sargent2stage: The Sargent 2-stage function

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

Description

This function calculates sample sizes of the Sargent 2-stage design.

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 2-stage design which is a three-outcome design that allows for three outcomes: reject H(0), reject H(a), or reject neither.

Usage

sargent2stage(
  p0,
  pa,
  alpha,
  beta,
  eta,
  pi,
  eps = 0,
  N_min,
  N_max,
  int = 0,
  int_window = 0.025,
  CI_type = "Koyama"
)

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
int	pre-specified interim analysis percentage information
int_window	window around interim analysis percentage (e.g. 0.5 +- 0.025). 0.025 is default value
CI_type	"Koyama", see getCI_Koyama, or any type for binom.confint

Details

if x1<=r1 –> stop futility
if (x1+x2)<=r –> futility
if (x1+x2)>=s –> efficacy

Value

a data.frame with elements

• n1: total number of patients in stage1

• n2: total number of patients in stage2

• N: total number of patients=n1+n2

• r1: critical value for the first stage

• r2: critical value for the second stage

• eff: s/N

• CI_LL: (1-2*alpha) CI lower limit

• CI_UL: (1-2*alpha) CI upper limit

• EN.p0: expected sample size under H0

• PET.p0: probability of terminating the trial at the end of the first stage under H0

• MIN: column indicating if the design is the minimal design

• OPT: column indicating if the setting is the optimal design

• ADMISS: column indicating if the setting is the admissible design

• 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

• lambda: 1-(eta+alpha)

• delta: 1-(beta+pi)

• 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

samplesize <- sargent2stage(p0 = 0.1, pa = 0.3, alpha = 0.05, beta = 0.1, eta = 0.8, pi = 0.8,
                            eps = 0.005, N_min = 15, N_max = 30)
plot(samplesize)


data(data_sargent2)
test <- data_sargent2
samplesize <- sargent2stage(p0 = test$p0, pa = test$pa, alpha = test$alpha, beta = test$beta,
                            eta = test$eta, pi = test$pi,
                            eps = 0.005,
                            N_min = test$N_min, N_max = test$N_max)
optimal <- lapply(samplesize, FUN=function(x) subset(x, OPT == "Optimal"))
optimal <- data.table::rbindlist(optimal)
minimax <- lapply(samplesize, FUN=function(x) subset(x, MIN == "Minimax"))
minimax <- data.table::rbindlist(minimax)

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