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\name{locfdr}
\alias{locfdr}
\title{Local False Discovery Rate Calculation}
\description{
Compute local false discovery rates, following the definitions and
description in references listed below.}
\usage{
locfdr(zz, bre = 120, df = 7, pct = 0, pct0 = 1/4, nulltype = 1, type =
0, plot = 1, mult, mlests, main = " ", sw = 0)
}
\arguments{
\item{zz}{A vector of summary statistics, one for each case under
simultaneous consideration. The
calculations assume a large number of cases, say
\code{length(zz)} exceeding 200. Results may be improved by transforming
zz so that its elements are theoretically distributed
as \eqn{N(0,1)} under the null hypothesis. See the locfdr vignette
for tips on creating zz.}
\item{bre}{Number of breaks in the discretization of the \eqn{z}-score axis,
or a vector of breakpoints fully describing the
discretization. If \code{length(zz)} is small, such as when the
number of cases is less than about 1000, set bre to a number
lower than the default of 120.}
\item{df}{Degrees of freedom for fitting the estimated
density \eqn{f(z)}.}
\item{pct}{Excluded tail proportions of \eqn{zz}'s when fitting
\eqn{f(z)}. \code{pct=0} includes full range of \eqn{zz}'s. pct can
also be a 2-vector, describing the fitting range.}
\item{pct0}{Proportion of the \eqn{zz} distribution used in fitting the
null density \eqn{f0(z)} by central matching. If a 2-vector,
e.g. \code{pct0=c(0.25,0.60)}, the range [pct0[1],
pct0[2]] is used. If a scalar, [pct0, 1-pct0] is used.}
\item{nulltype}{Type of null hypothesis assumed in estimating \eqn{f0(z)},
for use in the fdr calculations. 0 is the theoretical null
\eqn{N(0,1)}, 1 is maximum likelihood estimation, 2 is central
matching estimation, 3 is a split normal version of 2.}
\item{type}{Type of fitting used for \eqn{f}; 0 is a natural spline, 1 is
a polynomial, in either case with degrees of freedom df [so
total degrees of freedom including the intercept is \code{df+1}.]}
\item{plot}{Plots desired. 0 gives no plots. 1 gives single
plot showing the histogram of \eqn{zz} and fitted
densities \eqn{f} and \eqn{p0*f0}.
2 also gives plot of fdr, and the right and
left tail area Fdr curves. 3 gives instead the f1 cdf
of the estimated fdr curve; plot=4 gives all three plots.}
\item{mult}{Optional scalar multiple (or vector of multiples) of the
sample size for calculation of the corresponding
hypothetical Efdr value(s).}
\item{mlests}{Optional vector of initial values for (delta0, sigma0) in
the maximum likelihood iteration.}
\item{main}{Main heading for the histogram plot when \code{plot>0}.}
\item{sw}{Determines the type of output desired. 2 gives a list
consisting of the last 5 values listed under Value below.
3 gives the square matrix of dimension bre-1 representing the influence
function of log(fdr). Any other value
of sw returns a list consisting of the first 5 (6 if mult is
supplied) values listed below.}
}
\details{
See the locfdr vignette for details and tips.
}
\value{
\item{fdr}{the estimated local false discovery rate for each case,
using the selected type and nulltype.}
\item{fp0}{the estimated parameters delta (mean of f0), sigma
(standard deviation of f0), and p0, along with
their standard errors.}
\item{Efdr}{the expected false discovery rate for the non-null cases,
a measure of the experiment's power as described in Section 3
of the second reference. Overall Efdr and right and left values are
given, both for the specified nulltype and for nulltype 0. If
\code{nulltype==0}, values are given for nulltypes 1 and 0.}
\item{cdf1}{a 99x2 matrix giving the estimated cdf of fdr under the
non-null distribution f1. Large values of the cdf for small fdr
values indicate good power; see Section 3 of the second
reference. Set plot to 3 or 4 to see the cdf1 plot.}
\item{mat}{A matrix of estimates of \eqn{f(x)},
\eqn{f0(x)}, \eqn{fdr(x)}, etc. at the \eqn{bre-1} midpoints "x"
of the break discretization, convenient for comparisons and
plotting. Details are in the locfdr vignette.}
\item{z.2}{the interval along the zz-axis outside of which $fdr(z)<0.2$,
the locations of the yellow triangles in the histogram plot. If
no elements of zz on the left or right satisfy the criterion,
the corresponding element of z.2 is NA.}
\item{call}{the function call.}
\item{mult}{If the argument mult was supplied, vector of the ratios of
hypothetical Efdr for the supplied multiples of the sample
size to Efdr for the actual sample size.}
\item{pds}{The estimates of p0, delta, and sigma.}
\item{x}{The bin midpoints.}
\item{f}{The values of \eqn{f(z)} at the bin midpoints.}
\item{pds.}{The derivative of the estimates of p0, delta, and sigma with
respect to the bin counts.}
\item{stdev}{The delta-method estimates of the standard deviations of
the p0, delta, and sigma estimates.}
}
\references{
Efron, B. (2004) "Large-scale simultaneous hypothesis testing: the choice of
a null hypothesis", Jour Amer Stat Assoc, \bold{99}, pp. 96--104
Efron, B. (2006) "Size, Power, and False Discovery Rates"
Efron, B. (2007) "Correlation and Large-Scale Simultaneous Significance
Testing", Jour Amer Stat Assoc, \bold{102}, pp. 93--103
\url{http://statweb.stanford.edu/~ckirby/brad/papers/}
}
\author{Bradley Efron, Brit B. Turnbull, and Balasubramanian Narasimhan}
\examples{
## HIV data example
data(hivdata)
w <- locfdr(hivdata)
}
\keyword{htest}% at least one, from doc/KEYWORDS
\keyword{models}% __ONLY ONE__ keyword per line
|
