man/bdplogit.Rd
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/bdplogit.R
\name{bdplogit}
\alias{bdplogit}
\alias{bdplogit,ANY-method}
\title{Bayesian Discount Prior: Two-Arm Logistic Regression}
\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{
\item{formula}{an object of class "formula." See "Details" for
more information, including specification of treatment
data indicators.}
\item{data}{a data frame containing the current data variables in the model.
A column named \code{treatment} must be present; \code{treatment} must
be binary and indicate treatment group vs. control group.}
\item{data0}{a data frame containing the historical data variables in the model.
The column labels of data and data0 must match.}
\item{prior_treatment_effect}{scalar. The historical adjusted treatment effect.
If left \code{NULL}, value is estimated from the historical data.}
\item{prior_control_effect}{scalar. The historical adjusted control effect.
If left \code{NULL}, value is estimated from the historical data.}
\item{prior_treatment_sd}{scalar. The standard deviation of the historical
adjusted treatment effect. If left \code{NULL}, value is estimated from
the historical data.}
\item{prior_control_sd}{scalar. The standard deviation of the historical
adjusted control effect. If left \code{NULL}, value is estimated from
the historical data.}
\item{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.}
\item{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.}
\item{number_mcmc_alpha}{scalar. Number of Monte Carlo
simulations for estimating the historical data weight. Default is 5000.}
\item{number_mcmc_beta}{scalar. Number of Monte Carlo simulations for
estimating beta, the vector of regression coefficients. Default is 10000.}
\item{discount_function}{character. Specify the discount function to use.
Currently supports \code{weibull}, \code{scaledweibull}, and
\code{identity}. The discount function \code{scaledweibull} scales
the output of the Weibull CDF to have a max value of 1. The \code{identity}
discount function uses the posterior probability directly as the discount
weight. Default value is "\code{identity}".}
\item{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.}
\item{fix_alpha}{logical. Fix alpha at alpha_max? Default value is FALSE.}
\item{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 \code{discount_function} = "identity".}
\item{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 \code{discount_function} = "identity".}
\item{method}{character. Analysis method with respect to estimation of the weight
paramter alpha. Default method "\code{mc}" estimates alpha for each
Monte Carlo iteration. Alternate value "\code{fixed}" estimates alpha once and
holds it fixed throughout the analysis. See the the \code{bdplm} vignette \cr
\code{vignette("bdplm-vignette", package="bayesDP")} for more details.}
}
\value{
\code{bdplogit} returns an object of class "bdplogit".
An object of class "\code{bdplogit}" is a list containing at least
the following components:
\describe{
\item{\code{posterior}}{
data frame. The posterior draws of the covariates, the intercept, and
the treatment effect. The grid of sigma values are included.}
\item{\code{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 \code{method="mc"}, the result is a matrix of
estimates, otherwise for \code{method="fixed"}, the result is a vector
of estimates.}
\item{\code{estimates}}{
list. The posterior means and standard errors of the intercept,
treatment effect, covariate effect(s) and error variance.}
}
}
\description{
\code{bdplogit} is used to estimate the treatment effect
in the presence of covariates using the logistic regression analysis
implementation of the Bayesian discount prior. \code{summary} and
\code{print} methods are supported. Currently, the function only supports
a two-arm clinical trial where all of current treatment, current control,
historical treatment, and historical control data are present
}
\details{
\code{bdplogit} uses a two-stage approach for determining the
strength of historical data in estimation of an adjusted mean or covariate
effect. In the first stage, a \emph{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 two-arm regression analysis, the comparison is the
proability (\code{p}) that the covariate effect of an historical data indicator is
significantly different from zero. The comparison metric \code{p} is then
input into the discount function and the final strength of the
historical data is returned (\code{alpha}).
In the second stage, posterior estimation is performed where the discount
function parameter, \code{alpha}, is used to weight the historical data
effects.
The formula must include an intercept (i.e., do not use \code{-1} in
the formula) and both data and data0 must be present.
The column names of data and data0 must match. See \code{examples} below for
example usage.
The underlying model uses the \code{MCMClogit} function of the MCMCpack
package to carryout posterior estimation. Add more.
}
\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)
}