bdplm {bayesDP}  R Documentation 
Bayesian Discount Prior: TwoArm Linear Regression
Description
bdplm
is used to estimate the treatment effect in the
presence of covariates using the regression analysis implementation of the
Bayesian discount prior. summary
and print
methods are
supported. Currently, the function only supports a twoarm clinical trial
where all of current treatment, current control, historical treatment, and
historical control data are present
Usage
bdplm(
formula = formula,
data = data,
data0 = NULL,
prior_treatment_effect = NULL,
prior_control_effect = NULL,
prior_treatment_sd = NULL,
prior_control_sd = NULL,
prior_covariate_effect = 0,
prior_covariate_sd = 10000,
number_mcmc_alpha = 5000,
number_mcmc_sigmagrid = 5000,
number_mcmc_sigma = 100,
number_mcmc_beta = 10000,
discount_function = "identity",
alpha_max = 1,
fix_alpha = FALSE,
weibull_scale = 0.135,
weibull_shape = 3,
method = "mc"
)
Arguments
formula 
an object of class "formula." See "Details" for more information, including specification of treatment data indicators. 
data 
a data frame containing the current data variables in the model.
A column named 
data0 
a data frame containing the historical data variables in the model. The column labels of data and data0 must match. 
prior_treatment_effect 
scalar. The historical adjusted treatment
effect. If left 
prior_control_effect 
scalar. The historical adjusted control effect.
If left 
prior_treatment_sd 
scalar. The standard deviation of the historical
adjusted treatment effect. If left 
prior_control_sd 
scalar. The standard deviation of the historical
adjusted control effect. If left 
prior_covariate_effect 
vector. The prior mean(s) of the covariate effect(s). Default value is zero. If a single value is input, the the scalar is repeated to the length of the input covariates. Otherwise, care must be taken to ensure the length of the input matches the number of covariates. 
prior_covariate_sd 
vector. The prior standard deviation(s) of the covariate effect(s). Default value is 1e4. If a single value is input, the the scalar is repeated to the length of the input covariates. Otherwise, care must be taken to ensure the length of the input matches the number of covariates. 
number_mcmc_alpha 
scalar. Number of Monte Carlo simulations for estimating the historical data weight. Default is 5000. 
number_mcmc_sigmagrid 
scalar. Grid size for computing sigma. Default is 5000. See "Details" for more information. 
number_mcmc_sigma 
scalar. Number of Monte Carlo simulations for estimating sigma. Default is 1000. See "Details" for more information. 
number_mcmc_beta 
scalar. Number of Monte Carlo simulations for estimating beta, the vector of regression coefficients. Default is 10000. 
discount_function 
character. Specify the discount function to use.
Currently supports 
alpha_max 
scalar. Maximum weight the discount function can apply. Default is 1. Users may specify a vector of two values where the first value is used to weight the historical treatment group and the second value is used to weight the historical control group. 
fix_alpha 
logical. Fix alpha at alpha_max? Default value is FALSE. 
weibull_scale 
scalar. Scale parameter of the Weibull discount function
used to compute alpha, the weight parameter of the historical data. Default
value is 0.135. Users may specify a vector of two values where the first
value is used to estimate the weight of the historical treatment group and
the second value is used to estimate the weight of the historical control
group. Not used when 
weibull_shape 
scalar. Shape parameter of the Weibull discount function
used to compute alpha, the weight parameter of the historical data. Default
value is 3. Users may specify a vector of two values where the first value
is used to estimate the weight of the historical treatment group and the
second value is used to estimate the weight of the historical control
group. Not used when 
method 
character. Analysis method with respect to estimation of the
weight paramter alpha. Default method " 
Details
bdplm
uses a twostage approach for determining the strength
of historical data in estimation of an adjusted mean or covariate effect.
In the first stage, a discount function is used that that defines
the maximum strength of the historical data and discounts based on
disagreement with the current data. Disagreement between current and
historical data is determined by stochastically comparing the respective
posterior distributions under noninformative priors. Here with a twoarm
regression analysis, the comparison is the proability (p
) that the
covariate effect of an historical data indicator is significantly different
from zero. The comparison metric p
is then input into the discount
function and the final strength of the historical data is returned
(alpha
).
In the second stage, posterior estimation is performed where the discount
function parameter, alpha
, is used to weight the historical data
effects.
The formula must include an intercept (i.e., do not use 1
in the
formula) and both data and data0 must be present. The column names of data
and data0 must match. See examples
below for example usage.
The underlying model results in a marginal posterior distribution for the
error variance sigma2
that does not have a known distribution. Thus,
we use a grid search to draw samples of sigma2
. First, the marginal
posterior is evaluated at a grid of number_mcmc_sigmagrid
sigma2
values. The bounds of the grid are taken as approximately six
standard deviations from an estimate of sigma2
using the lm
function. Next, number_mcmc_sigma
posterior draws of sigma2
are made by sampling with replacement from the grid with each value having
the corresponding marginal posterior probability of being selected. With
posterior draws of sigma2
in hand, we can make posterior draws of
the regression coefficients.
Value
bdplm
returns an object of class "bdplm".
An object of class "bdplm
" is a list containing at least the
following components:
posterior
data frame. The posterior draws of the covariates, the intercept, and the treatment effect. The grid of sigma values are included.
alpha_discount

vector. The posterior probability of the stochastic comparison between the current and historical data for each of the treatment and control arms. If
method="mc"
, the result is a matrix of estimates, otherwise formethod="fixed"
, the result is a vector of estimates. estimates
list. The posterior means and standard errors of the intercept, treatment effect, covariate effect(s) and error variance.
Examples
# Set sample sizes
n_t < 30 # Current treatment sample size
n_c < 30 # Current control sample size
n_t0 < 80 # Historical treatment sample size
n_c0 < 80 # Historical control sample size
# Treatment group vectors for current and historical data
treatment < c(rep(1, n_t), rep(0, n_c))
treatment0 < c(rep(1, n_t0), rep(0, n_c0))
# Simulate a covariate effect for current and historical data
x < rnorm(n_t + n_c, 1, 5)
x0 < rnorm(n_t0 + n_c0, 1, 5)
# Simulate outcome:
#  Intercept of 10 for current and historical data
#  Treatment effect of 31 for current data
#  Treatment effect of 30 for historical data
#  Covariate effect of 3 for current and historical data
Y < 10 + 31 * treatment + x * 3 + rnorm(n_t + n_c, 0, 5)
Y0 < 10 + 30 * treatment0 + x0 * 3 + rnorm(n_t0 + n_c0, 0, 5)
# Place data into separate treatment and control data frames and
# assign historical = 0 (current) or historical = 1 (historical)
df_ < data.frame(Y = Y, treatment = treatment, x = x)
df0 < data.frame(Y = Y0, treatment = treatment0, x = x0)
# Fit model using default settings
fit < bdplm(
formula = Y ~ treatment + x, data = df_, data0 = df0,
method = "fixed"
)
# Look at estimates and discount weight
summary(fit)
print(fit)