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Decision cutpoints for boundary (based on posterior probability)

Source: R/boundsPostprob.R
boundsPostprob.Rd

This function is used to identify the efficacy and futility boundaries based on posterior probabilities, i.e.: Efficacy boundary: find minimum x (xU) where Pr(P>p0|x,n,a,b) >= tU and Futility boundary: find maximum x (xL) where Pr(P>p1|x,n,a,b) <= tL

Usage

boundsPostprob(nvec, p0, p1 = p0, tL, tU, a, b)

Arguments

nvec

a vector of number of patients

p0

the efficacy threshold parameter in the postprob function

p1

the futility threshold parameter in the postprob function (default = p0)

tL

futility boundary probability threshold

tU

efficacy boundary probability threshold

a

the alpha parameter of the beta prior of treatment group

b

the beta parameter of the beta prior of treatment group

Value

A matrix where for each sample size in nvec, this function returns the maximum number of responses that meet the futility threshold (xL), its corresponding response rate (pL), posterior probability (postL), upper bound of one sided 95% CI for the response rate based on an exact binomial test (UciL), and the same boundary parameters for efficacy: the minimal number of responses that meet the efficacy threshold (xU), the corresponding response rate (pU), posterior probability (postU) and the lower bound of one sided 95% CI for the response rate based on exact binomial test (LciU).

Examples

## 40 pts trial with interim looks after each 10 pts.,
## efficacy decision if more than 90% probability to be above 20% ORR,
## futility decision if less than 10% probability to be above 20% ORR,
## with uniform prior (i.e. beta(1, 1)) on the ORR:
boundsPostprob(
  nvec = c(10, 20, 30, 40), p0 = 0.20,
  tL = 0.10, tU = 0.90, a = 1, b = 1
)
#>    nvec xL     pL  postL   UciL xU   pU  postU   LciU
#> 10   10  0 0.0000 0.0859 0.2589  4 0.40 0.9496 0.1500
#> 20   20  1 0.0500 0.0576 0.2161  7 0.35 0.9569 0.1773
#> 30   30  2 0.0667 0.0374 0.1953  9 0.30 0.9254 0.1663
#> 40   40  4 0.1000 0.0664 0.2144 12 0.30 0.9479 0.1831
## From this we see e.g. that at the third IA at 30 pts, we would stop for futility
## if 5 or less patients responded, and for efficacy if 9 or more pts responded.