exact.n (version 1.1.1)

POWER: Exact Power of Test for Selected Sample Sizes.

Description

For known values of the sizes n0, this function computes the exact probability of rejecting the null as a function of baseline probability.

Usage

POWER(
  n0,
  n1,
  alpha = 0.05,
  delta = 0,
  psi = 0,
  type = "lr",
  sided = 1,
  p0 = NULL,
  obj = NULL
)

Value

list with element x (containing values of baseline probability) and element y (containing corresponding exact powers)

Arguments

n0

control sample size

n1

treatment sample size

alpha

value of nominal size of test

delta

value of clinically relevant difference

psi

null value of risk difference p1-p0

type

either "lr" for approximate or "elr" for quasi-exact test

sided

(1 or 2 sided test)

p0

baseline probability. If missing, a grid of values is created for plotting. A scalar value can also be supplied.

obj

Optional object with all possible p-values. Must be a list with elements y0, y1, P (typically output of lr.rd or ESTEP.rd). If not supplied then object is generated from n0, n1 and psi.

Author

Chris J. Lloyd

Details

p0 values must be between max(0,-delta) and min(1,1-delta)

References

C.J. Lloyd (2022) Exact samples sizes for clinical trials subject to size and power constraints. Preprint. tools:::Rd_expr_doi("10.13140/RG.2.2.11828.94085")

Examples

oldpar <- graphics::par()
# Typical usage
#       POWER(n0=65,n1=82,psi=0,type="lr") # Exact size of approximate lr test
#       POWER(n0=65,n1=82,psi=0,type="elr",delta=.2) # Exact power of quasi exact test
# To make examples run faster, the package includes objects that contain
# all possible values of various tests when n0=65, n1=82.
load(system.file('files', "lr.stats.Rdata", package = 'exact.n'))
# All possible values of LR statistic p-values for testing p1-p0>0
load(system.file('files', "elr.stats.Rdata", package = 'exact.n'))
# All possible values of ELR statistic p-values for testing p1-p0>0
load(system.file('files', "elr10.stats.Rdata", package = 'exact.n'))
# Object contains all exact p-values for testing if p1-p0>0.1
# All possible values of ELR statistic p-values for testing p1-p0>0.1
#
graphics::par(mfrow=c(1,2))
# When delta=0 this gives type 1 error. The first plot is for the approximate
# lr based p-value, the second is for the quasi-exact e-p-value (alpha=0.05)
plot(POWER(n0=65,n1=82,alpha=0.05,psi=0,delta=0),type="l",
     xlab=expression("p"[0]),ylab="exact size")
abline(h=.05,lty=2)
plot(POWER(obj=elr.stats,alpha=0.05,delta=0),type="l",
     xlab=expression("p"[0]),ylab="exact size")
abline(h=.05,lty=2)
#
# For these sample sizes, power curve is calculated below for
# values of delta=0.1, 0.12, 0.14, 0.16, 0.18, 0.20. Power
# is poor for detecting a difference of 0.1 (see red).
plot(POWER(obj=lr.stats,alpha=0.05,delta=0.1),type="l",
     xlab=expression("p"[0]),ylab="exact power")
TITLE=expression('Exact power of LR test of p'[1]*'-p'[0]*'>0.')
title(main=TITLE,cex.main=0.8)
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.12))
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.14))
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.16))
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.18))
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.20))
lines(POWER(obj=lr.stats,alpha=0.05,delta=0.10),col="red")
#
# The results below are for testing p1-p0>0.1.
plot(c(0,.9),c(0,1),type="n",
     xlab=expression("p"[0]),ylab="Pr(reject null)")
lines(POWER(obj=elr10.stats,alpha=0.05,psi=0.1,delta=0.1)) # Note delta=psi
abline(h=0.05,lty=2)
lines(POWER(obj=elr10.stats,alpha=0.05,delta=0.25),col="blue")
TITLE=expression('Exact size and power of test of p'[1]*'-p'[0]*'>0.1.')
title(main=TITLE,cex.main=0.8)
legend(.4,.4,lty=c(1,1),col=c("black","blue"),box.col="white",
    legend=c("size: p1-p0=0.1","power: p1-p0=0.25"),cex=.7)
# When using the package the above plots would be generated by
# lines(POWER(n0=65,n1=82,alpha=0.05,psi=0.1,delta=0.10,type="elr"))
# lines(POWER(n0=65,n1=82,alpha=0.05,psi=0.1,delta=0.25,type="elr"))
suppressWarnings(graphics::par(oldpar))