Description Usage Arguments Details Value Functions References See Also Examples
The function sets up a 2 sample onesided decision function with an arbitrary number of conditions on the difference distribution.
1 2 3 4 5 6 7 8 9 10 11 12 13  decision2S(
pc = 0.975,
qc = 0,
lower.tail = TRUE,
link = c("identity", "logit", "log")
)
oc2Sdecision(
pc = 0.975,
qc = 0,
lower.tail = TRUE,
link = c("identity", "logit", "log")
)

pc 
Vector of critical cumulative probabilities of the difference distribution. 
qc 
Vector of respective critical values of the difference
distribution. Must match the length of 
lower.tail 
Logical; if 
link 
Enables application of a link function prior to
evaluating the difference distribution. Can take one of the values

This function creates a onesided decision function on the
basis of the difference distribution in a 2 sample situation. To
support double criterion designs, see Neuenschwander et al.,
2010, an arbitrary number of criterions can be given. The decision
function demands that the probability mass below the critical value
qc
of the difference x_1  x_2 is at least
pc
. Hence, for lower.tail=TRUE
condition i is
equivalent to
P(x_1  x_2 ≤q q_{c,i}) > p_{c,i}
and the decision function is implemented as indicator function using the heavyside step function H which is 0 for x ≤q 0 and 1 for x > 0. As all conditions must be met, the final indicator function returns
Π_i H_i(P(x_1  x_2 ≤q q_{c,i})  p_{c,i} ),
which is 1 if all conditions are met and 0
otherwise. For lower.tail=FALSE
differences must be greater
than the given quantiles qc
.
Note that whenever a link
other than identity
is
requested, then the underlying densities are first transformed
using the link function and then the probabilties for the
differences are calculated in the transformed space. Hence, for a
binary endpoint the default identity
link will calculate
risk differences, the logit
link will lead to decisions
based on the differences in logit
s corresponding to a
criterion based on the logodds. The log
link will evaluate
ratios instead of absolute differences which could be useful for a
binary endpoint or counting rates. The respective critical
quantiles qc
must be given on the transformed scale.
The function returns a decision function which takes three arguments. The first and second argument are expected to be mixture (posterior) distributions from which the difference distribution is formed and all conditions are tested. The third argument determines if the function acts as an indicator function or if the function returns the distance from the decision boundary for each condition in logspace. That is, the distance is 0 at the decision boundary, negative for a 0 decision and positive for a 1 decision.
oc2Sdecision
: Deprecated old function name. Please use
decision2S
instead.
Gsponer T, Gerber F, Bornkamp B, Ohlssen D, Vandemeulebroecke M, Schmidli H.A practical guide to Bayesian group sequential designs. Pharm. Stat.. 2014; 13: 7180
Other design2S:
decision2S_boundary()
,
oc2S()
,
pos2S()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  # see Gsponer et al., 2010
priorT < mixnorm(c(1, 0, 0.001), sigma=88, param="mn")
priorP < mixnorm(c(1, 49, 20 ), sigma=88, param="mn")
# the success criteria is for delta which are larger than some
# threshold value which is why we set lower.tail=FALSE
successCrit < decision2S(c(0.95, 0.5), c(0, 50), FALSE)
# the futility criterion acts in the opposite direction
futilityCrit < decision2S(c(0.90) , c(40), TRUE)
print(successCrit)
print(futilityCrit)
# consider decision for specific outcomes
postP_interim < postmix(priorP, n=10, m=50)
postT_interim < postmix(priorT, n=20, m=80)
futilityCrit( postP_interim, postT_interim )
successCrit( postP_interim, postT_interim )
# Binary endpoint with double criterion decision on logodds scale
# 95% certain positive difference and an odds ratio of 2 at least
decL2 < decision2S(c(0.95, 0.5), c(0, log(2)), lower.tail=FALSE, link="logit")
# 95% certain positive difference and an odds ratio of 3 at least
decL3 < decision2S(c(0.95, 0.5), c(0, log(3)), lower.tail=FALSE, link="logit")
# data scenario
post1 < postmix(mixbeta(c(1, 1, 1)), n=40, r=10)
post2 < postmix(mixbeta(c(1, 1, 1)), n=40, r=18)
# positive outcome and a median odds ratio of at least 2 ...
decL2(post2, post1)
# ... but not more than 3
decL3(post2, post1)

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