Package 'globaltest'

Title: Testing Groups of Covariates/Features for Association with a Response Variable, with Applications to Gene Set Testing
Description: The global test tests groups of covariates (or features) for association with a response variable. This package implements the test with diagnostic plots and multiple testing utilities, along with several functions to facilitate the use of this test for gene set testing of GO and KEGG terms.
Authors: Jelle Goeman and Jan Oosting, with contributions by Livio Finos, Aldo Solari, Dominic Edelmann
Maintainer: Jelle Goeman <[email protected]>
License: GPL (>= 2)
Version: 5.59.0
Built: 2024-07-17 12:08:36 UTC
Source: https://github.com/bioc/globaltest

Help Index

Comparative proportions for the Global Test

Description

Comparing the result of a global test performed on a subset to the test results of random subsets of the same size.

Usage

comparative(object, N = 1e3, z.scores = TRUE, trace)

Arguments

object

A gt.object, usually one in which one or more subsets of a large number of covariates were tested.
N

The number of random subsets to generate.
z.scores

If set to TRUE, compares the subset to random subsets on the basis of the z-scores of the test. If FALSE, uses the p-values instead.
trace

If set to TRUE, reports progress information. The default is to set trace to TRUE if R is in interactive mode and more than one comparative proportion is to be calculated.

Details

In a situation when many covariates out of a large set are associated with the response, it is sometimes interesting to know p-value of the tested subset compares to random subsets of the same size. The comparative function calculates the proportion of random subsets of the covariates of the same size as the tested subset that have a better score than the tested subset. This proportion is a diagnostic tool to help interpret the test result; it should not be interpreted as a p-value.

Value

An object of class gt.object with an appropriate column added to the test results matrix.

Author(s)

Jelle Goeman: [email protected]; Jan Oosting

References

The comparative proportion is an enrichment type analysis. For the pros and cons of such an analysis, see

Goeman and Buhlmann (2007) Analyzing gene expression data in terms of gene sets: methodological issues. Bioinformatics 23 (8) 980-987.

See Also

The gt function. The gt.object function and useful functions associated with that object.

Examples

# Simple examples with random data here
    # Real data examples in the Vignette

    # Random data: covariates A,B,C are correlated with Y
    set.seed(1)
    Y <- rnorm(20)
    X <- matrix(rnorm(200), 20, 10)
    X[,1:3] <- X[,1:3] + Y
    colnames(X) <- LETTERS[1:10]

    # Some subsets of interest
    my.sets <- list(c("A", "B"), c("C","D"), c("D", "E"))

    # Comparative proportions
    res <- gt(Y, X, subsets = my.sets)
    comparative(res)
    comparative(res, z.scores=FALSE)

Global Test diagnostic plots

Description

Plots to visualize the result of a Global Test in terms of the contributions of the covariates and the subjects.

Usage

covariates(object,
            what = c("p-value", "statistic", "z-score", "weighted"),
            cluster = "average", alpha = 0.05, sort = TRUE, zoom = FALSE,
            legend = TRUE, plot = TRUE, colors, alias, help.lines = FALSE,
            cex.labels = 0.6, ylim, pdf, trace)

features(...)

subjects(object,
            what = c("p-value", "statistic", "z-score", "weighted"),
            cluster = "average", sort = TRUE, mirror = TRUE,
            legend = TRUE, colors, alias, help.lines = FALSE,
            cex.labels = 0.6, ylim, pdf)

Arguments

object

A gt.object, usually created by a call to gt. The object must contain only a single test result, unless the pdf argument is used. See the help page of gt.object on reducing such an object in case it contains more than one test.
what

Gives a choice between various presentations of the same plot. See below under details.
cluster

The type of hierarchical clustering performed for the dendrogram. Default is average linkage clustering. For other options, see hclust. Setting cluster = "none" or cluster = FALSE suppresses the dendrogram altogether.
alpha

Parameter between 0 and 1. Sets the level of family-wise error control in the multiple testing procedure performed on the dendrogram. See below under details.
sort

If TRUE, the plot sorts the bars with the most significant covariates and subjects to the left, as far as is possible within the constraints of the dendrogram (if present).
zoom

If TRUE, discards non-significant branches from the dendrogram with the corresponding covariates. This is especially useful for large sets to "zoom" in on the significant results. If no dendrogram is requested, zoom = TRUE discards all covariates that are not significant after Holm multiple testing correction.
legend

If TRUE, draws a legend in the plot. To override the default labels of the legend, legend may also be given as a character vector with the labels of the legend.
plot

If FALSE, suppress all plotting.
colors

The colors to be used for the bars. See rgb for details on color specification.
alias

Optional alternative labels for the bars in the plots. Should be a character vector of the same length as the number of covariates or subjects, respectively.
help.lines

If TRUE, prints grey dotted lines that help connect the dendrogram to the bars.
cex.labels

Magnification factor for the x-axis labels.
ylim

Override for the y axis limits of the barplot.
pdf

Optional filename (character) of the pdf file to which the plots are to be written. If a filename is provided in pdf, many covariates or subjects plots of multiple tests can be made with a single call to covariates or subjects, writing the results to a pdf file.
trace

If TRUE, prints progress information. Note that printing progress information involves printing of backspace characters, which is not compatible with use of Sweave. Defaults to gt.options()$trace.
mirror

If TRUE, plots the reverse of the scores for the subjects with negative residual response, so that "good" scores are positive for all subjects.
...

All arguments of features are identical to those of covariates.

Details

These two diagnostic plots decompose the test statistics into the contributions of the different covariates and subjects to make the influence of these covariates and subjects visible.

The covariates plot exploits the fact that the global test statistic for a set of alternative covariates can be written as a weighted sum of the global test statistics for each single contributing covariate. By displaying these component global test results in a bar plot the covariates plot gives insight into the subset of covariates that is most responsible for the significant test result. The plot can show the p-values of the component tests on a reversed log scale (the default); their test statistics, with stripes showing their mean and standard deviation under the null hypothesis; the z-scores of these test statistics, standardized to mean zero and standard deviation one; or the weighted test statistics, where the test statistics are multiplied by the relative weight that each covariate carries in the overall test. See the Vignette for more details.

