pmax_NIX {RARtrials}

Posterior Probability that a Particular Arm is the Best for Continuous Endpoint with Unknown 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-Inverse-Chi-Squared (NIX) distributions for continuous outcomes with unknown variance in each arm and can be specified individually.

Usage

pmax_NIX(
  armn,
  par1 = NULL,
  par2 = NULL,
  par3 = NULL,
  par4 = NULL,
  par5 = NULL,
  side,
  ...
)

Arguments

armn

number of arms in the trial with values up to 5. When armn=2, only par1 to par2 need to be specified. When par1 to par3 need to be specified. When par1 to par4 need to be specified. When par1 to par5 need to be specified.

par1

a vector of parameters including m, V, a, b for the arm with a Normal-Inverse-Chi-Squared prior to calculate the allocation probability of.

par2

a vector of parameters including m, V, a, b for one of the remaining arms with a Normal-Inverse-Chi-Squared prior.

par3

a vector of parameters including m, V, a, b for one of the remaining arms with a Normal-Inverse-Chi-Squared prior.

par4

a vector of parameters including m, V, a, b for one of the remaining arms with a Normal-Inverse-Chi-Squared prior.

par5

a vector of parameters including m, V, a, b for one of the remaining arms with a Normal-Inverse-Chi-Squared prior.

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. Parameters used in a Normal-Inverse-Gamma ((\mu,\sigma^2) \sim NIG(mean=m,variance=V \times \sigma^2,shape=a,rate=b)) distribution should be converted to parameters equivalent in a Normal-Inverse-Chi-Squared ((\mu,\sigma^2) \sim NIX(mean=\mu,effective sample size=\kappa,degrees of freedom=\nu,variance=\sigma^2/\kappa)) distribution using convert_gamma_to_chisq before applying this function.

Value

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

Examples

para<-list(V=1/2,a=0.8,m=9.1,b=1/2)
par<-convert_gamma_to_chisq(para)
set.seed(123451)
y1<-rnorm(100,9.1,1)
par11<-update_par_nichisq(y1, par)
set.seed(123452)
y2<-rnorm(90,9,1)
par22<-update_par_nichisq(y2, par)
set.seed(123453)
y3<-rnorm(110,8.92,1)
par33<-update_par_nichisq(y3, par)
y4<-rnorm(120,8.82,1)
par44<-update_par_nichisq(4, par)
pmax_NIX(armn=4,par1=par11,par2=par22,par3=par33,par4=par44,side='upper')
pmax_NIX(armn=4,par1=par11,par2=par22,par3=par33,par4=par44,side='lower')

para<-list(V=1/2,a=0.5,m=9.1/100,b=0.00002)
par<-convert_gamma_to_chisq(para)
set.seed(123451)
y1<-rnorm(100,0.091,0.009)
par11<-update_par_nichisq(y1, par)
set.seed(123452)
y2<-rnorm(90,0.09,0.009)
par22<-update_par_nichisq(y2, par)
set.seed(123453)
y3<-rnorm(110,0.0892,0.009)
par33<-update_par_nichisq(y3, par)
pmax_NIX(armn=3,par1=par11,par2=par22,par3=par33,side='upper')
pmax_NIX(armn=3,par1=par11,par2=par22,par3=par33,side='lower')