Compute Posterior Probability of Experimental Treatment Being Greater than Control

Function to perform statistical analysis using a Beta-Binomial Bayesian model. It computes the posterior probability that the success rate of an experimental treatment exceeds that of a control treatment, based on observed outcomes.

Usage

ProbExpGreaterCtrlBeta(
  vOutcomesS,
  vOutcomesE,
  dAlphaS,
  dBetaS,
  dAlphaE,
  dBetaE
)

Arguments

vOutcomesS

A vector of binary outcomes (0 or 1) for the control treatment.

vOutcomesE

A vector of binary outcomes (0 or 1) for the experimental treatment.

dAlphaS

The alpha parameter of the Beta prior for the control treatment.

dBetaS

The beta parameter of the Beta prior for the control treatment.

dAlphaE

The alpha parameter of the Beta prior for the experimental treatment.

dBetaE

The beta parameter of the Beta prior for the experimental treatment.

Value

A list containing:

dPostProb

The posterior probability that the success rate of the experimental treatment is greater than that of the control treatment.

Details

In the Beta-Binomial model, it is assumed that the probability of success (\(\pi\)) follows a Beta distribution: \(\pi \sim Beta(\alpha, \beta)\). Given observed binary outcomes, the posterior distribution of \(\pi\) is: \(\pi | \text{data} \sim \text{Beta}(\alpha + \text{\# successes}, \beta + \text{\# non-successes})\). This function samples from the posterior distributions of the success probabilities for both control and experimental treatments, and calculates the posterior probability that the experimental treatment has a higher success rate than the control treatment.