Factor Analysis for Multiple Testing (FAMT) : simultaneous tests under dependence in high-dimensional data

Description

The method proposed in this package takes into account the impact of dependence on multiple testing procedures for high-throughput data as proposed by Friguet et al. (2009). The common information shared by all the variables is modeled by a factor analysis structure. The number of factors considered in the model is chosen to reduce the variance of the number of false discoveries. The model parameters are estimated thanks to an EM algorithm. Factor-adjusted tests statistics are derived, as well as the associated p-values. The proportion of true null hypotheses (an important parameter when controlling the false discovery rate) is also estimated from the FAMT model. Diagnostic plots are proposed to interpret and describe the factors.

Details

The as.FAMTdata function creates a single R object containing the data stored: - in one mandatory data-frame: the 'expression' dataset with m rows (if m tests) and n columns (n is the sample size) containing the observations of the responses. - and two optional data-frames: the 'covariates' dataset with n rows and at least 2 columns, one giving the specification to match 'expression' and 'covariates' and the other one containing the observations of at least one covariate. The optional dataset, 'annotations' can be provided to help interpreting the factors: with m rows and at least one column to identify the variables (ID).

The whole multiple testing procedure is provided in a single function, modelFAMT, but you can also choose to apply the procedure step by step, using the functions :

nbfactors (Estimation of the optimal number of factors) emfa (EM fitting of the Factor Analysis model).

The modelFAMT also provides the individual test statistics and corresponding p-values like the raw.pvalues function.

A function summaryFAMT provides some key elements of classical summaries either on 'FAMTdata' or 'FAMTmodel'.

The estimation of the proportion of true null hypotheses from a 'FAMTmodel' is done by the function pi0FAMT.

The defacto function provides diagnostic plots to interpret and describe the factors.

Author(s)

David Causeur, Chloe Friguet, Magalie Houee-Bigot, Maela Kloareg.

Maintainer: David.Causeur@agrocampus-ouest.fr

References

Causeur D., Friguet C., Houee-Bigot M., Kloareg M. (2011). Factor Analysis for Multiple Testing (FAMT): An R Package for Large-Scale Significance Testing Under Dependence. Journal of Statistical Software, 40(14),1-19. https://www.jstatsoft.org/v40/i14

Friguet C., Kloareg M. and Causeur D. (2009). A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, p.1406-1415

http://famt.free.fr/

Gene annotations data frame

Description

A data frame with 6 columns describing the 9893 genes, which expressions are stored in the 'expression' dataset, in terms of functional categories, oligonucleotide size and location on the microarray. See also expression, covariates.

Usage

data(annotations)

Format

A data frame with 9893 observations on the following 6 variables.

ID

Gene identification

Name

Gene annotation (functional categories) (character)

Block

Location on the microarray(factor)

Column

Location on the microarray (factor)

Row

Location on the microarray (factor)

Length

Oligonucleotide size (numeric vector)

Source

UMR Genetique Animale - INRA/AGROCAMPUS OUEST - Rennes, France.

References

Blum Y., Le Mignon G., Lagarrigue S. and Causeur S. (2010) - A factor model to analyze heterogeneity in gene expression, BMC Bioinformatics, 11:368.

Le Mignon, G. and Desert, C. and Pitel, F. and Leroux, S. and Demeure, O. and Guernec, G. and Abasht, B. and Douaire, M. and Le Roy, P. and Lagarrigue S. (2009) - Using trancriptome profling to characterize QTL regions on chicken chromosome 5. BMC Genomics, 10:575.

Examples

data(annotations)
dim(annotations) 
summary(annotations)

Create a 'FAMTdata' object from an expression, covariates and annotations dataset

Description

The function creates a 'FAMTdata' object containing the expression, the covariates and the annotations dataset if provided. The function checks the consistency of dataframes between them. Then missing values of expression can be imputed.

