pos1S {RBesT} | R Documentation |
Probability of Success for a 1 Sample Design
Description
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.
Usage
pos1S(prior, n, decision, ...)
## S3 method for class 'betaMix'
pos1S(prior, n, decision, ...)
## S3 method for class 'normMix'
pos1S(prior, n, decision, sigma, eps = 1e-06, ...)
## S3 method for class 'gammaMix'
pos1S(prior, n, decision, eps = 1e-06, ...)
Arguments
prior |
Prior for analysis. |
n |
Sample size for the experiment. |
decision |
One-sample 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 |
Details
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
.
Calling the pos1S
function calculates the critical value
and returns a function which can be used to evaluate the
PoS for different predictive distributions and is evaluated as
where is the distribution function of the sampling
distribution and
specifies the assumed true
distribution of the parameter
. The distribution
is a mixture distribution and given as the
mix
argument to the function.
Value
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.
Methods (by class)
-
pos1S(betaMix)
: Applies for binomial model with a mixture beta prior. The calculations use exact expressions. -
pos1S(normMix)
: Applies for the normal model with known standard deviationand 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 argumenteps
(defaults to). The critical value
is searched in the region of probability mass
1-eps
for.
-
pos1S(gammaMix)
: Applies for the Poisson model with a gamma mixture prior for the rate parameter. The functionpos1S
takes an extra argumenteps
(defaults to) which determines the region of probability mass
1-eps
where the boundary is searched for.
See Also
Other design1S:
decision1S_boundary()
,
decision1S()
,
oc1S()
Examples
# non-inferiority example using normal approximation of log-hazard
# 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(1-alpha)
zb <- qnorm(1-beta)
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(1-alpha, 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)