The dendrogram of the covariates plot is based on correlation distance if the directional argument was set to TRUE in the call to gt, and uses absolute correlation distance otherwise. The coloring of the dendrogram is based on the multiple testing procedure of Meinshausen (2008): this procedure controls the family-wise error rate on all 2n-1 hypotheses associated with the subsets of covariates induced by the clustering graph. All significant subsets are colored black; non-significant ones remain grey. This coloring serves as an additional aid to find the subsets of the covariates most contributing to a significant test result.

The features function is a synonym for covariates, using exactly the same arguments.

The subjects plot exploits the fact that the global test can be written as a sum of contributions of each individual. Each of these contributions is itself a test statistic for the same null hypothesis as the full global test, but one which puts a greater weight on the observed information of a specific subject. These test statistic of subject i is significant if, for the other subjects, similarity in the alternative covariates to subject i tends to coincide with similarity in residual response to subject i. Like the covariates plot, the subjects plot can show the p-values of these component tests on a reversed log scale (the default); their test statistics, with stripes showing their mean and standard deviation under the null hypothesis; the z-scores of these test statistics, standardized to mean zero and standard deviation one; or the weighted test statistics, where the test statistics are multiplied by the relative weight that each covariate carries in the overall test. Setting mirror=FALSE reverses the bars of subjects with a negative residual response (not applicable if p-values are plotted). The resulting statistics values have the additional interpretation that they are proportional to the first order estimates of the linear predictors of each subject under the alternative, i.e. subjects with positive values have higher means under the alternative than under the null, and subjects with negative values have lower means under the alternative than under the null. See the Vignette for more details.

The dendrogram of the subjects plot is always based on correlation distance. There is no analogue to Meinshausen's multiple testing method for this dendrogram, so multiple testing is not performed.

Value

If called to make a single plot, the covariates function returns an object of class gt.object. Several methods are available to access this object: see gt.object. The subjects function returns a matrix. If called to make multiple plots, both functions return NULL.

Note

The term "z-score" is not meant to imply a normal distribution, but just refers to a studentized score. The z-scores of the subjects plot are asymptotically normal under the null hypothesis; the z-scores of the covariates plot are asymptotically distributed as a chi-squared variable with one degree of freedom.

Author(s)

Jelle Goeman: [email protected]; Livio Finos.

References

General theory and properties of the global test are described in

Goeman, Van de Geer and Van Houwelingen (2006) Journal of the Royal Statistical Society, Series B 68 (3) 477-493.

Meinshausen's method for multiple testing

Meinshausen (2008) Biometrika 95 (2) 265-278.

For more references related to applications of the test, see the vignette GlobalTest.pdf included with this package.

See Also

Diagnostic plots: covariates, subjects.

The gt.object function and useful functions associated with that object.

Many more examples in the vignette!

Examples

# Simple examples with random data here
    # Real data examples in the Vignette

    # Random data: covariates A,B,C are correlated with Y
    set.seed(1)
    Y <- rnorm(20)
    X <- matrix(rnorm(200), 20, 10)
    X[,1:3] <- X[,1:3] + Y
    colnames(X) <- LETTERS[1:10]

    # Preparation: test
    res <- gt(Y,X)

    # Covariates
    covariates(res)
    covariates(res, what = "w")
    covariates(res, zoom = TRUE)

    # Subjects
    subjects(res)
    subjects(res, what = "w", mirror = FALSE)

    # Change legend, colors or labels
    covariates(res, legend = c("upregulated", "downregulated"))
    covariates(res, col = rainbow(2))
    covariates(res, alias = letters[1:10])

    # Extract data from the plot
    out <- covariates(res)
    result(out)
    extract(out)

Global Test

Description

Tests a low-dimensional null hypothesis against a potentially high-dimensional alternative in regression models (linear regression, logistic regression, poisson regression, Cox proportional hazards model).

Usage

gt(response, alternative, null, data, test.value,
     model = c("linear", "logistic", "cox", "poisson", "multinomial"), levels,
     directional = FALSE, standardize = FALSE, permutations = 0, subsets,
     weights, alias, x = FALSE, trace)

Arguments

response

The response vector of the regression model. May be supplied as a vector or as a formula object. In the latter case, the right hand side of response is passed on to alternative if that argument is missing, or otherwise to null.
alternative

The part of the design matrix corresponding to the alternative hypothesis. The covariates of the null model do not have to be supplied again here. May be given as a half formula object (e.g. ~a+b). In that case the intercept is always suppressed. When using the dot in a formula, make sure to avoid the half formula (~., but repeat the response on the left hand side. Alternatively, the alternative argument may also be given as an ExpressionSet object, in which case t(exprs(alternative)) is used for the alternative argument, and pData(alternative) is passed on to the data argument if that argument is missing.
null

The part of the design matrix corresponding to the null hypothesis. May be given as a design matrix or as a half formula object (e.g. ~a+b). The default for null is ~1, i.e. only an intercept. This intercept may be suppressed, if desired, with null = ~0. When given as a half formula object, one may also specifiy strata (e.g. ~strata(a)+b)

).

data

Only used when response, alternative, or null is given in formula form. An optional data frame, list or environment containing the variables used in the formulae. If the variables in a formula are not found in data, the variables are taken from environment(formula), typically the environment from which gt is called.
test.value

An optional vector regression coefficients to test. The default is to test the null hypothesis that all regression coefficients of the covariates of the alternative are zero. The test.value argument can be used to test a value other than zero. The coefficients are applied to the design matrix of alternative before any standardization (see the standardize argument).
model

The type of regression model to be tested. If omitted, the function will try to determine the model from the class and values of the response argument.
levels

Only used if response is factor. Selects a subset of levels(response) to be tested, given as a character vector. If a vector of length >1, the test uses only the subjects with the specified outcome categories. If levels is of length 1, the test reduces the response to a two-valued factor, testing the specified outcome category against the others combined.
directional

If set to TRUE, directs the power of the test especially against the alternative that the true regression coefficients under the alternative have the same sign. The default is that the power of the test does not depend on the sign of the true regression coefficients. Set negative weights for covariates that are expected to have opposite sign.
standardize

