pi0FAMT {FAMT}

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

model

'FAMTmodel' object (see modelFAMT)

method

algorithm used to estimate the proportion of null p-values. Available options are "density" and "smoother" (as described in Friguet and Causeur, 2010)

diagnostic.plot

if TRUE the histogram of the p-values with the estimate of pi0 horizontal line is plotted. With the "smoother" method, an additional graph is displayed showing the spline curve used to estimate pi0. With the "density" method, the estimated convex density of the p-values is plotted onto the histogram

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)