getCI_Koyama: Koyama confidence interval.
In IDDI-BE/PhIIdesign: Sample Size Calculation for Phase II Designs

Description Usage Arguments References Examples

Calculates the two sided 1-2*alpha confidence interval based, by inverting the "rejection probability function" (or the "p value function") at every possible value for the null hypothesis between [0,1]. A two-sided (1 − 2*alpha) CI interval includes then all values of binomial proportions for which the p value for testing H0, lays within the interval [alpha, 1 − alpha] A stage-wise ordering of the sample space is used: Let m be the stopping stage and x the total number of responses. A trial outcome (m'; x') is at least as extreme (against H0) as the observed trial outcome (m; x), if one of the 3 following conditions is met: (A) m' = m and x'>=x (B) m' = 1, m = 2 and x'>=a (C) m' = 2, m = 1 and x <=r1 In the case of Simon’s and Fleming's 2-stage design, stage-wise ordering means that outcomes observed in the second stage of the trial are more extreme than outcomes observed in the first stage of the trial. In the case of Fleming's 2-stage design, stage-wise ordering means that rejection of H0 in the first stage is more extreme than rejection in the second stage

1	getCI_Koyama(N, n1, r1, a = NULL, k, alpha, design, precision = 3)

`N`	overall sample size.
`n1`	sample size for the first stage.
`r1`	critical value for futility decision first stage (Simon's or Sargent's 2-stage)
`a`	critical value for efficacy decision first stage (Fleming's 2-stage)
`k`	overall observed responses (must be larger than r1).
`alpha`	determining the two sided 1-2*alpha confidence interval.
`design`	3 choices for 2-stage design: "Simon","Sargent" or "Fleming"
`precision`	gives the precision (in decimal numbers) to which the confidence interval should be calculated (should be less than 10).

Koyama T and Chen H (2008): Proper inference from Simon's two-stage designs. Statistics in Medicine, 27(16):3145-3154. Nhacolo A, Brannath W. Interval and point estimation in adaptive Phase II trials with binary endpoint. Stat Methods Med Res 2019;28:2635-2648

#Calculate a Simon's two-stage design
res <- simon2stage(p0 = 0.1, pa = 0.3, alpha = 0.05, beta = 0.2,eps = 0.005, N_min = 1, N_max = 50)
CI <- mapply(a_ = res$N, b_ = res$n1 , c_ = res$r1, d_ = res$r2 + 1, FUN = function(a_, b_, c_, d_)
getCI_Koyama(N = a_,  n1 = b_, r1 = c_, k = d_, a=NULL, alpha = 0.05, design="Simon",precision = 3))
getCI_Koyama(N = 21,  n1 = 14, r1 = 1, k = 5, a=NULL, alpha = 0.05, design="Simon",precision = 3)