oc2S: Operating Characteristics for 2 Sample Design

Description Usage Arguments Details Value Methods (by class) References See Also Examples

View source: R/oc2S.R

Description

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.

Usage

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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 = 1e-06,
  Ngrid = 10,
  ...
)

## S3 method for class 'gammaMix'
oc2S(prior1, prior2, n1, n2, decision, eps = 1e-06, ...)

Arguments

prior1

Prior for sample 1.

prior2

Prior for sample 2.

n1, n2

Sample size of the respective samples. Sample size n1 must be greater than 0 while sample size n2 must be greater or equal to 0.

decision

Two-sample decision function to use; see decision2S.

...

Optional arguments.

eps

Support of random variables are determined as the interval covering 1-eps probability mass. Defaults to 10^{-6}.

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).

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_2|θ_2) F_1(D_1(y_2)|θ_1) dy_2.

See below for examples and specifics for the supported mixture priors.

Value

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.

Methods (by class)

References

Schmidli H, Gsteiger S, Roychoudhury S, O'Hagan A, Spiegelhalter D, Neuenschwander B. Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics 2014;70(4):1023-1032.

See Also

Other design2S: decision2S_boundary(), decision2S(), pos2S()

Examples

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# 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)

RBesT documentation built on Nov. 24, 2021, 5:07 p.m.