fedesign function

Trial Designs Based On Fisher's Exact Test

Calculates sample size, effect size and power based on Fisher's exact test

fe.ssize(p1, p2, alpha=0.05, power=0.8, r=1, npm=5, mmax=1000)
CPS.ssize(p1, p2, alpha=0.05, power=0.8, r=1)
fe.mdor(ncase, ncontrol, pcontrol, alpha=0.05, power=0.8)
mdrr(n, cprob, presp, alpha=0.05, power=0.8, niter=15)
fe.power(d, n1, n2, p1, alpha = 0.05)
or2pcase(pcontrol, OR)

Arguments

• p1: response rate of standard treatment
• p2: response rate of experimental treatment
• d: difference = p2-p1
• pcontrol: control group probability
• n1: sample size for the standard treatment group
• n2: sample size for the standard treatment group
• ncontrol: control group sample size
• ncase: case group sample size
• alpha: size of the test (default 5%)
• power: power of the test (default 80%)
• r: treatments are randomized in 1:r ratio (default r=1)
• npm: the sample size program searches for sample sizes in a range (+/- npm) to get the exact power
• mmax: the maximum group size for which exact power is calculated
• n: total number of subjects
• cprob: proportion of patients who are marger positive
• presp: probability of response in all subjects
• niter: number of iterations in binary search
• OR: odds-ratio

Details

CPS.ssize returns Casagrande, Pike, Smith sample size which is a very close to the exact. Use this for small differences p2-p1 (hence large sample sizes) to get the result instantaneously.

Since Fisher's exact test orders the tables by their probability the test is naturally two-sided.

fe.ssize return a 2x3 matrix with CPS and Fisher's exact sample sizes with power.

fe.mdor return a 3x2 matrix with Schlesselman, CPS and Fisher's exact minimum detectable odds ratios and the corresponding power.

fe.power returns a Kx2 matrix with probabilities (p2) and exact power.

mdrr computes the minimum detectable P(resp|marker+) and P(resp|marker-) configurations when total sample size (n), P(response) (presp) and proportion of subjects who are marker positive (cprob) are specified.

or2pcase give the probability of disease among the cases for a given probability of disease in controls (pcontrol) and odds-ratio (OR).

References

Casagrande, JT., Pike, MC. and Smith PG. (1978). An improved approximate formula for calculating sample sizes for comparing two binomial distributions. Biometrics 34, 483-486.

Fleiss, J. (1981) Statistical Methods for Rates and Proportions.

Schlesselman, J. (1987) Re: Smallest Detectable Relative Risk With Multiple Controls Per Case. Am. J. Epi.