Description Usage Arguments Details Value See Also Examples
View source: R/des_admissable.R
Determines admissable group sequential single-arm clinical trial designs for a single binary primary endpoint, using exact binomial calculations.
1 2 3 | des_admissable(J = 2, pi0 = 0.1, pi1 = 0.3, alpha = 0.05,
beta = 0.2, Nmin = 1, Nmax = 50, futility = T, efficacy = F,
equal_n = F, ensign = F, summary = F)
|
J |
The maximal number of stages to allow. |
pi0 |
The (undesirable) response probability used in the definition of the null hypothesis. |
pi1 |
The (desiable) response probability at which the trial is powered. |
alpha |
The desired maximal type-I error-rate. |
beta |
The desired maximal type-II error-rate. |
Nmin |
The minimal total sample size to allow in considered designs. |
Nmax |
The maximal total sample size to allow in considered designs. |
futility |
A logical variable indicating whether early stopping for futility should be allowed. |
efficacy |
A logical variable indicating whether early stopping for efficacy should be allowed. |
equal_n |
A logical variable indicating that the sample size of each stage should be equal. |
ensign |
A logical variable indicating that the design of Ensign et al (1994) should be mimicked, and the first stage futility boundary forced to be 0. |
summary |
A logical variable indicating a summary of the function's progress should be printed to the console. |
des_admissable()
supports the determination of admissable
group sequential single-arm clinical trial designs for a single binary
primary endpoint. For all supported designs, the following hypotheses are
tested for the response probability
π
for π0, specified
using the argument pi0
.
In each instance, the optimal design is required to meet the following operating characteristics
where P(π) is the
probability of rejecting H0
when the true response probability is
π, and the values of
α and
β are specified using the
arguments alpha
and beta
respectively. Moreover,
π1, satisfying
π0 <
π1, is specified using the
argument pi1
.
A group sequential single-arm design for a single binary endpoint, with a
maximum of J allowed stages (specifying
J through the argument J
) is
then indexed by three vectors: a =
(a1,…,aJ), r = (r1
,…,rJ), and n = (n1
,…,nJ).
With these vectors, and denoting the number of responses after m patients have been observed by sm, the stopping rules for a trial are then as follows
For j = 1,…,J - 1
If sNj ≤ aj, then stop the trial and do not reject H0.
Else if sNj ≥ rj, then stop the trial and reject H0.
Else if aj < sNj < rj , then continute to stage j + 1.
For j = J
If sNj ≤ aj, then do not reject H0.
Else if sNj ≥ rj, then reject H0.
Here, Nj = n1 + ⋯ + nj.
The purpose of this function is then to optimise a , r , and n , accounting for the chosen restrictions placed on these vectors, and the chosen optimality criteria.
The arguments Nmin
, Nmax
, and equal_n
allow restrictions
to be placed on n.
Precisely, Nmin
and Nmax
set an inclusive range of allowed
values for NJ, while
if set to TRUE
, equal_n
enforces that n
1 = ⋯ = nJ.
The arguments futility
, efficacy
, and ensign
allow restrictions to be placed on
a and
r. If futility
is
set to FALSE
, early stopping for futility (to not reject
H0) is prevented by
enforcing a1 = ⋯ = a
J - 1 = -∞.
Similarly, if efficacy
is set to FALSE
, early stopping for
efficacy (to reject H0) is
prevented by enforcing r1 = ⋯ =
rJ - 1 = ∞. Finally, if set to TRUE
, ensign
enforces the
restriction that a1 = 0, as suggested for 3-stage designs by Ensign et al (1994).
Note that to ensure a decision is made about H 0, this function enforces that aJ + 1 = r J.
To describe the admissability criteria, denote the expected sample size when the true response probability is π by ESS(π). Then, the following admissability criteria are currently supported:
The designs which minimise w0ESS(π0) + w1ESS(π1) + (1 - w0 - w1)NJ for 0 ≤ w0 + w1 ≤ 1.
A list of class "sa_des_admissable"
containing the following
elements
A list of lists in the slot $des
containing details of the
identified admissable design(s). Each element will contain
details of each admissable design.
A tibble in the slot $feasible
, consisting of the
identified designs which met the required operating characteristics.
A tibble in the slot $admissable
,
summarising the performance of the admissable designs.
A tibble in the slot $weights
containing details of which design
is admissable for each considered combination of w
0 and w1
.
Each of the input variables as specified.
opchar_admissable
, and their associated plot
family of functions.
1 2 | # The admissable designs for the default parameters
admissable <- des_admissable()
|
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