
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.
pos1S(prior, n, decision, ...)# S3 method for betaMix
pos1S(prior, n, decision, ...)
# S3 method for normMix
pos1S(prior, n, decision, sigma, eps = 1e-06, ...)
# S3 method for gammaMix
pos1S(prior, n, decision, eps = 1e-06, ...)
Prior for analysis.
Sample size for the experiment.
One-sample decision function to use; see decision1S
.
Optional arguments.
The fixed reference scale. If left unspecified, the default reference scale of the prior is assumed.
Support of random variables are determined as the
interval covering 1-eps
probability mass. Defaults to
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 pos1S
has an extra
argument eps
(defaults to 1-eps
for
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 1-eps
where
the boundary is searched for
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
where mix
argument to the function.
Other design1S: decision1S_boundary
,
decision1S
, oc1S
# NOT RUN {
# 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)
# }
Run the code above in your browser using DataLab