power2x2: Calculate exact power or sample size for conditional tests...

View source: R/power2x2.R

power2x2R Documentation

Calculate exact power or sample size for conditional tests 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

must be FALSE, for TRUE instead use powerPaired2x2

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

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 the calculations may be slow, so use print.steps=TRUE to see progress.

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.

Note

The calculations in ss2x2 can be slow when p0 is close to p1 and/or the power is large. If p0 and p1 are close with large power, it may be safer to first calculate ss2x2 with approx=TRUE to see what the starting value will be close to. If the starting sample sizes are large (>100), it may take a while.

Note when strict=FALSE (default), the two.sided results at the 0.05 level for Fisher's exact test are like the one.sided Fisher's exact test at the 0.025 level.

Author(s)

Michael P. Fay

References

Fleiss. JL (1981) Statistical Methods for Rates and Proportions (second edition). Wiley.

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. For power for McNemar-like test see powerPaired2x2

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)

exact2x2 documentation built on May 29, 2024, 10:51 a.m.