POWER: Exact Power of Test for Selected Sample Sizes.

In exact.n: Exact Samples Sizes and Inference for Clinical Trials with Binary Endpoint

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
)

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.

Details

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

Value

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

Author(s)

Chris J. Lloyd

References

C.J. Lloyd (2022) Exact samples sizes for clinical trials subject to size and power constraints. Preprint. \Sexpr[results=rd]{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))

exact.n documentation built on Nov. 9, 2023, 9:06 a.m.