calc_power_prior_beta {beastt}

Calculate Power Prior Beta

Description

Calculate a (potentially inverse probability weighted) beta power prior for the control response rate using external control data.

Usage

calc_power_prior_beta(external_data, response, prior)

Arguments

external_data

This can either be a prop_scr_obj created by calling create_prop_scr() or a tibble of the external data. If it is just a tibble the weights will be assumed to be 1.

response

Name of response variable

prior

A beta distributional object that is the initial prior for the control response rate before the external control data are observed

Details

Weighted participant-level response data from an external study are incorporated into an inverse probability weighted (IPW) power prior for the control response rate \theta_C. When borrowing information from an external control arm of size N_{EC}, the components of the IPW power prior for \theta_C are defined as follows:

Initial prior:

\theta_C \sim \mbox{Beta}(\nu_0, \phi_0)

IPW likelihood of the external response data \boldsymbol{y}_E with weights \hat{\boldsymbol{a}}_0:

\mathcal{L}_E(\theta_C \mid \boldsymbol{y}_E, \hat{\boldsymbol{a}}_0) \propto \exp \left( \sum_{i=1}^{N_{EC}} \hat{a}_{0i} \left[ y_i \log(\theta_C) + (1 - y_i) \log(1 - \theta_C) \right] \right)

IPW power prior:

\theta_C \mid \boldsymbol{y}_E, \hat{\boldsymbol{a}}_0 \sim \mbox{Beta} \left( \sum_{i=1}^{N_{EC}} \hat{a}_{0i} y_i + \nu_0, \sum_{i=1}^{N_{EC}} \hat{a}_{0i} (1 - y_i) + \phi_0 \right)

Defining the weights \hat{\boldsymbol{a}}_0 to equal 1 results in a conventional beta power prior.

Value

Beta power prior object

See Also

Other power prior: calc_power_prior_norm()

Examples

library(distributional)
library(dplyr)
# This function can be used directly on the data
calc_power_prior_beta(external_data = ex_binary_df,
  response = y,
  prior = dist_beta(0.5, 0.5))

# Or this function can be used with a propensity score object
ps_obj <- calc_prop_scr(internal_df = filter(int_binary_df, trt == 0),
  external_df = ex_binary_df,
  id_col = subjid,
  model = ~ cov1 + cov2 + cov3 + cov4)

calc_power_prior_beta(ps_obj,
  response = y,
  prior = dist_beta(0.5, 0.5))