calc_post_beta {beastt}

Calculate Posterior Beta

Description

Calculate a posterior distribution that is beta (or a mixture of beta components). Only the relevant treatment arms from the internal dataset should be read in (e.g., only the control arm if constructing a posterior distribution for the control response rate).

Usage

calc_post_beta(internal_data, response, prior)

Arguments

internal_data

This can either be a propensity score object or a tibble of the internal data.

response

Name of response variable

prior

A distributional object corresponding to a beta distribution or a mixture distribution of beta components

Details

For a given arm of an internal trial (e.g., the control arm or an active treatment arm) of size N_I, suppose the response data are binary such that y_i \sim \mbox{Bernoulli}(\theta), i=1,\ldots,N_I. The posterior distribution for \theta is written as

\pi( \theta \mid \boldsymbol{y} ) \propto \mathcal{L}(\theta \mid \boldsymbol{y}) \; \pi(\theta),

where \mathcal{L}(\theta \mid \boldsymbol{y}) is the likelihood of the response data from the internal arm and \pi(\theta) is a prior distribution on \theta (either a beta distribution or a mixture distribution with an arbitrary number of beta components). The posterior distribution for \theta is either a beta distribution or a mixture of beta components depending on whether the prior is a single beta distribution or a mixture distribution.

Value

distributional object

Examples

library(dplyr)
library(distributional)
calc_post_beta(internal_data = filter(int_binary_df, trt == 1),
                              response = y,
                              prior = dist_beta(0.5, 0.5))