Usage

as.FAMTdata(expression, covariates = NULL, annotations = NULL, idcovar = 1, 
idannot = NULL, na.action=TRUE)

Arguments

Details

The as.FAMTdata function creates a single R object containing the data stored: - in one mandatory data-frame: the 'expression' dataset with m rows (if m tests) and n columns (n is the sample size) containing the observations of the responses. - and two optional data frames: the 'covariates' dataset with n rows and at least 2 columns, one giving the specification to match 'expression' and 'covariates' and the other one containing the observations of at least one covariate. The optional dataset,'annotations', can be provided to help interpreting the factors: with m rows and at least one column to identify the variables (ID).

Value

Note

The class of the data produced with the as.FAMTdata function is called 'FAMTdata'. We advise to carry out a summary of FAMT data with the function summaryFAMT.

Author(s)

David Causeur

See Also

summaryFAMT

Examples

# The data are divided into one mandatory data-frame, the gene expressions, 
#  and two optional datasets: the covariates, and the annotations.

# The expression dataset with 9893 rows (genes) and 43 columns (arrays)
#  containing the observations of the responses.
# The covariates dataset with 43 rows (arrays) and 6 columns: 
#  the second column gives the specification to match 'expression' 
#  and 'covariates' (array identification), the other ones contain
#  the observations of covariates.
# The annotations dataset contains 9893 rows (genes) and 
#  6 columns to help interpreting the factors, the first one (ID) 
#  identifies the variables (genes). 

data(expression)
data(covariates)
data(annotations)

# Create the 'FAMTdata'
############################################
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)
# 'FAMTdata' summary
summaryFAMT(chicken)

Covariates data frame

Description

A data frame with 6 covariates in columns and 43 arrays in rows, describing the arrays of the expression dataset. See also expression, annotations

Usage

data(covariates)

Format

A data frame with 43 observations on the following 6 variables.

AfClass

a factor with levels F (Fat) L (Lean) NC (Intermediate) giving the abdominal fatness class

ArrayName

Identifying the arrays (character)

Mere

a factor with 8 levels giving the dam of the offsprings

Lot

a factor with 4 levels giving the hatch

Pds9s

a numeric vector giving the body weight

Af

a numeric vector giving the abdominal fatness, the experimental condition of main interest in this example

Source

UMR Genetique Animale - INRA/AGROCAMPUS OUEST - Rennes, France.

References

Blum Y., Le Mignon G., Lagarrigue S. and Causeur S. (2010) - A factor model to analyze heterogeneity in gene expression, BMC Bioinformatics, 11:368.

Le Mignon, G. and Desert, C. and Pitel, F. and Leroux, S. and Demeure, O. and Guernec, G. and Abasht, B. and Douaire, M. and Le Roy, P. and Lagarrigue S. (2009) - Using trancriptome profling to characterize QTL regions on chicken chromosome 5. BMC Genomics, 10:575.

Examples

data(covariates)
dim(covariates) 
summary(covariates)

FAMT factors description

Description

This function helps the user to describe and interpret the factors using some available external information on either genes or arrays. Diagnostic plots are provided.

Usage

defacto(model, plot = TRUE, axes = c(1, 2), select.covar = NULL, 
select.annot = NULL, lim.b = 0.01, lab = TRUE, cex = 1)

Arguments

Value

Author(s)

David Causeur, Maela Kloareg

See Also

as.FAMTdata, modelFAMT

Examples

## FAMT data
data(expression)
data(covariates)
data(annotations)

# Create the 'FAMTdata'
############################################
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)
# 'FAMTdata' summary 
## Not run: summaryFAMT(chicken)

# FAMT complete multiple testing procedure
############################################
model = modelFAMT(chicken,x=c(3,6),test=6,nbf=3)
# summary on the 'FAMT model'
## Not run: summaryFAMT(model)

# Factors description
############################################
chicken.defacto = defacto(model,axes=1:2,select.covar=4:5,select.annot=3:6,
cex=0.6)

Factor Analysis model adjustment with the EM algorithm

Description

A function to fit a Factor Analysis model with the EM algorithm.

Usage

emfa(data, nbf, x = 1, test = x[1], pvalues = NULL, min.err = 0.001)

Arguments

Details

In order to use this function, the number of factors is needed (otherwise, use nbfactors).

