SAMprior (version 2.0.0)

get_OC: Generating Operating Characteristics of SAM Priors

Description

The get_OC function is designed to generate the operating characteristics of SAM priors (Yang, et al., 2023), including the relative bias, relative mean squared error, and type I error and power under a two-arm comparative trial design. As an option, the operating characteristic of robust MAP priors (Schmidli, et al., 2014) can also be generated for comparison.

Usage

get_OC(
  if.prior,
  theta.h,
  method.w,
  prior.odds,
  nf.prior,
  delta,
  n,
  n.t,
  decision,
  ntrial,
  if.MAP,
  weight,
  theta,
  theta.t,
  ...
)
# S3 method for betaMix
get_OC(
  if.prior,
  theta.h,
  method.w,
  prior.odds,
  nf.prior,
  delta,
  n,
  n.t,
  decision,
  ntrial,
  if.MAP,
  weight,
  theta,
  theta.t,
  ...
)
# S3 method for normMix
get_OC(
  if.prior,
  theta.h,
  method.w,
  prior.odds,
  nf.prior,
  delta,
  n,
  n.t,
  decision,
  ntrial,
  if.MAP,
  weight,
  theta,
  theta.t,
  ...,
  sigma
)

Value

Returns dataframe that contains the relative bias, relative MSE, type I error, and power for both SAM priors, as well as robust MAP priors. Additionally, the mixture weight of the SAM prior is also displayed.

Arguments

if.prior

Informative prior constructed from historical data, represented (approximately) as a mixture of conjugate distributions.

theta.h

Estimate of the treatment effect based on historical data. If missing, the default value is set to be the posterior mean estimate from if.prior.

method.w

Methods used to determine the mixture weight for SAM priors. The default method is LRT (Likelihood Ratio Test), the alternative option can be PPR (Posterior Probability Ratio). See SAM_weight for more details.

prior.odds

The prior probability of \(H_0\) being true compared to the prior probability of \(H_1\) being true using PPR method. The default value is 1. See SAM_weight for more details.

nf.prior

Non-informative prior used for constructing the SAM prior and robust MAP prior.

delta

Clinically significant difference used for the SAM prior.

n

Sample size for the control arm.

n.t

Sample size for the treatment arm.

decision

Decision rule to compare the treatment with the control; see decision2S.

ntrial

Number of trials simulated.

if.MAP

Whether to simulate the operating characteristics of the robust MAP prior for comparison, the default value is FALSE.

weight

Weight assigned to the informative prior component (\(0 \leq\) weight \(\leq 1\)) for the robust MAP prior, the default value is 0.5.

theta

A vector of the response rate (binary endpoints) or mean (continuous endpoints) for the control arm.

theta.t

A vector of the response rate (binary endpoints) or mean (continuous endpoints) for the treatment arm.

...

Additional parameters for continuous endpoints.

sigma

Variance to simulate the continuous endpoint under normality assumption.

Methods (by class)

• get_OC(betaMix): The function is designed to generate the operating characteristics of SAM priors for binary endpoints.

• get_OC(normMix): The function is designed to generate the operating characteristics of SAM priors for continuous endpoints.

Details

The get_OC function is designed to generate the operating characteristics of SAM priors, including the relative bias, relative mean squared error, and type I error, and power under a two-arm comparative trial design. As an option, the operating characteristics of robust MAP priors (Schmidli, et al., 2014) can also be generated for comparison.

The relative bias is defined as the difference between the bias of a method and the bias of using a non-informative prior. The relative mean squared error is the difference between the mean squared error (MSE) of a method and the MES of using a non-informative prior.

To evaluate type I error and power, the determination of whether the treatment is superior to the control is calculated based on function decision2S.

References

Yang P, Zhao Y, Nie L, Vallejo J, Yuan Y. SAM: Self-adapting mixture prior to dynamically borrow information from historical data in clinical trials. Biometrics 2023; 79(4), 2857-2868.

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.

Examples

set.seed(123)
## Example of a binary endpoint
## Consider a randomized comparative trial designed to borrow information
## from historical data on the control. We assumed a non-informative prior
## beta(1, 1) and an informative prior beta(30, 50) after incorporating
## the historical data. The treatment is regarded as superior to the control
## if Pr(RR.t > RR.c | data) > 0.95, where RR.t and RR.c are response rates
##  of the treatment and control, respectively. The operating characteristics
##  were assessed under the scenarios of (RR.c, RR.t) = (0.3, 0.36) and (0.3, 0.56).
## OC <- get_OC(## Informative prior constructed based on historical data
##              if.prior = mixbeta(c(1, 30, 50)),
##              ## Non-informative prior used for constructing the SAM prior
##              nf.prior = mixbeta(c(1,1,1)),
##              delta    = 0.2,  ## Clinically significant difference
##              n = 35,          ## Sample size for the control arm
##              n.t = 70,        ## Sample size for the treatment arm
##              ## Decision rule to compare the whether treatment is superior
##              ## than the control
##              decision = decision2S(0.95, 0, lower.tail=FALSE),
##              ntrial   = 1000,  ## Number of trials simulated
##              ## Weight assigned to the informative component for MAP prior
##              weight = 0.5,
##              ## A vector of response rate for the control arm
##              theta    = c(0.3, 0.36),
##              ## A vector of response rate for the treatment arm
##              theta.t  = c(0.3, 0.56))
## OC

## Example of continuous endpoint
## Consider a randomized comparative trial designed to borrow information
## from historical data on the control. We assumed a non-informative prior
## N(0, 1e4) and an informative prior N(0.5, 2) after incorporating
## the historical data. The treatment is regarded as superior to the control
## if Pr(mean.t > mean.c | data) > 0.95, where mean.t and mean.c are mean
##  of the treatment and control, respectively. The operating characteristics
##  were assessed under the scenarios of (mean.c, mean.t) = (0.1, 0.1) and
## (0.5, 1.0).
sigma      <- 2
prior.mean <- 0.5
prior.se   <- sigma/sqrt(100)
## OC <- get_OC(## Informative prior constructed based on historical data
##              if.prior = mixnorm(c(1, prior.mean, prior.se)),
##              ## Non-informative prior used for constructing the SAM prior
##              nf.prior = mixnorm(c(1, 0, 1e4)),
##              delta    = 0.2 * sigma,  ## Clinically significant difference
##              n = 100,                 ## Sample size for the control arm
##              n.t = 200,               ## Sample size for the treatment arm
##              ## Decision rule to compare the whether treatment is superior
##              ## than the control
##              decision = decision2S(0.95, 0, lower.tail=FALSE),
##              ntrial   = 1000,  ## Number of trials simulated
##              ## A vector of mean for the control arm
##              theta    = c(0.1, 0.5),
##              ## A vector of mean for the treatment arm
##              theta.t  = c(0.1, 1.0),
##              sigma = sigma)
## OC