If set to TRUE, standardizes all covariates of the alternative to have unit second central moment. This makes sure that the test result is independent of the relative scaling of the covariates. The default is to let covariates with more variance have a greater weight in the test.
permutations

The number of permutations to use. The default, permutations = 0, uses the asymptotic distribution. The asymptotic distribution is the exact distribution in case of the linear model with normal errors.
subsets

Optional argument that can be used to test one or more subsets of the covariates in alternative. Can be a vector of column names or column indices of alternative, or a list of such vectors. In the latter case, a separate test will be performed for each subset.
weights

Optional argument that can be used to give certain covariates in alternative greater weight in the test. Can be a vector or a list of vectors. In the latter case, a separate test will be performed for each weight vector. If both subsets and weights are specified as a list, they must have the same length. In that case, weights vectors may have either the same length as the number of covariates in alternative, or the same length as the corresponding subset vector. Weights can be negative; the sign has no effect unless directional is TRUE.
alias

Optional second label for each test. Should be a vector of the same length as subsets. See also alias.
x

If TRUE, gives back the null and alternative design matrices. Default is not to return these matrices.
trace

If TRUE, prints progress information. This is useful if many tests are performed, i.e.\ if subsets or weights is a list. Note that printing progress information involves printing of backspace characters, which is not compatible with use of Sweave. Defaults to gt.options()$trace.

Details

The Global Test tests a low-dimensional null hypothesis against a (potentially) high-dimensional alternative, using the locally most powerful test of Goeman et al (2006). In this regression model implementation, it tests the null hypothesis response ~ null, that the covariates in alternative are not associated with the response, against the alternative model response ~ null + alternative that they are.

The test has a wide range of applications. In gene set testing in microarray data analysis alternative may be a matrix of gene expression measurements, and the aim is to find which of a collection of predefined subsets of the genes (e.g. Gene Ontology terms or KEGG pathways) is most associated with the response. In penalized regression or other machine learning techniques, alternative may be a collection of predictor variables that may be used to predict a response, and the test may function as a useful pre-test to see if training the classifier is worthwhile. In goodness-of-fit testing, null may be a model with linear terms fitted to the response, and alternative may be a large collection of non-linear terms. The test may be used in this case to test the fit of the null model with linear terms against a non-linear alternative.

See the vignette for extensive examples of these applications.

Value

The function returns an object of class gt.object. Several operations and diagnostic plots can be made from this object. See also Diagnostic plots.

Note

If null is supplied as a formula object, an intercept is automatically included. As a consequence gt(Y, X, Z) will usually give a different result from gt(Y, X, ~Z). The first call is equivalent to gt(Y, X, ~0+Z), whereas the second call is equivalent to gt(Y, X, cbind(1,Z)).

P-values from the asymptotic distribution are accurate to at least two decimal places up to a value of around 1e-12. Lower p-values are numerically less reliable.

Missing values are allowed in the alternative matrix only. Missing values are imputed conservatively (i.e. under the null hypothesis). Covariates with many missing values get reduced variance and therefore automatically carry less weight in the test result.

Author(s)

Jelle Goeman: [email protected]; Jan Oosting

References

General theory and properties of the global test are described in

Goeman, Van de Geer and Van Houwelingen (2006) Journal of the Royal Statistical Society, Series B 68 (3) 477-493.

For references related to applications of the test, see the vignette GlobalTest.pdf included with this package.

See Also

Diagnostic plots: covariates, subjects.

The gt.object function and useful functions associated with that object.

Many more examples in the vignette!

Examples

# Simple examples with random data here
    # Real data examples in the Vignette

    # Random data: covariates A,B,C are correlated with Y
    set.seed(1)
    Y <- rnorm(20)
    X <- matrix(rnorm(200), 20, 10)
    X[,1:3] <- X[,1:3] + Y
    colnames(X) <- LETTERS[1:10]

    # Compare the global test with the F-test
    gt(Y, X)
    anova(lm(Y~X))

    # Using formula input
    res <- gt(Y, ~A+B, null=~C+E, data=data.frame(X))
    summary(res)

    # Beware: null models with and without intercept
    Z <- rnorm(20)
    summary(gt(Y, X, null=~Z))
    summary(gt(Y, X, null=Z))

    # Logistic regression
    gt(Y>0, X)

    # Subsets and weights (1)
    my.sets <- list(c("A", "B"), c("C","D"), c("D", "E"))
    gt(Y, X, subsets = my.sets)
    my.weights <- list(1:2, 2:1, 3:2)
    gt(Y, X, subsets = my.sets, weights=my.weights)

    # Subsets and weights (2)
    gt(Y, X, subset = c("A", "B"))
    gt(Y, X, subset = c("A", "A", "B"))
    gt(Y, X, subset = c("A", "A", "B"), weight = c(.5,.5,1))

    # Permutation testing
    summary(gt(Y, X, perm=1e4))

Gene set testing of gene set databases using Global Test

Description

A collection of procedures for performing the Global Test on gene set databases. Three function are provided for KEGG, for Gene Ontology and for the Broad Institute's gene sets.

Usage

gtKEGG (response, exprs, ..., id, annotation, probe2entrez,
           multtest = c("Holm", "BH", "BY"), sort = TRUE)

gtGO (response, exprs, ..., id, annotation, probe2entrez,
           ontology = c("BP", "CC", "MF"), minsize=1, maxsize=Inf,
           multtest = c("Holm", "focuslevel", "BH", "BY"),
           focuslevel = 10, sort = TRUE)

gtConcept (response, exprs, ..., annotation, probe2entrez,
           conceptmatrix, concept2name = "conceptID2name.txt",
           entrez2concept = "entrezGeneToConceptID.txt", threshold = 1e-4,
           share = TRUE, multtest = c("Holm", "BH", "BY"),
           sort = TRUE)

gtBroad (response, exprs, ..., id, annotation, probe2entrez, collection,
           category = c("c1", "c2", "c3", "c4", "c5"),
           multtest = c("Holm", "BH", "BY"), sort = TRUE)

Arguments

response

The response variable of the regression model. This is passed on to the response argument of gt.
exprs

The expression measurements. May be ExpressionSet or matrix. Passed on to the alternative argument of gt.
...

