fleming1stage: The Fleming 1-stage function

In IDDI-BE/PhIIdesign: Sample Size Calculation for Phase II Designs

Description

Therapeutic efficacy in clinical trials is often evaluated principally on the basis of the probability p that an eligible patient receiving the treatment regimen will experience a regression (like a tumor e.g.).
This function calculates sample sizes of the Fleming single-stage design, for p_0 < p_a for the requested Type I (alpha) and Type II error (beta).

Usage

fleming1stage(p0, pa, alpha = 0.05, beta = 0.2, eps = 0.005, CI_type = "exact")

Arguments

p0	probability of the uninteresting response (null hypothesis H0)
pa	probability of the interesting response (alternative hypothesis Ha)
alpha	Type I error rate P(reject H0|H0)
beta	Type II error rate P(reject Ha|Ha)
eps	tolerance default value = 0.005
CI_type	any type for binom.confint

Value

a data.frame with elements

• n: total number of patients

• r: quantile function of 1 - (alpha + eps) at n under p0. Note if n <= r –> futility

• eff: r/N

• CI_LL: exact 1-2*alpha confidence interval lower limit

• CI_UL: exact 1-2*alpha confidence interval upper limit

• alpha: the actual alpha value which is smaller than alpha_param + eps

• beta: the actual beta value where which is smaller than beta_param + eps

• p0: your provided p0 value

• pa: your provided pa value

• alpha_param: your provided alpha value

• beta_param: your provided beta value

References

Fleming TR. One-sample multiple testing procedure for phase II clinical trials. Biometrics. 1982;38(1):143-151.

Examples

fleming1stage(p0 = 0.45, pa = 0.7, alpha = 0.05, beta = 0.2)
fleming1stage(p0 = 0.1, pa = 0.3, alpha = 0.05, beta = 0.1, eps = 0.005)
fleming1stage(p0 = 0.1, pa = 0.3, alpha = 0.05, beta = 0.1, eps = 0.00001)

## For several combinations of p0 and pa
## not it is important that p0 is not equal to pa
test <- expand.grid(p0 = seq(0, 0.95, by = 0.05),
                    pa = seq(0, 0.95, by = 0.05))
test <- subset(test, (pa - p0) > 0.00001)
samplesize <- fleming1stage(p0 = test$p0, pa = test$pa, alpha = 0.05, beta = 0.2, eps = 0.0005)
samplesize <- fleming1stage(p0 = test$p0, pa = test$pa, alpha = 0.05, beta = 0.1, eps = 0.0005)
samplesize <- fleming1stage(p0 = test$p0, pa = test$pa, alpha = 0.01, beta = 0.2, eps = 0.0005)
samplesize <- fleming1stage(p0 = test$p0, pa = test$pa, alpha = 0.01, beta = 0.1, eps = 0.0005)

## these 2 are the same
samplesize <- fleming1stage(p0 = test$p0, pa = test$pa, alpha = 0.05, beta = 0.2)
samplesize <- mapply(p0 = test$p0, pa = test$pa, FUN=function(p0, pa){
  fleming1stage(p0 = p0, pa = pa, alpha = 0.05, beta = 0.2)
}, SIMPLIFY = FALSE)
samplesize <- do.call(rbind, samplesize)

IDDI-BE/PhIIdesign documentation built on June 5, 2021, 2:03 p.m.