    lod.thrs = lod.thrs,
                    alpha.levels = alphas,
                    drop.lod = 1.5,
                    verbose = FALSE)
save(hotperm1, file = "hotperm1.RData", compress = TRUE)
# data(hotperm1) 
summary(hotperm1)

## End(Not run)

Hotspot Permutation Sample

Description

Created with 'hotperm()'.

Details

'hotperm1' is created with 'hotperm()' and used in several examples.

Source

'SimCrossCausal'

Examples

data(hotperm1)

Hotspot size routines.

Description

Determine hotspot sizes and display. Use individual threshold and quantile thresholds as provided.

Usage

hotsize(hotobject, ...)

## S3 method for class 'scanone'
hotsize(hotobject, lod.thr = NULL, drop.lod = 1.5, ...)

## S3 method for class 'highlod'
hotsize(hotobject, lod.thr = NULL, window = NULL, quant.level = NULL, ...)

## S3 method for class 'hotsize'
print(x, ...)

## S3 method for class 'hotsize'
summary(object, ...)

## S3 method for class 'hotsize'
plot(
  x,
  ylab = "counts",
  quant.axis = pretty(x$max.N),
  col = c("black", "red", "blue"),
  by.chr = FALSE,
  maps = NULL,
  title = "",
  ...
)

## S3 method for class 'hotsize'
max(x, ...)

Arguments

Value

hotsize methods return an object of class hotsize, which is essentially an object of class summary.scanone with additional attributes for lod.thr, window, and quant.level.

Author(s)

Brian S Yandell and Elias Chaibub Neto

See Also

highlod, hotperm

Examples

example(highlod)
hots1 <- hotsize(high1)
summary(hots1)
plot(hots1)

Generate hotspots for the simulated examples in the manuscript.

Description

Generate hotspots for the simulated examples in the manuscript.

Usage

include.hotspots(
  cross,
  hchr,
  hpos,
  hsize,
  Q.eff,
  latent.eff,
  lod.range.1,
  lod.range.2,
  lod.range.3,
  res.var = 1,
  n.pheno,
  init.seed
)

Arguments

neqtl.R Ported from http://github.com/kbroman/neqtl

Description

neqtl.R Ported from http://github.com/kbroman/neqtl

Usage

neqtl(sigpos.out, chr, pos, win = 5)

Arguments

Code for parallelizing R/qtlhot.

Description

Code for parallelizing R/qtlhot. See installed parallel directory for proper use. There is apparently an S3 parallel method, so doc has to be as shown below, even though it is called as parallel.qtlhot.

Usage

parallel.qtlhot(x, data = 1, ..., dirpath = ".")

Arguments

Author(s)

Brian S Yandell and Elias Chaibub Neto

See Also

read.cross

Compute Quantiles of High LOD Scores

Description

The 'quantile_highlod' function calculates quantiles of high LOD scores from a 'highlod' object. It is used to summarize the distribution of LOD scores across the genome.

Usage

quantile_highlod(
  x,
  probs = NULL,
  lod.thr = NULL,
  n.quant,
  n.pheno,
  max.quantile = TRUE,
  ...
)

Arguments

Value

A numeric vector or matrix of quantiles, depending on the input parameters.

Examples

## Not run: 
highlod_obj <- highlod(scan1, lod.thr = 2.5)
quantiles <- quantile_highlod(highlod_obj, probs = seq(0.1, 0.9, by = 0.1))

## End(Not run)

Compute Quantiles for Hotperm Results

Description

The 'quantile_hotperm' function calculates quantiles for permutation test results. It is used to summarize the distribution of hotspot sizes and LOD scores.

Usage

quantile_hotperm(x, probs = attr(x, "alpha.levels"), ..., lod.thr = NULL)

Arguments

Value

A numeric vector or matrix of quantiles, depending on the input parameters.

Examples

## Not run: 
hotperm_obj <- hotperm(cross, n.quant = 300, n.perm = 100, lod.thrs = c(2.5, 3.0))
quantiles <- quantile_hotperm(hotperm_obj, probs = seq(0.1, 0.9, by = 0.1))

## End(Not run)

Wrapper routine for simulations.

Description

Simulate 'nSim' realizations of cross object with 'n.pheno' phenotypes with correlation 'latent.eff'. All simulations use the same genotypes in the 'cross' object.

