clinfun (version 1.0.15)

pselect: Probability of selection under pick the winner rule

Description

Calculates the probability of selecting the treatment with the higher response rate under the pick the winner rule.

Usage

pselect(n, p, min.diff=NULL, min.resp=NULL)

Arguments

n

sample size for each treatment arm. This is either a single integer or a vector of two integers for the special case of comparing two treatments with unequal sample sizes

p

vector of response rates for the treatments.

min.diff

this is the number of responses or the rate by which the best treatment should be superior to the others to be chosen. This must be a positive integer or a rate between 0 and 1. If missing it defaults to 1 for the equal sample size case but quits with a warning for the unequal sample size case.

min.resp

the minimum number of responses in each treatment arm for it to be considered further. If missing defaults to 0.

Value

the function returns a list with:

prob.none.worthy

is the probability that no treatment has the minimum number of responses specified in min.resp. this element is present only if min.resp is greater than 0 for at least one arm.

prob.inconclusive

this is the probability that the best treatment has the requisite min.resp responses but exceeds the second best by less than min.diff responses (rate) provided the second best also has at least min.resp responses.

prob.selection

this is a matrix which for each treatment gives the response probability and the probability of selecting it i.e. the number of responses in the chosen arm is at least min.resp and either none of the remaining arms exceed the min.resp threshold or the chosen (best) arm is better than the second best by at least min.diff responses (rate).

References

Simon R, Wittes RE, Ellenberg SS. (1985). Randomized phase II clinical trials. Cancer Treat Rep 69, 1375-1381.

Examples

# NOT RUN {
  # selection when no diffrence i.e. type I error
  pselect(18, c(0.2, 0.2, 0.2))
  # selection probability
  pselect(18, c(0.2, 0.2, 0.4))
  pselect(26, c(0.2, 0.2, 0.4), min.diff=2, min.resp=3)
  # unequal sample size case
  pselect(c(27,54), c(0.5, 0.65), min.diff=0.05)
  # unequal sample size case
  pselect(c(27,54), c(0.5, 0.65), min.diff=0.05, min.resp=c(14,27))
# }