binomial_analysis {bayesCT}  R Documentation 
Function to analyze Bayesian trial for binomial count data which allows early stopping and incorporation of historical data using the discount function approach
binomial_analysis( treatment, outcome, complete = NULL, y0_treatment = NULL, N0_treatment = NULL, y0_control = NULL, N0_control = NULL, alternative = "greater", N_impute = 10, h0 = 0, number_mcmc = 10000, prob_ha = 0.95, futility_prob = 0.1, expected_success_prob = 0.9, prior = c(1, 1), discount_function = "identity", fix_alpha = FALSE, alpha_max = 1, weibull_scale = 0.135, weibull_shape = 3, method = "fixed" )
treatment 
vector. treatment assignment for patients, 1 for treatment group and 0 for control group 
outcome 
vector. binomial outcome of the trial, 1 for response (success or failure), 0 for no response. 
complete 
vector. similar length as treatment and outcome variable, 1 for complete outcome, 0 for loss to follow up. If complete is not provided, the dataset is assumed to be complete. 
y0_treatment 
scalar. Number of events for the historical treatment arm. 
N0_treatment 
scalar. Number of observations of the historical treatment group. 
y0_control 
scalar. Number of events for the historical control arm. 
N0_control 
scalar. Number of observations of the historical control group. 
alternative 
character. The string specifying the alternative
hypothesis, must be one of 
N_impute 
scalar. Number of imputations for Monte Carlo simulation of missing data. 
h0 
scalar. Threshold for comparing two mean values. Default is

number_mcmc 
scalar. Number of Monte Carlo Markov Chain draws in sampling posterior. 
prob_ha 
scalar. Probability of alternative hypothesis. 
futility_prob 
scalar. Probability of stopping early for futility. 
expected_success_prob 
scalar. Probability of stopping early for success. 
prior 
vector. Prior values of beta rate, Beta(a0, b0). The default is set to Beta(1, 1). 
discount_function 
character. If incorporating historical data, specify
the discount function. Currently supports the Weibull function
( 
fix_alpha 
logical. Fix alpha at alpha_max? Default value is FALSE. 
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. 
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 discount_function = "identity". 
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 discount_function = "identity". 
method 
character. Analysis method with respect to estimation of the weight
paramter alpha. Default method " 
a list of output for the Bayesian trial for binomial count.
prob_of_accepting_alternative
scalar. The input parameter of probability of accepting the alternative.
margin
scalar. The margin input value of difference between mean estimate of treatment and mean estimate of the control.
alternative
character. The input parameter of alternative hypothesis.
N_treatment
scalar. The number of patients enrolled in the experimental group for each simulation.
N_control
scalar. The number of patients enrolled in the control group for each simulation.
N_enrolled
vector. The number of patients enrolled in the trial (sum of control and experimental group for each simulation. )
N_complete
scalar. The number of patients who completed the trial and had no loss to followup.
post_prob_accept_alternative
vector. The final probability of accepting the alternative hypothesis after the analysis is done.
est_final
scalar. The final estimate of the difference in posterior estimate of treatment and posterior estimate of the control group.
stop_futility
scalar. Did the trial stop for futility during imputation of patient who had loss to follow up? 1 for yes and 0 for no.
stop_expected_success
scalar. Did the trial stop for early success during imputation of patient who had loss to follow up? 1 for yes and 0 for no.