Any other arguments are also passed on to gt.
id

The identifier(s) of gene sets to be tested (character vector). If omitted, tests all gene sets in the database.
annotation

The name of the probe annotation package for the microarray that was used, or the name of the genome wide annotation package for the species (e.g. org.Hs.eg.db for human). If an organism package is given, the argument probe2entrez must be supplied. If annotation is missing, the function will attempt to retrieve the annotation information from the exprs argument.
probe2entrez

Use only if no probe annotation package is available. A mapping from probe identifiers to entrez gene ids. May be an environment, named list or named vector.
multtest

The method of multiple testing correction. Choose from: Benjamini and Hochberg FDR control (BH); Benjamini and Yekutieli FDR control (BY) or Holm familywise error fontrol (Holm). For gtGO also the focus level method is available. See focusLevel.
sort

If TRUE, sorts the results to increasing p-values.
ontology

The ontology or ontologies to be used. Default is to use all three ontologies.
minsize

The minimum number of probes that may be annotated to a gene set. Gene sets with fewer annotated probes are discarded.
maxsize

The maximum number of probes that may be annotated to a gene set. Gene sets with more annotated probes are discarded.
focuslevel

The focus level to be used for the focus level method. Either a vector of gene set ids, or a numerical level. In the latter case, findFocus is called with maxsize at the specified level to find a focus level.
collection

The Broad gene set collection, created by a call to getBroadSets.
conceptmatrix

The name of the file containing the importance weights, i.e. concept profile associations between Anni concepts. In the matrix contained in the file, columns correspond to testable concepts, and rows correspond to entrez-concepts. Useable files can be downloaded from http://biosemantics.org/index.php/software/weighted-global-test.
concept2name

The name of the file containing a mapping between Anni concepts and entrez identifiers. Useable files can be downloaded from http://biosemantics.org/index.php/software/weighted-global-test.
entrez2concept

The name of the file containing a mapping between Anni concept numbers and names. Useable files can be downloaded from http://biosemantics.org/index.php/software/weighted-global-test.
threshold

The relevance threshold for importance weights. Importance weights below the threshold are treated as zero.
share

If TRUE, the function divides the importance weight of a gene over all probes corresponding to the same entrez identifier. If FALSE, all probes get the full importance weight of the gene.
category

The subcategory of the Broad collection to be tested. The default is to test all sets.

Details

These are utility functions to make it easier to do gene set testing of gene sets available in gene set databases. The functions automatically retrieve the gene sets, preprocess and select them, perform global test, do multiple testing correction, and sort the results on the basis of their p-values.

The four functions use different databases for testing. gtKEGG and gtGO use KEGG (http://www.genome.jp/kegg) and GO (http://www.geneontology.org); gtConcept uses the Anni database (http://www.biosemantics.org/anni), and gtBroad uses the MSigDB database (http://www.broadinstitute.org/gsea/msigdb). The gtConcept function differs from the other three in that it uses association weights between 0 and 1 for genes within sets, rather than having a hard cut-off for membership of a gene in a set.

All functions require that annotate and the appropriate annotation packages are installed. gtKEGG additionally requires the KEGG.db package; gtGO requires the GO.db package; gtBroad requires the user to download the XML file "msigdb_v2.5.xml" from \ http://www.broad.mit.edu/gsea/downloads.jsp, and to preprocess that file using the getBroadSets function. gtConcept requires files that can be downloaded from http://biosemantics.org/index.php/software/weighted-global-test.

Value

A gt.object.

Author(s)

Jelle Goeman: [email protected]; Jan Oosting

References

Goeman, Van de Geer, De Kort and Van Houwelingen (2004). A global test for groups of genes: testing association with a clinical outcome. Bioinformatics 20 (1) 93-99.

Goeman, Oosting, Cleton-Jansen, Anninga and Van Houwelingen (2005). Testing association of a pathway with survival using gene expression data. Bioinformatics 21 (9) 1950-1957.

See Also

The gt function. The gt.object and useful functions associated with that object.

Examples

# Examples in the Vignette

Goodness of fit testing in regression models using Global Test

Description

Tests the goodness of fit of a regression model against a specified alternative using the Global Test. Three main functions are provided: gtPS uses Penalized Splines, gtKS uses Kernel Smoothers and gtLI uses Linear Interactions. The other functions are for external use in combination with gt.

Usage

gtPS(response, null, data, 
      model = c("linear", "logistic", "cox", "poisson", "multinomial"),
      ..., covs, bdeg = 3, nint= 10, pord = 2, interact = FALSE, robust = FALSE, 
      termlabels = FALSE, returnZ = FALSE)
  
gtKS(response, null, data, 
      model = c("linear", "logistic", "cox", "poisson", "multinomial"),
      ..., covs, quant = .25, metric = c("euclidean", "pearson"), 
      kernel=c("uniform", "exponential", "triangular", "neighbours", "gauss"),
      robust = FALSE, scale = TRUE, termlabels = FALSE, returnZ = FALSE)
	
gtLI(response, null, data, ..., covs, iorder=2, termlabels = FALSE, standardize = FALSE)

bbase(x, bdeg, nint)

btensor(xs, bdeg, nint, pord, returnU=FALSE)

reparamZ(Z, pord, K=NULL, tol = 1e-10, returnU=FALSE)

reweighZ(Z, null.fit)

sterms(object, ...)

Arguments

response

The response vector of the regression model. May be supplied as a vector, as a formula object, or as an object of class lm, glm or coxph. In the last two cases, the specification of null is not required.
null

The null design matrix. May be given as a matrix or as a half formula object (e.g. ~a+b).
data

Only used when response or null is given in formula form. An optional data frame, list or environment containing the variables used in the formulae.
model

The type of regression model to be tested. If omitted, the function will try to determine the model from the class and values of the response argument.
...

