Description Usage Arguments Details Value Methods (by class) See Also Examples
The pos1S
function defines a 1 sample design (prior, sample
size, decision function) for the calculation of the frequency at
which the decision is evaluated to 1 when assuming a distribution
for the parameter. A function is returned which performs the
actual operating characteristics calculations.
1 2 3 4 5 6 7 8 9 10 
prior 
Prior for analysis. 
n 
Sample size for the experiment. 
decision 
Onesample decision function to use; see 
... 
Optional arguments. 
sigma 
The fixed reference scale. If left unspecified, the default reference scale of the prior is assumed. 
eps 
Support of random variables are determined as the
interval covering 
The pos1S
function defines a 1 sample design and
returns a function which calculates its probability of success.
The probability of success is the frequency with which the decision
function is evaluated to 1 under the assumption of a given true
distribution of the data implied by a distirbution of the parameter
θ.
Calling the pos1S
function calculates the critical value
y_c and returns a function which can be used to evaluate the
PoS for different predictive distributions and is evaluated as
\int F(y_cθ) p(θ) dθ,
where F is the distribution function of the sampling
distribution and p(θ) specifies the assumed true
distribution of the parameter θ. The distribution
p(θ) is a mixture distribution and given as the
mix
argument to the function.
Returns a function that takes as single argument
mix
, which is the mixture distribution of the control
parameter. Calling this function with a mixture distribution then
calculates the PoS.
betaMix
: Applies for binomial model with a mixture
beta prior. The calculations use exact expressions.
normMix
: Applies for the normal model with known
standard deviation σ and a normal mixture prior for the
mean. As a consequence from the assumption of a known standard
deviation, the calculation discards sampling uncertainty of the
second moment. The function pos1S
has an extra
argument eps
(defaults to 10^{6}). The critical value
y_c is searched in the region of probability mass
1eps
for y.
gammaMix
: Applies for the Poisson model with a gamma
mixture prior for the rate parameter. The function
pos1S
takes an extra argument eps
(defaults to 10^{6})
which determines the region of probability mass 1eps
where
the boundary is searched for y.
Other design1S:
decision1S_boundary()
,
decision1S()
,
oc1S()
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  # noninferiority example using normal approximation of loghazard
# ratio, see ?decision1S for all details
s < 2
flat_prior < mixnorm(c(1,0,100), sigma=s)
nL < 233
theta_ni < 0.4
theta_a < 0
alpha < 0.05
beta < 0.2
za < qnorm(1alpha)
zb < qnorm(1beta)
n1 < round( (s * (za + zb)/(theta_ni  theta_a))^2 )
theta_c < theta_ni  za * s / sqrt(n1)
# assume we would like to conduct at an interim analysis
# of PoS after having observed 20 events with a HR of 0.8.
# We first need the posterior at the interim ...
post_ia < postmix(flat_prior, m=log(0.8), n=20)
# dual criterion
decComb < decision1S(c(1alpha, 0.5), c(theta_ni, theta_c), lower.tail=TRUE)
# ... and we would like to know the PoS for a successful
# trial at the end when observing 10 more events
pos_ia < pos1S(post_ia, 10, decComb)
# our knowledge at the interim is just the posterior at
# interim such that the PoS is
pos_ia(post_ia)

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