sargent1stage: The Sargent 1-stage function

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

Description

The goal of a phase II trial is to make a preliminary determination regarding the activity and tolerability of a new treatment and thus to determine whether the treatment warrants further study in the phase III setting.
This function calculates the sample size needed in a Sargent 1-stage design which is a three-outcome design that allows for three outcomes: reject H(0), reject H(a), or reject neither.

Usage

sargent1stage(
  p0,
  pa,
  alpha,
  beta,
  eta,
  pi,
  eps = 0.005,
  N_min,
  N_max,
  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)
eta	P(reject Ha|H0)
pi	P(reject H0|Ha)
eps	tolerance default value = 0.005
N_min	minimum sample size value for grid search
N_max	maximum sample size value for grid search
CI_type	any type for binom.confint
...	further arguments passed on to the methods

Value

a data.frame with elements

• N: total number of patients

• r: cutoff point r. Note if n <= r –> futility.

• s: cutoff point s. Note if n >= s –> efficacy.

• 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

• eta: the actual eta value which is smaller than eta_param - eps

• pi: the actual pi value which is smaller than pi_param - eps

• p0: your provided p0 value

• pa: your provided pa value

• alpha_param: your provided alpha value

• beta_param: your provided beta value

• eta_param: your provided eta value

• pi_param: your provided pi value

References

Sargent DJ, Chan V, Goldberg RM. A three-outcome design for phase II clinical trials. Control Clin Trials. 2001;22(2):117-125. doi:10.1016/s0197-2456(00)00115-x

Examples

sargent1stage(p0 = 0.5, pa = 0.65, alpha = 0.1, beta = 0.1, eta = 0.8, pi = 0.8,
              eps = 0.005, N_min = 0, N_max = 100)
sargent1stage(p0 = 0.2, pa = 0.35, alpha = 0.1, beta = 0.1, eta = 0.8, pi = 0.8,
              eps = 0.005, N_min = 35, N_max = 50)

test <- data.frame(p0 = c(0.05,0.1,0.2,0.3,0.4,0.5),
                   pa = c(0.05,0.1,0.2,0.3,0.4,0.5) + 0.15)
test <- merge(test,
              expand.grid(alpha = 0.05, beta = 0.1, eta = 0.8, pi = 0.8))
samplesize <- sargent1stage(p0 = test$p0, pa = test$pa,
                            alpha = test$alpha, beta = test$beta,
                            eta = test$eta, pi = test$pi,
                            eps = 0.005, N_min = 20, N_max = 70)
samplesize <- lapply(seq_len(nrow(test)), FUN=function(i){
  setting <- test[i, ]
  sargent1stage(p0 = setting$p0, pa = setting$pa,
                alpha = setting$alpha, beta = setting$beta, eta = setting$eta, pi = setting$pi,
                eps = 0.005, N_min = 20, N_max = 70)
})
samplesize <- do.call(rbind, samplesize)

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