[Gsdesign-commits] r146 - pkg/man

[noreply at r-forge.r-project.org]

Author: keaven
Date: 2009-05-04 22:42:23 +0200 (Mon, 04 May 2009)
New Revision: 146

Removed:
   pkg/man/sflogisitic.Rd
Log:
Renamed sflogisitic.Rd to sfLogistic.Rd

Deleted: pkg/man/sflogisitic.Rd
===================================================================
--- pkg/man/sflogisitic.Rd	2009-05-04 20:38:31 UTC (rev 145)
+++ pkg/man/sflogisitic.Rd	2009-05-04 20:42:23 UTC (rev 146)
@@ -1,128 +0,0 @@
-\name{sfLogistic}
-\alias{sfLogistic}
-\alias{sfNormal}
-\alias{sfExtremeValue}
-\alias{sfExtremeValue2}
-\alias{sfCauchy}
-\alias{sfBetaDist}
-
-\title{4.6: Two-parameter Spending Function Families}
-\description{The functions \code{sfLogistic()}, \code{sfNormal()}, \code{sfExtremeValue()}, \code{sfExtremeValue2()}, \code{sfCauchy()}, 
-and \code{sfBetaDist()} are all 2-parameter spending function families.
-These provide increased flexibility in some situations where the flexibility of a one-parameter spending function 
-family is not sufficient.
-These functions all allow fitting of two points on a cumulative spending function curve; in this case, four parameters
-are specified indicating an x and a y coordinate for each of 2 points.
-Normally each of these functions will be passed to \code{gsDesign()} in the parameter 
-\code{sfu} for the upper bound or
-\code{sfl} for the lower bound to specify a spending function family for a design.
-In this case, the user does not need to know the calling sequence.
-The calling sequence is useful, however, when the user wishes to plot a spending function as demonstrated in the examples; note, however, that an automatic \eqn{\alpha}{alpha}- and \eqn{\beta}{beta}-spending function plot is also available.
-}
-
-\usage{
-sfLogistic(alpha, t, param)
-sfNormal(alpha, t, param)
-sfExtremeValue(alpha, t, param)
-sfExtremeValue2(alpha, t, param)
-sfCauchy(alpha, t, param)
-sfBetaDist(alpha, t, param)
-}
-\arguments{
-	\item{alpha}{Real value \eqn{> 0} and no more than 1. Normally, 
-\code{alpha=0.025} for one-sided Type I error specification
-	or \code{alpha=0.1} for Type II error specification. However, this could be set to 1 if for descriptive purposes
-	you wish to see the proportion of spending as a function of the proportion of sample size or information.}
-	\item{t}{A vector of points with increasing values from 0 to 1, inclusive. Values of the proportion of 
-	sample size or information for which the spending function will be computed.}
-	\item{param}{In the two-parameter specification, \code{sfBetaDist()} requires 2 positive values, while
-	\code{sfLogistic()}, \code{sfNormal()}, \code{sfExtremeValue()}, \code{sfExtremeValue2()} and \code{sfCauchy()} require the first parameter 
-	to be any real value and the second to be a positive value. 
-	The four parameter specification is \code{c(t1,t2,u1,u2)}
-	where the objective is that \code{sf(t1)=alpha*u1} and \code{sf(t2)=alpha*u2}.
-	In this parameterization, all four values must be between 0 and 1 and \code{t1 < t2}, \code{u1 < u2}.
-}}
-\value{An object of type \code{spendfn}. See \code{\link{Spending Functions}} for further details.}
-\details{
-\code{sfBetaDist(alpha,t,param)} is simply \code{alpha} times the incomplete beta cumulative distribution 
-function with parameters
-\eqn{a} and \eqn{b} passed in \code{param} evaluated at values passed in \code{t}. 
-
-The other spending functions take the form
-\deqn{\alpha F(a+bF^{-1}(t))}
-where \eqn{F()} is a cumulative distribution function with values \eqn{> 0} on the real line (logistic for \code{sfLogistic()}, 
