bdplogit {bayesDP}  R Documentation 
Bayesian Discount Prior: TwoArm Logistic Regression
Description
bdplogit
is used to estimate the treatment effect
in the presence of covariates using the logistic 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
bdplogit(
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_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_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
bdplogit
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 uses the MCMClogit
function of the MCMCpack
package to carryout posterior estimation. Add more.
Value
bdplogit
returns an object of class "bdplogit".
An object of class "bdplogit
" 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)