exact2x2 (version 1.4.0)

power2x2: Calculate exact power or sample size for two independent binomials.

Description

Power is calculated by power2x2 which calls exact2x2 function repeatedly. Default (strict=FALSE) does not count rejections in the wrong direction. Sample size is calculated by ss2x2 which calls power2x2 repeatedly finding the lowest sample size that has at least the nominal power, using the uniroot.integer function from the ssanv package.

Usage

power2x2(p0,p1,n0,n1=NULL,sig.level=0.05,
 alternative=c("two.sided","one.sided"),paired=FALSE,
 strict=FALSE,tsmethod=NULL,nullOddsRatio=1,
 errbound=10^-6,approx=FALSE)

ss2x2(p0,p1,power=.80,n1.over.n0=1,sig.level=0.05,
 alternative=c("two.sided","one.sided"),paired=FALSE,
 strict=FALSE,tsmethod=NULL,nullOddsRatio=1,
 errbound=10^-6,print.steps=FALSE, approx=FALSE)

Arguments

p0

true event rate in control group

p1

true event rate in treatment group

n0

number of observations in control group

n1

number of observations in treatment group (if NULL n1=n0)

sig.level

significance level (Type I error probability)

power

minimum power for sample size calculation

n1.over.n0

ratio of n1 over n0, allows for non-equal sample size allocation

alternative

character, either "two.sided" or "one.sided", one sided tests the proper direction according to p0 and p1

strict

use strict interpretation of two-sided test, if TRUE counts rejections in wrong direction

tsmethod

two.sided method, ignored if strict=FALSE, or alternative equals 'less' or 'greater'. see exact2x2 for details.

nullOddsRatio

null odds ratio value for tests

paired

logical. TRUE gives power for McNemar's test, FALSE are all other tests (see warning)

print.steps

logical, print steps for calculation of sample size?

errbound

bound on error of calculation

approx

give sample size or power using normal approximation only

Value

• Both power2x2 and ss2x2 return an object of class 'power.htest'. A list with elements
• power
  power to reject
• n0
  sample size in control group
• n1
  sample size in treatment group
• p0
  true event rate in control group
• p1
  true event rate in treatment group
• sig.level
  Significance level (Type I error probability)
• alternative
  alternative hypothesis
• note
  note about error bound
• method
  description

Warning

There may be convergence issues using strict=FALSE with tsmethod="minlike" or "blaker" since the power is not guaranteed to be increasing in the sample size. When paired=TRUE the model for the power calculation is fairly restrictive. It assumes that there is no correlation between the two groups. A better power function is probably needed for this case.

Details

Assuming X0 ~ Binomial(n0,p0) and X1 ~ Binomial(n1,p1), calculates the power by repeatedly calling exact2x2 and summing probability of rejection. For speed, the function does not calculate the very unlikely values of X0 and X1 unless errbound=0. Power is exact, but may underestimate by at most errbound. When strict=FALSE we do not count rejections in the wrong direction. This means that we must know the direction of the rejection, so two.sided tests are calculated as one.sided tests (in the correct direction) with level equal to sig.level/2. This is like using the tsmethod='central'. When approx=TRUE for power2x2 use a continuity corrected normal approximation (Fleiss, 1981, p. 44). For ss2x2

See Also

See ss.nonadh function (refinement="Fisher.exact") from the ssanv package for calculation that accounts for nonadherence in proportion of subjects. That function calls fisher.test

Examples

power2x2(.2,.8,12,15)
# calculate sample size with 2:1 allocation to groups
ss2x2(.2,.8,n1.over.n0=2,power=.8,approx=TRUE)
ss2x2(.2,.8,n1.over.n0=2,power=.8,print.steps=TRUE)