Any other arguments are also passed on to gt.
covs

A variable or a vector of variables that are the covariates the smooth terms are function of.
bdeg

A vector or a list of vectors which specifies the degree of the B-spline basis, with default bdeg=3.
nint

A vector or a list of vectors which specifies the number of intervals determined by equally-spaced knots, with default nint=10.
pord

A vector or a list of vectors which specifies the order of the differences indicating the type of the penalty imposed to the coefficients, with default pord=2.
interact

TRUE to consider a multidimensional smooth function of covs.
termlabels

TRUE to consider e.g. s(log(cov)) instead of s(cov) when null=~ log(cov) and covs is missing.
robust

TRUE to obtain an overall test which combines multiple specifications of the B-spline basis arguments (when bdeg, nint and pord are lists) or multiple specifications of the bandwidth (when quant is a vector of quantiles).
returnZ

TRUE gives back the alternative design matrix used in the test.
quant

The smoothing bandwidth to be used, expressed as the percentile of the distribution of distance between observations, with default the 25th percentile. To investigate the sensitivity to different choices, quant can be a vector of percentiles. See also robust argument.
metric

A character string specifying the metric to be used. The available options are "euclidean" (the default), "pearson" and "mixed" (to be implemented). "mixed" distance is chosen automatically if some of the selected covariates are not numeric.
kernel

A character string giving the smoothing kernel to be used. This must be one of "uniform", "exponential", "triangular", "neighbours", or "Gauss", with default "uniform".
scale

TRUE to center and scale the covariates before computing the distance.
iorder

Order of the linear interactions, e.g. second order interactions, third order etc., with default iorder=2.
standardize

TRUE standardizes all covariates of the alternative to have unit second central moment. This makes sure that the test result is independent of the relative scaling of the covariates.
x

A numeric vector of values at which to evaluate the B-spline basis.
xs

A matrix or dataframe where the columns correspond to covariates values.
returnU

codeTRUE gives back the nonpenalized part.
Z

Alternative design matrix.
K

Penalty matrix (i.e. the penalty term is the quadratic form of K and the spline coefficients).
tol

Eigenvalues smaller than tol are considered zero.
null.fit

Fitted null model.
object

A gt.object from gtPS, gtKS or gtLI.

Details

These are functions to test for specific types of lack of fit by using the Global Test. Suppose that we are concerned with the adequacy of some regression model response ~ null, such as Y ~ X1 + X2. The alternative model can be cast into the generic form response ~ null + alternative, which comprises different models that accomodate to different types of lack of fit. Thus, the specification of alternative is required. It identifies the type of lack of fit the test is directed against.

By using gtPS, the alternative is given by a user specified sum of smooth functions of continuous covariates, e.g. alternative= ~ s(X1) when covs="X1" and alternative= ~ s(X1) + s(X2) when covs=c("X1","X2"). Smooth terms are constructed using P-splines as proposed by Eilers and Marx (1996). This approach consists in constructing a B-spline basis of degree bdeg with nint + 1 equidistant knots, where a difference penalty of order pord is applied to the basis coefficients. If interact=TRUE, the alternative is given by a multidimensional smooth function of covs, which is represented by a tensor product of marginal B-splines bases and Kronecker sum of the marginal penalties, e.g. alternative= ~ s(X1,X2) when covs=c("X1","X2") and interact=TRUE.

By using gtKS the alternative is given by a user specified multidimensional smooth term, e.g. alternative= ~ s(X1, X2) when covs=c("X1","X2"). Multidimensional smooth terms are represented by a kernel smoother defined by a distance measure (metric), a kernel shape (kernel) and a bandwidth (quant). Because the test is sensitive to the chosen value of quant, it is possible to specify quant as a vector of different values in combination with robust=TRUE. Distance measures for factor covariates and for the situation that both continuous and factor covariates are present are constructed as in le Cessie and van Houwelingen (1995), e.g. covs=c("X1","X2") and distance="mixed" when X1 continuous and X2 factor (to be implemented).

By using gtLI, the alternative is given by all the possible ith-order linear interactions between covs, e.g. alternative= ~ X1:X2 + X1:X3 + X2:X3 when covs=c("X1","X2","X3") and iorder=2.

The remaining functions are meant for constructing the alternative design matrix that will be used in the alternative argument of the gt function. bbase constructs the B-spline basis for the covariate x. This function is based on the functions provided by Eilers and Marx (1996). btensor builts a tensor product of B-splines for the covariates xs, which is reparameterized according with a Kroneker sum of penalties. reparamZ reparameterizes the alternative design matrix (e.g. a spline basis B) according with the order of differences pord or via the spectral decomposition of a roughness matrix K. When several smooth terms are to be combined, reweighZ assigns equal weight to each component term.

See the vignette for more examples.

Value

The function returns an object of class gt.object. Several operations and diagnostic plots can be made from this object.

Methods

sterms

(gt.object): Prints the smooth terms specified by gtPS, gtKS or gtLI.

Note

Currently linear (normal), logistic, multinomial logistic and Poisson regression models with canonical links and Cox's proportional hazards regression model are supported.

Author(s)

Aldo Solari: [email protected]

References

Eilers, Marx (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11: 89-121.

le Cessie, van Houwelingen (1995). Testing the Fit of a Regression Model Via Score Tests in Random Effects Models. Biometrics 51: 600-614.

For references related to applications of the test, see the vignette GlobalTest.pdf included with this package.

See Also

The gt function. The gt.object and useful functions associated with that object.