Usage

sim.hotspot(
  nSim,
  cross,
  n.pheno,
  latent.eff,
  res.var = 1,
  n.quant,
  n.perm,
  alpha.levels,
  lod.thrs,
  drop.lod = 1.5,
  verbose = FALSE
)

Arguments

Value

'sim.null.cross' simulates an object of class 'cross'. 'sim.null.pheno.data' simulates a data frame of phenotypes. 'sim.hotspot' uses these other routines to simulate a hotspot, returning an list object.

Author(s)

Elias Chaibub Neto and Brian S. Yandell

See Also

sim.null.cross, read.cross.

Examples

ncross1 <- sim.null.cross(chr.len = rep(100, 4),
                          n.mar = 51,
                          n.ind = 100,
                          type = "bc",
                          n.phe = 1000,
                          latent.eff = 3,
                          res.var = 1,
                          init.seed = 123457)
cross1 <- include.hotspots(cross = ncross1,
                           hchr = c(2, 3, 4),
                           hpos = c(25, 75, 50),
                           hsize = c(100, 50, 20),
                           Q.eff = 2,
                           latent.eff = 3,
                           lod.range.1 = c(2.5, 2.5),
                           lod.range.2 = c(5, 8),
                           lod.range.3 = c(10, 15),
                           res.var = 1,
                           n.phe = 1000,
                           init.seed = 12345)

Generates a "null dataset" cross

Description

Generates a "null dataset" cross

Usage

sim.null.cross(
  chr.len = rep(400, 16),
  n.mar = 185,
  n.ind = 112,
  type = "bc",
  n.pheno = 6000,
  latent.eff = 1.5,
  res.var = 1,
  init.seed = 92387475
)

Arguments

Conduct West-Wu (Q) permutation tests

Description

This function computes the West/Wu permutation thresholds. The output is a nlod (number of LOD thresholds) by nalpha (number of significance levels) matrix, where each entry shows the hotspot size significance threshold of the West/Wu approach. Note we have two "alphas" here, one for the QTL mapping (the LOD thresholds) and one for the permutation significance (alpha levels of lod.thrs).

Usage

ww.perm(highobj, n.perm, lod.thrs, alpha.levels, verbose = FALSE)

## S3 method for class 'ww.perm'
print(x, ...)

## S3 method for class 'ww.perm'
summary(object, alpha.levels = attr(object, "alpha.levels"), ...)

Arguments

Details

Note that I separated the original ww.permutations() into a piece that do the actual permutations [ww.perm.matrix() function] and a piece that summarizes it [the ww.summary() function] in the same way you did with the NL.N.permutations() function.

Perform permutation tests to assess the statistical significance of the hotspots detected using the West-Wu Q-method permutations. The ww.perm function implements the Q-method's permutation scheme (see the Method's section of Chaibub Neto et a. 2012, for details). The n.perm parameter specifies the number of simulations. Here we set it to 100 in order to save time. In practice, we recommend at least 1,000 permutations. The function's output is a matrix with 100 rows representing the permutations, and 10 columns representing the QTL mapping thresholds. Each entry ij, represents the maximum number of significant linkages across the entire genome detected at permutation i, using the LOD threshold j. The ww.summary function computes the Q-method's hotspot size permutation thresholds, that is, the 1-alpha quantiles for each one of the QTL mapping LOD thrsholds in lod.thrs. For instance, the entry at row 10 and column 1 of the Q.1.thr matrix tells us that the 99% percentile of the permutation distribution of genome wide maximum hotspot size based on a QTL mapping threshold of 2.11 is 27.00. In other words, any hotspot greater than 27 is considered statistically significant at a 0.01 significance level when QTL mapping is done using a 2.11 LOD threshold. In general, we are often interested in using the same error rates for the QTL mapping and hotspot analysis. That is, if we adopt a QTL mapping threshold that controls GWER at a 1% level (in our case, 3.11) we will also want to consider alpha = 0.01 for the hotspot analysis, leading to a hotspot threshold of 12.00. Therefore, we are usually more interested in the diagonal of Q.1.thr. We adopted a GWER of 5%, and the corresponding Q-method's permutation threshold is 18. According to this threshold, all hotspots are significant.

Author(s)

Elias Chaibub Neto and Brian S Yandell

Examples

## Not run: 
## All unspecified objects come from vignette qtlhot.
set.seed(12345)
Q.1 <- ww.perm(high1, n.perm = 100, lod.thrs, alphas)
Q.1.thr <- summary(Q.1, alphas)
Q.1.thr
diag(Q.1.thr)

set.seed(12345)
Q.2 <- ww.perm(high2, 100, lod.thrs, alphas)
Q.2.thr <- summary(Q.2, alphas)

## End(Not run)