Value

Author(s)

David Causeur

References

Friguet C., Kloareg M. and Causeur D. (2009). A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, p.1406-1415

See Also

as.FAMTdata, nbfactors

Examples

## Reading 'FAMTdata'
data(expression)
data(covariates)
data(annotations)
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)

# EM fitting of the Factor Analysis model
chicken.emfa = emfa(chicken,nbf=3,x=c(3,6),test=6)
chicken.emfa$commonvar

Gene expressions data frame

Description

This dataset concerns hepatic transciptome profiles of 43 half sib male chickens selected for their variability on abdominal fatness (AF). Genes are in rows (9893 genes) and arrays in columns (43 arrays).

Usage

data(expression)

Format

A data frame with 9893 genes on 43 arrays.

Source

UMR Genetique Animale - INRA/AGROCAMPUS OUEST - Rennes, France.

References

Blum Y., Le Mignon G., Lagarrigue S. and Causeur S. (2010) - A factor model to analyze heterogeneity in gene expression, BMC Bioinformatics, 11:368.

Le Mignon, G. and Desert, C. and Pitel, F. and Leroux, S. and Demeure, O. and Guernec, G. and Abasht, B. and Douaire, M. and Le Roy, P. and Lagarrigue S. (2009) - Using trancriptome profling to characterize QTL regions on chicken chromosome 5. BMC Genomics, 10:575.

Examples

data(expression)
dim(expression)
summary(expression)

The FAMT complete multiple testing procedure

Description

This function implements the whole FAMT procedure (including nbfactors and emfa). The number of factors considered in the model is chosen to reduce the variance of the number of the false discoveries. The model parameters are estimated using an EM algorithm. Factor-adjusted tests statistics are derived, as well as the corresponding p-values.

Usage

modelFAMT(data, x = 1, test = x[1], nbf = NULL, maxnbfactors = 8, 
min.err = 0.001)

Arguments

Value

Note

The user can perform individual test statistics putting the number of factors (nbf) equal to zero. The result of this function is a 'FAMTmodel'. It is used as argument in other functions of the package : summaryFAMT, pi0FAMT or defacto. We advise to carry out a summary of FAMT model with the function summaryFAMT.

Author(s)

David Causeur

References

Friguet C., Kloareg M. and Causeur D. (2009). A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, p.1406-1415

See Also

as.FAMTdata, raw.pvalues, nbfactors, emfa, summaryFAMT

Examples

## Reading 'FAMTdata'
data(expression)
data(covariates)
data(annotations)

chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)

# Classical method with modelFAMT 
## Not run: modelpval=modelFAMT(chicken,x=c(3,6),test=6,nbf=0)
## Not run: summaryFAMT(modelpval)

# FAMT complete multiple testing procedure
# when the optimal number of factors is unknown
## Not run: model = modelFAMT(chicken,x=c(3,6),test=6)

# when the optimal number of factors has already been estimated 
 model = modelFAMT(chicken,x=c(3,6),test=6,nbf=3)

summaryFAMT(model)
hist(model$adjpval)
## End(Not run)

Estimation of the optimal number of factors of the FA model

Description

The optimal number of factors of the FA model is estimated to minimize the variance of the number of false positives (see Friguet et al., 2009).

Usage

nbfactors(data, x = 1, test = x[1], pvalues = NULL, maxnbfactors = 8, 
diagnostic.plot = FALSE, min.err = 0.001)

Arguments

Value

Author(s)

David Causeur

References

Friguet C., Kloareg M. and Causeur D. (2009). A factor model approach to multiple testing under dependence. Journal of the American Statistical Association, 104:488, p.1406-1415

See Also

as.FAMTdata, emfa

Examples

 
## Reading 'FAMTdata'
data(expression)
data(covariates)
data(annotations)
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)

# Estimation of the number of factors 
## Not run: nbfactors(chicken,x=c(3,6),test=6)

# Estimation of the number of factors with a graph of variance inflation 
# criterion
## Not run: nbfactors(chicken,x=c(3,6),test=6, diagnostic.plot=TRUE)

Estimation of the Proportion of True Null Hypotheses

Description

A function to estimate the proportion pi0 of true null hypotheses from a 'FAMTmodel' (see also function "pval.estimate.eta0" in package "fdrtool").