Examples

# Random data
    set.seed(0)
    X1<-runif(50)
    s1 <- function(x) exp(2 * x)
    e <- rnorm(50)
    Y <-  s1(X1) + e
    
    ### gtPS
    res<-gtPS(Y~X1)
    res@result
    sterms(res)
    
    # model input
    rdata<-data.frame(Y,X1)
    nullmodel<-lm(Y~X1,data=rdata)
    gtPS(nullmodel)
    
    # formula input and termlabels
    gtPS(Y~exp(2*X1),data=rdata)
    gtPS(Y~exp(2*X1),covs="exp(2 * X1)",data=rdata)
    sterms(gtPS(Y~exp(2*X1),data=rdata,termlabels=TRUE))
    
    # P-splines arguments 
    gtPS(Y~X1, bdeg=3, nint=list(a=10, b=30), pord=0)
    gtPS(Y~X1, bdeg=3, nint=list(a=10, b=30), pord=0, robust=TRUE)

    # Random data: additive model 
    X2<-runif(50)
    s2 <- function(x) 0.2 * x^11 * (10 * (1 - x))^6 + 10 * (10 * x)^3 * (1 - x)^10
    Y <-  s1(X1) + s2(X2) + e
    gtPS(Y~X1+X2)
    gtPS(Y~X1+X2, covs="X2")
    sterms(gtPS(Y~X1+X2, nint=list(a=c(10,30), b=20)))
    
    # Random data: smooth surface
    s12 <- function(a, b, sa = 1, sb = 1) {
            (pi^sa * sb) * (1.2 * exp(-(a - 0.2)^2/sa^2 - (b - 0.3)^2/sb^2) + 
            0.8 * exp(-(a - 0.7)^2/sa^2 - (b - 0.8)^2/sb^2))
            }
    Y <- s12(X1,X2) + e
    
    # Tensor product of P-splines
    res<-gtPS(Y~X1*X2, interact=TRUE)
    res@result
    sterms(res)

    ### gtKS  
    res<-gtKS(Y~X1*X2)
    res@result
    sterms(res)
    gtKS(Y~X1*X2, quant=seq(.05,.95,.05), robust=TRUE)
    
    ### gtLI  
    library(MASS)
    data(Boston)
    gtLI(medv~., data=Boston, standardize=TRUE)

Class "gt.object" for storing the result of the function gt

Description

The class gt.object is the output of a call to gt. It stores the information needed for various diagnostic plots.

Slots

These slots are not meant to be directly accessed by the user.

result:

Object of class "matrix". The number of rows of this matrix is the number of tests performed. The matrix has at least the columns "p-value", "Statistic" "Expected", "Std.dev", and "#Cov".

extra:

Object of class "data.frame". Holds additional information that may be added later about the tests performed, such as multiplicity-adjusted p-values (see p.adjust), alias names for tests and comparative proportions (see comparative).

call:

The matched call to gt.

functions:

A "list" of various functions used by the covariates and subjects functions and the various methods.

subsets:

A "list" or "NULL". Stores the subsets tested, if more than one.

structure:

A "list" or "NULL". Stores subset and superset relationships between the sets in the "subsets" slot.

weights:

A "list" or "NULL". Stores the weight vectors used for testing, if more than one.

alternative:

If gt was called with x = TRUE, stores the design matrix of the alternative hypothesis; "NULL" otherwise.

null:

If gt was called with x = TRUE, stores the design matrix of the null hypothesis; "NULL" otherwise.

directional

Stores the directional argument of the call to gt.

legend

Object of class "list". Stores appropriate legends for the covariates and subjects plots.

model

Object of class "character". Stores the model.

Methods

show

(gt.object): Prints the test results: p-value, test statistic, expected value of the test statistic under the null hypothesis, standard deviation of the test statistic under the null hypothesis, and number of covariates tested.

summary

(gt.object): Prints the test results (as show) plus additional information on the model and the test.

p.value

(gt.object): Extracts the p-values.

z.score

(gt.object): Extracts z-score: (Test statistic - Expected value) / Standard deviation.

result

(gt.object): Extracts the results matrix together with the additional (e.g. multiple testing) information in the extra slot.

extract

(gt.object): Extracts the results matrix for the leaf nodes after a call to link{covariates}, with information on direction of association.

sort

(gt.object): Sorts the pathways to increasing p-values. Equal p-values are sorted on decreasing z-scores.

"["

(gt.object): Extracts results of one or more test results if multiple tests were performed. Identical to "[[".

"[["

(gt.object): Extracts results of one or more test results if multiple tests were performed. Identical to "[".

length

(gt.object): The number of tests performed.

size

(gt.object): Extracts a vector with the number of alternative covariates tested for each test.

names

(gt.object): Extracts the row names of the results matrix.

names<-

(gt.object): Changes the row names of the results matrix. Duplicate names are not allowed, but see alias.

alias

(gt.object): Extracts the "alias" column of the results matrix that can be used to add additional information on each test perfomed.

alias<-

(gt.object): Changes the "alias" column of the results matrix. Note that unlike for names, duplicate aliases are allowed.

weights

(gt.object): extracts the effective weights of the covariates as they are used internally by the test.

subsets

(gt.object): extracts the "subsets" slot.

hist

(gt.object): Produces a histogram to visualize the permutation test statistics. Only relevant after permutation testing.

covariates

(gt.object): Produces a plot to show the influence of individual covariates on the test result. See covariates for details.

subjects

(gt.object): Produces a plot to show the influence of individual subjects on the test result. See subjects for details.

p.adjust

(gt.object): Performs multiple testing correction and produces multiplicity-corrected p-values. See p.adjust for details.

comparative

(gt.object): Compares the p-values of tests performed on a subsets or weights with p-values of random subsets of covariates of same size or randomly distributed weights. See comparative for details.

sterms

(gt.object): Prints the smooth terms specified by gtPS, gtKS or gtLI.

Author(s)

Jelle Goeman: [email protected]; Jan Oosting

See Also

gt, covariates, subjects.

Examples

# Simple examples with random data here
    # Real data examples in the Vignette

    # Random data: covariates A,B,C are correlated with Y
    Y <- rnorm(20)
    X <- matrix(rnorm(200), 20, 10)
    X[,1:3] <- X[,1:3] + 0.5*Y
    colnames(X) <- LETTERS[1:10]

    # Make a gt.object
    sets <- list(odd = c(1,3,5,7,9), even = c(2,4,6,8,10))
    res <- gt(Y, X, subsets=sets)

    # Show the results
    res
    summary(res)
    sort(res)
    p.value(res)
    subsets(res)

    # Names
    names(res)
    names(res) <- c("ODD", "EVEN")
    alias(res) <- c("odd covariates", "even covariates")

    # Multiple testing
    p.adjust(res, method = "holm")
    p.adjust(res, method = "BH")

    # Diagnostics
    weights(res)
    covariates(res[1])
    extract(covariates(res[1]))
    subjects(res[1])

    # Permutation testing
    res <- gt(Y, X, perm = 1e4)
    hist(res)

Options for globaltest package

Description

Sets various global options for the functions in the globaltest package.

