pgreater_normal {RARtrials}

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,
  ...
)

Arguments

mean1, sd1

mean and sd in N(mean,sd), current estimated mean and sd for the control group.

mean2, sd2

mean and sd in N(mean,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_{control}+\delta|data) for side equals to 'upper' and the results of Pr(\mu_{control}>\mu_k+\delta|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.

Value

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

References

Wathen J, Thall P (2017). “A simulation study of outcome adaptive randomization in multi-arm clinical trials.” Clinical Trials, 14, 174077451769230. doi:10.1177/1740774517692302. Murphy K (2007). “Conjugate Bayesian analysis of the Gaussian distribution.” University of British Columbia. https://www.cs.ubc.ca/~murphyk/Papers/bayesGauss.pdf.

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')