Description Usage Arguments Details Value Methods (by class) References See Also Examples
The oc2S
function defines a 2 sample design (priors, sample
sizes & decision function) for the calculation of operating
characeristics. A function is returned which calculates the
calculates the frequency at which the decision function is
evaluated to 1 when assuming known parameters.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  oc2S(prior1, prior2, n1, n2, decision, ...)
## S3 method for class 'betaMix'
oc2S(prior1, prior2, n1, n2, decision, eps, ...)
## S3 method for class 'normMix'
oc2S(
prior1,
prior2,
n1,
n2,
decision,
sigma1,
sigma2,
eps = 1e06,
Ngrid = 10,
...
)
## S3 method for class 'gammaMix'
oc2S(prior1, prior2, n1, n2, decision, eps = 1e06, ...)

prior1 
Prior for sample 1. 
prior2 
Prior for sample 2. 
n1, n2 
Sample size of the respective samples. Sample size 
decision 
Twosample decision function to use; see 
... 
Optional arguments. 
eps 
Support of random variables are determined as the
interval covering 
sigma1 
The fixed reference scale of sample 1. If left unspecified, the default reference scale of the prior 1 is assumed. 
sigma2 
The fixed reference scale of sample 2. If left unspecified, the default reference scale of the prior 2 is assumed. 
Ngrid 
Determines density of discretization grid on which decision function is evaluated (see below for more details). 
The oc2S
function defines a 2 sample design and
returns a function which calculates its operating
characteristics. This is the frequency with which the decision
function is evaluated to 1 under the assumption of a given true
distribution of the data defined by the known parameter
θ_1 and θ_2. The 2 sample design is defined
by the priors, the sample sizes and the decision function,
D(y_1,y_2). These uniquely define the decision boundary , see
decision2S_boundary
.
Calling the oc2S
function calculates the decision boundary
D_1(y_2) (see decision2S_boundary
) and returns
a function which can be used to calculate the desired frequency
which is evaluated as
\int f_2(y_2θ_2) F_1(D_1(y_2)θ_1) dy_2.
See below for examples and specifics for the supported mixture priors.
Returns a function which when called with two arguments
theta1
and theta2
will return the frequencies at
which the decision function is evaluated to 1 whenever the data is
distributed according to the known parameter values in each
sample. Note that the returned function takes vector arguments.
betaMix
: Applies for binomial model with a mixture
beta prior. The calculations use exact expressions. If the
optional argument eps
is defined, then an approximate method
is used which limits the search for the decision boundary to the
region of 1eps
probability mass. This is useful for designs
with large sample sizes where an exact approach is very costly to
calculate.
normMix
: Applies for the normal model with known
standard deviation σ and normal mixture priors for the
means. As a consequence from the assumption of a known standard
deviation, the calculation discards sampling uncertainty of the
second moment. The function has two extra arguments (with
defaults): eps
(10^{6}) and Ngrid
(10). The
decision boundary is searched in the region of probability mass
1eps
, respectively for y_1 and y_2. The
continuous decision function is evaluated at a discrete grid, which
is determined by a spacing with δ_2 =
σ_2/√{N_{grid}}. Once the decision boundary is evaluated
at the discrete steps, a spline is used to interpolate the
decision boundary at intermediate points.
gammaMix
: Applies for the Poisson model with a gamma
mixture prior for the rate parameter. The function
oc2S
takes an extra argument eps
(defaults to 10^{6}) which
determines the region of probability mass 1eps
where the
boundary is searched for y_1 and y_2, respectively.
Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B. Robust metaanalyticpredictive priors in clinical trials with historical control information. Biometrics 2014;70(4):10231032.
Other design2S:
decision2S_boundary()
,
decision2S()
,
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  # example from Schmidli et al., 2014
dec < decision2S(0.975, 0, lower.tail=FALSE)
prior_inf < mixbeta(c(1, 4, 16))
prior_rob < robustify(prior_inf, weight=0.2, mean=0.5)
prior_uni < mixbeta(c(1, 1, 1))
N < 40
N_ctl < N  20
# compare designs with different priors
design_uni < oc2S(prior_uni, prior_uni, N, N_ctl, dec)
design_inf < oc2S(prior_uni, prior_inf, N, N_ctl, dec)
design_rob < oc2S(prior_uni, prior_rob, N, N_ctl, dec)
# type I error
curve(design_inf(x,x), 0, 1)
curve(design_uni(x,x), lty=2, add=TRUE)
curve(design_rob(x,x), lty=3, add=TRUE)
# power
curve(design_inf(0.2+x,0.2), 0, 0.5)
curve(design_uni(0.2+x,0.2), lty=2, add=TRUE)
curve(design_rob(0.2+x,0.2), lty=3, add=TRUE)

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