Usage

gt.options (trace, trim, transpose, max.print, warn.deprecated)

Arguments

trace

(Default: TRUE). If TRUE, prints progress information whenever many tests are to be performed. Such printing of progress information involves the printing of backspace characters, which is not compatible with use of Sweave.
trim

(Default: FALSE). If FALSE, returns an error if covariates in the subsets argument of gt are not present in the data; if TRUE, silently removes these covariates, and remove duplicates.
transpose

(Default: FALSE). If TRUE, gt expects the transposed data format that is usual in genomics, in which the subjects correspond to the columns of the data matrix and the covariates (or probes) are the rows. If FALSE, gt expects the usual statistical format instead.
max.print

(Default: Inf). The maximum number of characters to print for the alias.
warn.deprecated

(Default: TRUE). Whether or not to give a warning when the deprecated globaltest function is called.

Details

The globaltest options can be set during a session, and apply to all calls to functions in the globaltest package for the rest of the session. They are not remembered between sessions.

Author(s)

Jelle Goeman: [email protected]

See Also

The gt function.

Examples

# setting options
  gt.options(max.print=45, trim=TRUE)

  # reading options
  gt.options()

Multinomial Logistic Regression

Description

Fits a multinomial logistic regression model to a nominal scale outcome.

Usage

mlogit(formula, data, control = glm.control())

Arguments

formula

An object of class formula containing a symbolic description of the model to be fit. See the documentation of formula for details.
data

An optional data frame containing the variables in the model. If not found in 'data', the variables are taken from the environment from which 'mlogit' is called.
control

A list of parameters for controlling the fitting process. See the documentation of glm.control for details.

Details

The function mlogit fits a multinomial logistic regression model for a multi-valued outcome with nominal scale. The implementation and behaviour are designed to mimic those of glm, but the options are (as yet) more limited. Missing values are not allowed in the data.

The model is fitted without using a reference outcome category; the parameters are made identifiable by the requirement that the sum of corresponding regression coefficients over the outcome categories is zero.

Value

An object of (S4) class mlogit. The class has slots: coefficients (matrix), standard.err (matrix), fitted.values (matrix), x (matrix), y (matrix), formula (formula), call (call), df.null (numeric), df.residual (numeric), null.deviance (numeric), deviance (numeric), iter (numeric), converged (logical).

Methods implemented for the mlogit class are coefficients, fitted.values, residuals and which extract the relevant quantities, and summary, which gives the same output as with a glm object.

Author(s)

Jelle Goeman: [email protected]; Jan Oosting

See Also

glm, multinom.

Examples

y <- factor(rep(1:4, 5))
  x <- 1:20
  fit <- mlogit(y ~ x)
  summary(fit)
  residuals(fit)

Multiple testing correction for the Global Test

Description

A collection of multiple testing procedures for the Global Test. Methods for the focus level procedure of Goeman and Mansmann for graph-structured hypotheses, and for the inheritance procedure based on Meinshausen.

Usage

# The focus level method:
focusLevel (test, sets, focus, ancestors, offspring,
           stop = 1, atoms = TRUE, trace)

findFocus (sets, ancestors, offspring, maxsize = 10, atoms = TRUE)


# The inheritance method:
inheritance (test, sets, weights, ancestors, offspring, Shaffer,
            homogeneous = TRUE, trace)


# Utilities for focus level and inheritance method:
leafNodes (object, alpha=0.05, type = c("focuslevel","inheritance"))

draw (object, alpha = 0.05, type = c("focuslevel","inheritance"),
      names=FALSE, sign.only = FALSE, interactive = FALSE)

Arguments

object

A gt.object, usually one in which more than one test was performed.
test

Either a function or gt.object. If a function, that function should take as its argument a vector of covariate labels, and return (raw) p-value. See the examples below. If a gt.object the call to gt that created it must have had all the covariates of sets (below) in its alternative argument.
sets

A named list representing covariate sets of the hypotheses of interest, for which adjusted p-values are to be calculated. If it is missing but test is a gt.object, the subsets slot of that object will be used. If used in the inheritance, sets describe a tree structure of hypotheses. In this case, object of class hclust or dendrogram.
focus

The focus level of the focus level method. Must be a subset of names(sets). Represents the level of the graph at which the method is focused, i.e. has most power.
ancestors

An environment or list that maps each set in sets to all its ancestors, i.e. its proper supersets. If missing, ancestors is determined from the input of offspring, or, if that is also missing, from the input of sets (time-consuming).
offspring

An environment or list that maps each set in sets to all its offspring, i.e. its proper subsets. If missing, offspring is determined from the input of ancestors, or, if that is also missing, from the input of sets (time-consuming).
stop

Determines when to stop the algorithm. If stop is set to a value smaller than or equal to 1, the algorithm only calculates familywise error rate corrected p-values of at most stop. If stop is set to a value greater than 1, the algorithm stops when it has rejected at least stop hypotheses. If set to exactly 1, the algorithm calculates all familywise error rate corrected p-values. Corrected p-values that are not calculated are reported as NA.
atoms

If set to TRUE, the focus level algorithm partitions the offspring of each focus level set into the smallest possible building blocks, called atoms. Doing this often greatly accelerates computation, but sometimes at the cost of some power.
trace

If set to TRUE, reports progress information. The default is obtained from gt.options()$trace. Alternatively, setting trace = 2 gives much more extensive output (focusLevel only).
maxsize

Parameter to choose the height of the focus level. The focus level sets are chosen in such a way that the number of tests that is to be done for each focus level set is at most 2^maxsize - 1.
alpha

The alpha level of familywise error control for the significant subgraph.
Shaffer

If set to TRUE, it applys the Shaffer improvement. If Shaffer is NULL and object is a gt.object the procedure checks whether Shaffer=TRUE is valid, and sets the value accordingly.
weights

Optional weights vector for the leaf nodes. If it is missing but test is a gt.object, the result of weights(object) will be used. In all other cases weights is set to be uniform among all leaf nodes.
homogeneous

If set to TRUE, redistributes the alpha of rejected leaf node hypotheses homogeneously over the hypotheses under test, rather than to closest related hypotheses.
type

Argument for specifying which multiple testing correction method should be used. Only relevant if both the inheritance and the focuslevel procedures were performed on the same set of test results.
names

If set to TRUE, draws the graph with node names rather than numbers.
sign.only

If set to TRUE, draws only the subgraph corresponding to the significant nodes. If FALSE, draws the full graph with the non-significant nodes grayed out.
interactive

If set to TRUE, creates an interactive graph in which the user can see the node label by clicking on the node.

