pgreater_normal: Calculate the Futility Stopping Probability for Continuous...

In RARtrials: Response-Adaptive Randomization in Clinical Trials

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({\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.

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'.

References

\insertRef

Wathen2017RARtrials \insertRefKevin2007RARtrials

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')

RARtrials documentation built on April 4, 2025, 1:21 a.m.