Description Usage Arguments Details Value References See Also Examples
Determines group sequential single-arm clinical trial designs for a single binary primary endpoint. In particular, this allows Simon's two-stage designs (Simon, 1989) to be identified.
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J |
The maximal number of stages to allow. |
pi0 |
The (undesirable) response probability used in the definition of the null hypothesis. |
pi1 |
The (desirable) 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. |
optimality |
Choice of optimal design criteria. Must be one of
|
point_prior |
Value of the response probability to minimise the expected
sample size at. Only (potentially) required if |
beta_prior |
Shape parameters of the beta distribution to optimise the
expected sample over. Only (potentially) required if
|
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_gs()
supports the determination of a variety of (optimised)
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 the 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
n1 = ⋯ = 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 in Ensign et al (1994) for 3-stage designs.
Note that to ensure a decision is made about H 0, this function enforces a J + 1 = rJ.
To describe the supported optimality criteria, denote the expected sample size and median required sample size when the true response probability is π by ESS(π) and Med(π) respectively. Then, the following optimality criteria are currently supported:
"minimax"
: The design which minimises
NJ.
"null_ess"
: The design which minimises
ESS(π0).
"alt_ess"
: The design which minimises
ESS(π1).
"null_med"
: The design which minimises
Med(π0).
"alt_med"
: The design which minimises
Med(π1).
"prior"
: Either the design which minimises
ESS(π) for the value of
π specified using
"point_prior"
. Or, the design which minimises
∫ESS(π)Beta(π,
a,b)dπ
over [0,1], where Beta(π,x,
y) is the PDF of a beta distribution with shape
parameters x and
y, specified through "beta_prior"
as a vector,
evaluated at point π.
Note that when J ≤ 3, the
optimal design is determined by an exhaustive search. This means that vast
speed improvements can be made by carefully choosing the values of
Nmin
and Nmax
. In contrast, if J >
3, simulated annealing is employed to stochastically search
for the optimal design, as proposed by Chen and Lee (2013).
A list of class "sa_des_gs"
containing the following elements
A list in the slot $des
containing details of the identified
optimal design.
A tibble in the slot $feasible
, consisting of the
identified designs which met the required operating characteristics.
Each of the input variables as specified.
Chen K, Shan M (2008) Optimal and minimax three-stage designs for phase II oncology trials. Contemporary Clinical Trials 29:32-41.
Chen N, Lee JJ (2013) Optimal continuous-monitoring design of single-arm phase II trial based on the simulated annealing method Contemporary Clinical Trials 35:170-8.
Chen TT (1997) Optimal three-stage designs for phase II cancer clinical trials. Statistics in Medicine 16:2701-11.
Ensign LG et al. (1994) An optimal three-stage design for phase II clinical trials. Statistics in Medicine 13:1727-36.
Hanfelt JJ et al. (1999) A modification of Simon's optimal design for phase II trials when the criterion is median sample size. Controlled Clinical Trials 20:555-66.
Mander AP, Thompson SG (2010) Two-stage designs optimal under the alternative hypothesis for phase II cancer clinical trials. Contemporary Clinical Trials 31:572-8.
Simon R (1989) Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials 10:1-10.
Shuster J (2002) Optimal two-stage designs for single arm phase II cancer trials. Journal of Biopharmaceutical Statistics 12: 39-51.
opchar_gs
, est_gs
,
pval_gs
, ci_gs
, and their associated plot
family of functions. Note that similar functionality is available through
ph2simon
and
getSolutions
.
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