bdpbinomial {bayesDP}  R Documentation 
Bayesian Discount Prior: Binomial counts
Description
bdpbinomial
is used for estimating posterior samples from a
binomial outcome where an informative prior is used. The prior weight
is determined using a discount function. This code is modeled after
the methodologies developed in Haddad et al. (2017).
Usage
bdpbinomial(
y_t = NULL,
N_t = NULL,
y0_t = NULL,
N0_t = NULL,
y_c = NULL,
N_c = NULL,
y0_c = NULL,
N0_c = NULL,
discount_function = "identity",
alpha_max = 1,
fix_alpha = FALSE,
a0 = 1,
b0 = 1,
number_mcmc = 10000,
weibull_scale = 0.135,
weibull_shape = 3,
method = "mc",
compare = TRUE
)
Arguments
y_t 
scalar. Number of events for the current treatment group. 
N_t 
scalar. Sample size of the current treatment group. 
y0_t 
scalar. Number of events for the historical treatment group. 
N0_t 
scalar. Sample size of the historical treatment group. 
y_c 
scalar. Number of events for the current control group. 
N_c 
scalar. Sample size of the current control group. 
y0_c 
scalar. Number of events for the historical control group. 
N0_c 
scalar. Sample size of the historical control group. 
discount_function 
character. Specify the discount function to use.
Currently supports 
alpha_max 
scalar. Maximum weight the discount function can apply. Default is 1. For a twoarm trial, 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. 
a0 
scalar. Prior value for the beta rate. Default is 1. 
b0 
scalar. Prior value for the beta rate. Default is 1. 
number_mcmc 
scalar. Number of Monte Carlo simulations. Default is 10000. 
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. For a twoarm trial, 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. For a twoarm trial, 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 " 
compare 
logical. Should a comparison object be included in the fit?
For a onearm analysis, the comparison object is simply the posterior
chain of the treatment group parameter. For a twoarm analysis, the comparison
object is the posterior chain of the treatment effect that compares treatment and
control. If 
Details
bdpbinomial
uses a twostage approach for determining the
strength of historical data in estimation of a binomial count mean outcome.
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. With binomial data,
the comparison is the proability (p
) that the current count is less
than the historical count. The comparison metric p
is then input
into the Weibull 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 incorporated in all posterior
estimation procedures.
To carry out a single arm (OPC) analysis, data for the current treatment
(y_t
and N_t
) and historical treatment (y0_t
and
N0_t
) must be input. The results are then based on the posterior
distribution of the current data augmented by the historical data.
To carry our a twoarm (RCT) analysis, data for the current treatment and at least one of current or historical control data must be input. The results are then based on the posterior distribution of the difference between current treatment and control, augmented by available historical data.
For more details, see the bdpbinomial
vignette:
vignette("bdpbinomialvignette", package="bayesDP")
Value
bdpbinomial
returns an object of class "bdpbinomial". The
functions summary
and
print
are used to obtain and
print a summary of the results, including user inputs. The
plot
function displays visual
outputs as well.
An object of class bdpbinomial
is a list containing at least
the following components:
posterior_treatment

list. Entries contain values related to the treatment group:
alpha_discount
numeric. Alpha value, the weighting parameter of the historical data.p_hat
numeric. The posterior probability of the stochastic comparison between the current and historical data.posterior
vector. A vector of lengthnumber_mcmc
containing posterior Monte Carlo samples of the event rate of the treatment group. If historical treatment data is present, the posterior incorporates the weighted historical data.posterior_flat
vector. A vector of lengthnumber_mcmc
containing Monte Carlo samples of the event rate of the current treatment group under a flat/noninformative prior, i.e., no incorporation of the historical data.prior
vector. If historical treatment data is present, a vector of lengthnumber_mcmc
containing Monte Carlo samples of the event rate of the historical treatment group under a flat/noninformative prior.
posterior_control

list. Similar entries as
posterior_treament
. Only present if a control group is specified. final

list. Contains the final comparison object, dependent on the analysis type:
Onearm analysis: vector. Posterior chain of binomial proportion.
Twoarm analysis: vector. Posterior chain of binomial proportion difference comparing treatment and control groups.
args1

list. Entries contain user inputs. In addition, the following elements are ouput:
arm2
binary indicator. Used internally to indicate onearm or twoarm analysis.intent
character. Denotes current/historical status of treatment and control groups.
References
Haddad, T., Himes, A., Thompson, L., Irony, T., Nair, R. MDIC Computer Modeling and Simulation working group.(2017) Incorporation of stochastic engineering models as prior information in Bayesian medical device trials. Journal of Biopharmaceutical Statistics, 115.
See Also
summary
,
print
,
and plot
for details of each of the
supported methods.
Examples
# Onearm trial (OPC) example
fit < bdpbinomial(
y_t = 10,
N_t = 500,
y0_t = 25,
N0_t = 250,
method = "fixed"
)
summary(fit)
print(fit)
## Not run:
plot(fit)
## End(Not run)
# Twoarm (RCT) example
fit2 < bdpbinomial(
y_t = 10,
N_t = 500,
y0_t = 25,
N0_t = 250,
y_c = 8,
N_c = 500,
y0_c = 20,
N0_c = 250,
method = "fixed"
)
summary(fit2)
print(fit2)
## Not run:
plot(fit2)
## End(Not run)