-normal for \code{sfNormal()}, extreme value for \code{sfExtremeValue()} and Cauchy for \code{sfCauchy()}) and
-\eqn{F^{-1}()} is its inverse.
-
-For the logistic spending function this simplifies to
-\deqn{\alpha (1-(1+e^a(t/(1-t))^b)^{-1}).}
-
-For the extreme value distribution with \deqn{F(x)=\exp(-\exp(-x))} this simplifies to 
-\deqn{\alpha \exp(-e^a (-\ln t)^b).} Since the extreme value distribution is not symmetric, there is also a version
-where the standard distribution is flipped about 0. This is reflected in \code{sfExtremeValue2()} where
-\deqn{F(x)=1-\exp(-\exp(x)).}
-
-}
-
-\seealso{\link{Spending Functions}, \code{\link{gsDesign}}, \link{gsDesign-package}}
-\note{The manual is not linked to this help file, but is available in library/gsdesign/doc/manual.pdf
-in the directory where R is installed.}
-
-\author{Keaven Anderson \email{keaven\_anderson at merck.com}, Jennifer Sun, John Zhang}
-\references{
-Jennison C and Turnbull BW (2000), \emph{Group Sequential Methods with Applications to Clinical Trials}.
-Boca Raton: Chapman and Hall.
-}
-
-\examples{
-# design a 4-analysis trial using a Kim-DeMets spending function 
-# for both lower and upper bounds 
-x<-gsDesign(k=4, sfu=sfPower, sfupar=3, sfl=sfPower, sflpar=1.5)
-
-# print the design
-x
-
-# plot the alpha- and beta-spending functions
-plot(x, plottype=5)
-
-# start by showing how to fit two points with sfLogistic
-# plot the spending function using many points to obtain a smooth curve
-# note that curve fits the points x=.1,  y=.01 and x=.4,  y=.1 
-# specified in the 3rd parameter of sfLogistic
-plot(0:100/100,  sfLogistic(1, 0:100/100, c(.1, .4, .01, .1))$spend, 
-    xlab="Proportion of final sample size", 
-    ylab="Cumulative Type I error spending", 
-    main="Logistic Spending Function Examples", 
-    type="l", cex.main=.9)
-lines(0:100/100, sfLogistic(1, 0:100/100, c(.01, .1, .1, .4))$spend, lty=2)
-
-# now just give a=0 and b=1 as 3rd parameters for sfLogistic 
-lines(0:100/100, sfLogistic(1, 0:100/100, c(0, 1))$spend, lty=3)
-
-# try a couple with unconventional shapes again using the xy form in the 3rd parameter
-lines(0:100/100, sfLogistic(1, 0:100/100, c(.4, .6, .1, .7))$spend, lty=4)
-lines(0:100/100, sfLogistic(1, 0:100/100, c(.1, .7, .4, .6))$spend, lty=5)
-legend(x=c(.0, .475), y=c(.76, 1.03), lty=1:5, 
-legend=c("Fit (.1, 01) and (.4, .1)", "Fit (.01, .1) and (.1, .4)", 
-    "a=0,  b=1", "Fit (.4, .1) and (.6, .7)", "Fit (.1, .4) and (.7, .6)"))
-
-# set up a function to plot comparsons of all 2-parameter spending functions
-plotsf <- function(alpha, t, param)
-{   
-    plot(t, sfCauchy(alpha, t, param)$spend, xlab="Proportion of enrollment", 
-    ylab="Cumulative spending", type="l", lty=2)
-    lines(t, sfExtremeValue(alpha, t, param)$spend, lty=5)
-    lines(t, sfLogistic(alpha, t, param)$spend, lty=1)
-    lines(t, sfNormal(alpha, t, param)$spend, lty=3)
-    lines(t, sfExtremeValue2(alpha, t, param)$spend, lty=6, col=2)
-    lines(t, sfBetaDist(alpha, t, param)$spend, lty=7, col=3)
-    legend(x=c(.05, .475), y=.025*c(.55, .9), lty=c(1, 2, 3, 5, 6, 7), col=c(1, 1, 1, 1, 2, 3), 
-        legend=c("Logistic", "Cauchy", "Normal", "Extreme value", 
-        "Extreme value 2", "Beta distribution"))
-}
-# do comparison for a design with conservative early spending
-# note that Cauchy spending function is quite different from the others
-param <- c(.25, .5, .05, .1)
-plotsf(.025, t=seq(0, 1, .01), param)
-}
-\keyword{design}