RARtrials (version 0.0.2)

pgreater_normal: Calculate the Futility Stopping Probability for Continuous Endpoint with Known Variances Using Normal Distribution

Description

Calculate the futility stopping probability in Bayesian response-adaptive randomization with a control group using the Thall \(\&\) Wathen method for continuous outcomes with known variances. The conjugate prior distributions follow Normal (\(N(mean,sd)\)) distributions and can be specified individually for each treatment group.

Usage

pgreater_normal(
  mean1 = NULL,
  sd1 = NULL,
  mean2 = NULL,
  sd2 = NULL,
  delta = 0,
  side,
  ...
)

Value

a posterior probability of \(Pr(\mu_k>\mu_{{\sf control}}+\delta|{\sf data})\) with side equals to 'upper'; a posterior probability of \(Pr(\mu_{{\sf control}}>\mu_k+\delta|{\sf data})\) with side equals to 'lower'.

Arguments

mean1, sd1

mean and sd in \(N({\sf mean},{\sf sd})\), current estimated mean and sd for the control group.

mean2, sd2

mean and sd in \(N({\sf mean},{\sf sd})\), current estimated mean and sd for the treatment group which is compared to the control group.

delta

pre-specified minimal effect size expected to be observed between the control group and the compared treatment group.

side

direction of a one-sided test, with values 'upper' or 'lower'.

...

additional arguments to be passed to stats::integrate() (such as rel.tol) from this function.

Details

This function calculates the results of \(Pr(\mu_k>\mu_{{\sf control}}+\delta|{\sf data})\) for side equals to 'upper' and the results of \(Pr(\mu_{{\sf control}}>\mu_k+\delta|{\sf data})\) for side equals to 'lower'. The result indicates the posterior probability of stopping a treatment group due to futility around \(1\%\) in Bayesian response-adaptive randomization with a control arm using Thall \(\&\) Wathen method, with accumulated results during the conduct of trials.

References

Wathen2017RARtrials Kevin2007RARtrials

Examples

pgreater_normal(mean1=0.091,sd1=0.09,mean2=0.097,sd2=0.08,delta=0,side='upper')
pgreater_normal(mean1=0.091,sd1=0.09,mean2=0.087,sd2=0.1,delta=0,side='lower')