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

In exact2x2: Exact Tests and Confidence Intervals for 2x2 Tables

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

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.

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.

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

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)

Example output

Loading required package: exactci
Loading required package: ssanv

     Power for Fisher's Exact Test 

          power = 0.8475728
             n0 = 12
             n1 = 15
             p0 = 0.2
             p1 = 0.8
      sig.level = 0.05
    alternative = two.sided
  nullOddsRatio = 1

NOTE: errbound= 1e-06


     Approximate Power for Fisher's Exact Test 

          power = 0.8
             p0 = 0.2
             p1 = 0.8
             n0 = 9.340086
             n1 = 18.68017
      sig.level = 0.05
    alternative = two.sided
         strict = FALSE
       tsmethod = NULL
  nullOddsRatio = 1

NOTE: errbound= 1e-06

[1] "starting calculation at n0= 8  n1= 16"
[1] "n0=8 n1=16 power=0.704214110731463"
[1] "n0=16 n1=32 power=0.9781897271243"
[1] "n0=12 n1=24 power=0.921321775957463"
[1] "n0=10 n1=20 power=0.850961443071942"
[1] "n0=9 n1=18 power=0.799603779627725"

     Power for Fisher's Exact Test 

          power = 0.8509614
             n0 = 10
             n1 = 20
             p0 = 0.2
             p1 = 0.8
      sig.level = 0.05
    alternative = two.sided
  nullOddsRatio = 1

NOTE: errbound= 1e-06

exact2x2 documentation built on Dec. 11, 2021, 9:43 a.m.