pmax_normal {RARtrials}

Posterior Probability that a Particular Arm is the Best for Continuous Endpoint with Known Variances

Description

Calculate posterior probability that a particular arm is the best in a trial using Bayesian response-adaptive randomization with a control group (the Thall \& Wathen method). The conjugate prior distributions follow Normal (N(mean,sd)) distributions for continuous outcomes with known variance in each arm and can be specified individually.

Usage

pmax_normal(
  armn,
  mean1 = NULL,
  sd1 = NULL,
  mean2 = NULL,
  sd2 = NULL,
  mean3 = NULL,
  sd3 = NULL,
  mean4 = NULL,
  sd4 = NULL,
  mean5 = NULL,
  sd5 = NULL,
  side,
  ...
)

Arguments

armn

number of arms in the trial with values up to 5. When armn=2, only mean1 to mean2 and sd1 to sd2 need to be specified. When armn=3, only mean1 to mean3 and sd1 to sd3 need to be specified. When armn=4, only mean1 to mean4 and sd1 to sd4 need to be specified. When armn=5, mean1 to mean5 and sd1 to sd5 need to be specified.

mean1, sd1

mean and sd in Normal(mean,sd) for the arm to calculate the allocation probability of.

mean2, sd2

mean and sd in Normal(mean,sd) for one of the remaining arms.

mean3, sd3

mean and sd in Normal(mean,sd) for one of the remaining arms.

mean4, sd4

mean and sd in Normal(mean,sd) for one of the remaining arms.

mean5, sd5

mean and sd in Normal(mean,sd) for one of the remaining arms.

side

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

...

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

Details

This function calculates the results of formula Pr(\mu_k=max\{\mu_1,...,\mu_K\}) for side equals to 'upper' and the results of formula Pr(\mu_k=min\{\mu_1,...,\mu_K\}) for side equals to 'lower'. This function returns the probability that the posterior probability of arm k is maximal or minimal in trials with up to five arms.

Value

a probability that a particular arm is the best in trials up to five arms.

Examples

pmax_normal(armn=5,mean1=0.8,sd1=0.2,mean2=0.5,sd2=0.1,mean3=0.8,
sd3=0.5,mean4=0.6,sd4=0.2,mean5=0.6,sd5=0.2,side='upper')
pmax_normal(armn=4,mean1=8,sd1=2,mean2=8.5,sd2=2,mean3=8.3,
sd3=1.8,mean4=8.7,sd4=2,side='lower')
pmax_normal(armn=3,mean1=80,sd1=20,mean2=50,sd2=10,mean3=80,
sd3=15,side='upper')