Details

Multiple testing correction becomes important if the Global Test is performed on many covariate subsets.

If the hypotheses are structured in such a way that many of the tested subsets are subsets of other sets, more powerful procedures can be applied that take advantage of this structure to gain power. Two methods are implemented in the globaltest package: the inheritance method for tree-structured hypotheses and the focusLevel method for general directed acyclic graphs. For simple multiple testing that does not use such structure, see p.adjust.

The focusLevel procedure makes use of the fact that some sets are subsets or supersets of each other, as specified by the user in the offspring and ancestors arguments. Viewing the subset and superset structure as a graph, the procedure starts testing at a focus level: a subset of the nodes of the graph. If the procedure finds significance at this focus level, it proceeds to find significant subsets and supersets of the focus level sets. Like Holm's procedure, the focus level procedure is valid regardless of the correlation structure between the test statistics.

The focus level method requires the choice of a “focus level” in the graph. The findFocus function is a utility function for automatically choosing a focus level. It chooses a collection of focus level sets in such a way that the number of tests to be done for each focus level node is at most 2^maxsize. In practice this usually means that each focus level node has at most maxsize leaf nodes as offspring. Choosing focus level nodes with too many offspring nodes may result in excessively long computation times.

The inheritance method is an alternative method for calculating familywise error rate corrected p-values. Like the focus level method, inheritance also makes use of the structure of the tested sets to gain power. In this case, however, the graph is restricted to a tree, as can be obtained for example if the tested subsets are obtained from a hierarchical clustering. The inheritance procedure is used in the covariates function. Like Holm's method and the focus level method, the inheritance procedure makes no assumptions on the joint distribution of the test statistics.

The leafNodes function extracts the leaf nodes of the significant subgraph after a focus level procedure was performed. As this graph is defined by its leaf nodes, this is the most efficient summary of the test result. Only implemented for gt.object input.

The draw function draws the graph, displaying the significant nodes. It either draws the full graph with the non-significant nodes grayed out (sign.only = TRUE), or it draws only the subgraph corresponding to the significant nodes.

See the vignette for extensive applications.

Value

The function multtest returns an object of class gt.object with an appropriate column added to the test results matrix.

The focusLevel and inheritance functions returns a gt.object if a gt.object argument was given as input, otherwise it returns a matrix with a column of raw p-values and a column of corrected p-values.

The function leafNodes returns a gt.object.

findFocus returns a character vector.

Note

In the graph terminology of the focus level method, ancestor means superset, and offspring means subset.

The validity of the focus level procedure depends on certain assumptions on the null hypothesis that is tested for each set. See the paper by Goeman and Mansmann (cited below) for the precise assumptions. Similar assumptions are necessary for the Shaffer improvement of the inheritance procedure.

Author(s)

Jelle Goeman: [email protected]; Livio Finos

References

The methods used by multtest:

Holm (1979) A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6: 65-70.

Benjamini and Hochberg (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B 57: 289-300.

Benjamini and Yekutieli (2001) The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29 (4) 1165-1188.

The focus level method:

Goeman and Mansmann (2008) Multiple testing on the directed acyclic graph of gene ontology. Bioinformatics 24 (4) 537-544.

The inheritance method:

Meinshausen (2008) Hierarchical testing of variable importance. Biometrika 95 (2), 265-278.

For references related to applications of the test, see the vignette GlobalTest.pdf included with this package.

See Also

The gt function. The gt.object function and useful functions associated with that object.

Many more examples in the vignette!

Examples

# Simple examples with random data here
    # Real data examples in the Vignette

    # Random data: covariates A,B,C are correlated with Y
    set.seed(1)
    Y <- rnorm(20)
    X <- matrix(rnorm(200), 20, 10)
    X[,1:3] <- X[,1:3] + Y
    colnames(X) <- LETTERS[1:10]

    # Some subsets of interest
    my.sets1 <- list(abc = LETTERS[1:3], cde  = LETTERS[3:5],
                     fgh = LETTERS[6:8], hij = LETTERS[8:10])
    res <- gt(Y, X, subsets = my.sets1)

    # Simple multiple testing
    p.adjust(res)
    p.adjust(res, "BH")

    # A whole structure of sets
    my.sets2 <- as.list(LETTERS[1:10])
    names(my.sets2) <- letters[1:10]
    my.sets3 <- list(all = LETTERS[1:10])
    my.sets <- c(my.sets2,my.sets1,my.sets3)

    # Do the focus level procedure
    # Choose a focus level by hand
    my.focus <- c("abc","cde","fgh","hij")
    # Or automated
    my.focus <- findFocus(my.sets, maxsize = 8)
    resF <- focusLevel(res, sets = my.sets, focus = my.focus)
    leafNodes(resF, alpha = .1)

    # Compare
    p.adjust(resF, "holm")

    # Focus level with a custom test
    Ftest <- function(set) anova(lm(Y~X[,set]))[["Pr(>F)"]][1]
    focusLevel(Ftest, sets=my.sets, focus=my.focus)

    # analyze data using inheritance procedure
    res <- gt(Y, X, subsets = list(colnames(X)))
    # define clusters on the covariates X
    hcl=hclust(dist(t(X)))
    # Do inheritance procedure
    resI=inheritance(res, sets = hcl)
    resI
    leafNodes(resI, alpha = .1)

    # inheritance procedure with a custom test
    inheritance(Ftest, sets = hcl, Shaffer=TRUE)