calc_power_prior_norm {beastt} | R Documentation |
Calculate a (potentially inverse probability weighted) normal power prior using external data.
calc_power_prior_norm(
external_data,
response,
prior = NULL,
external_sd = NULL
)
external_data |
This can either be a |
response |
Name of response variable |
prior |
Either |
external_sd |
Standard deviation of external response data if assumed
known. It can be left as |
Weighted participant-level response data from an external study are
incorporated into an inverse probability weighted (IPW) power prior for the
parameter of interest \theta
(e.g., the control mean if borrowing
from an external control arm). When borrowing information from an external
dataset of size N_{E}
, the IPW likelihood of the external response
data y_E
with weights \hat{\boldsymbol{a}}_0
is defined as
\mathcal{L}_E(\theta \mid \boldsymbol{y}_E, \hat{\boldsymbol{a}}_0,
\sigma_{E}^2) \propto \exp \left( -\frac{1}{2 \sigma_{E}^2}
\sum_{i=1}^{N_{E}} \hat{a}_{0i} (y_i - \theta)^2 \right).
The prior
argument should be either a distributional object with a family
type of normal
or NULL
, corresponding to the use of a normal initial
prior or an improper uniform initial prior (i.e., \pi(\theta) \propto
1
), respectively.
The external_sd
argument can be a positive value if the external standard
deviation is assumed known or left as NULL
otherwise. If external_sd = NULL
, then prior
must be NULL
to indicate the use of an improper
uniform initial prior for \theta
, and an improper prior is defined
for the unknown external standard deviation such that \pi(\sigma_E^2)
\propto (\sigma_E^2)^{-1}
. The details of the IPW power prior for each
case are as follows:
external_sd = positive value
(\sigma_E^2
known):With
either a proper normal or an improper uniform initial prior, the IPW
weighted power prior for \theta
is a normal distribution.
external_sd = NULL
(\sigma_E^2
unknown):With improper
priors for both \theta
and \sigma_E^2
, the marginal IPW weighted
power prior for \theta
after integrating over \sigma_E^2
is
a non-standardized t
distribution.
Defining the weights \hat{\boldsymbol{a}}_0
to equal 1 results in a
conventional normal (or t
) power prior if the external standard
deviation is known (unknown).
Normal power prior object
Other power prior:
calc_power_prior_beta()
library(distributional)
library(dplyr)
# This function can be used directly on the data
calc_power_prior_norm(ex_norm_df,
response = y,
prior = dist_normal(50, 10),
external_sd = 0.15)
# Or this function can be used with a propensity score object
ps_obj <- calc_prop_scr(internal_df = filter(int_norm_df, trt == 0),
external_df = ex_norm_df,
id_col = subjid,
model = ~ cov1 + cov2 + cov3 + cov4)
calc_power_prior_norm(ps_obj,
response = y,
prior = dist_normal(50, 10),
external_sd = 0.15)