Usage

pi0FAMT(model, method = c("smoother", "density"), 
diagnostic.plot = FALSE)

Arguments

Details

The quantity pi0, i.e. the proportion of null hypotheses, is an important parameter when controlling the false discovery rate (FDR). A conservative choice is pi0 = 1 but a choice closer to the true value will increase efficiency and power - see Benjamini and Hochberg (1995, 2000), Black(2004) and Storey (2002) for details. The function pi0FAMT provides 2 algorithms to estimate this proportion. The "density" method is based on Langaas et al. (2005)'s approach where the density of p-values f(p) is first estimated considering f as a convex function, and the estimation of pi0 is got for p=1. The "smoother" method uses the smoothing spline approach proposed by Storey and Tibshirani(2003).

Value

pi0The estimated proportion pi0 of null hypotheses.

Author(s)

Chloe Friguet & David Causeur

References

Friguet C. and Causeur D. (2010) Estimation of the proportion of true null hypohteses in high-dimensional data under dependence. Submitted.

"density" procedure: Langaas et al (2005) Estimating the proportion of true null hypotheses, with application to DNA microarray data. JRSS. B, 67, 555-572.

"smoother" procedure: Storey, J. D., and R. Tibshirani (2003) Statistical significance for genome-wide experiments. Proc. Nat. Acad. Sci. USA, 100, 9440-9445.

See Also

modelFAMT

Examples

# Reading 'FAMTdata'
data(expression)
data(covariates)
data(annotations)
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)

# FAMT complete multiple testing procedure
model = modelFAMT(chicken,x=c(3,6),test=6,nbf=3)

# Estimation of the Proportion of True Null Hypotheses
# "density" method 
## Not run:  pi0FAMT(model,method="density",diagnostic.plot=TRUE)

# "smoother" method
pi0FAMT(model,method="smoother",diagnostic.plot=TRUE)

Calculation of classical multiple testing statistics and p-values

Description

Calculates for each gene expression, the Fisher test statistics and the corresponding p-value for H0: the gene expression does not depend on the experimental condition in a model with possible covariates.

Usage

raw.pvalues(data, x = 1, test = x[1])

Arguments

Value

Author(s)

David Causeur

See Also

as.FAMTdata

Examples

data(expression)
data(covariates)
data(annotations)

# Create the 'FAMTdata'
############################################
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)
# 'FAMTdata' summary
summaryFAMT(chicken)

# Calculation of classical p-values
############################################
# test on the 6th covariate: 
rawpval = raw.pvalues(chicken,x=6)
hist(rawpval$pval)

# with a supplementary covariate (third column of the covariates data frame)
## Not run: rawpval = raw.pvalues(chicken,x=c(3,6),test=6)
## Not run: hist(rawpval$pval)

Calculation of residual under null hypothesis

Description

internal function

Summary of a FAMTdata or a FAMTmodel

Description

The function produces summaries of 'FAMTdata' or 'FAMTmodel'. The function involves a specific method depending on the class of the main argument.

If the main argument is a 'FAMTdata' object, the function provides, for the 'expression file', the number of tests (which corresponds to the number of genes or rows), the sample size (which is the number of arrays or columns). The function provides classical summaries for 'covariates' and 'annotations' data (see summary in FAMT-package).

If the argument is a 'FAMTmodel', the function provides the numbers of rejected genes using classical and FAMT analyses, the annotation characteristics of significant genes, and the estimated proportion of true null hypotheses.

Usage

summaryFAMT(obj, pi0 = NULL, alpha = 0.15, info = c("ID", "Name"))

Arguments

Value

If the argument is a 'FAMTdata': a list with components expression:

If the argument is a 'FAMTmodel':

Author(s)

David Causeur

See Also

as.FAMTdata, modelFAMT

Examples

## Reading 'FAMTdata'
data(expression)
data(covariates)
data(annotations)
chicken = as.FAMTdata(expression,covariates,annotations,idcovar=2)

## Summary of a 'FAMTdata'
#############################################
summaryFAMT(chicken)

## Summary of a 'FAMTmodel'
#############################################
# FAMT complete multiple testing procedure 
model = modelFAMT(chicken,x=c(3,6),test=6,nbf=3)
summaryFAMT(model)