binomialBACT: Binomial counts for Bayesian Adaptive Trials
In bayesCT: Simulation and Analysis of Adaptive Bayesian Clinical Trials

Simulation for binomial counts for Bayesian Adaptive trial with different inputs to control for power, sample size, type 1 error rate, etc.

binomialBACT(
  p_treatment,
  p_control = NULL,
  y0_treatment = NULL,
  N0_treatment = NULL,
  y0_control = NULL,
  N0_control = NULL,
  N_total,
  lambda = 0.3,
  lambda_time = NULL,
  interim_look = NULL,
  EndofStudy,
  prior = c(1, 1),
  block = 2,
  rand_ratio = c(1, 1),
  prop_loss_to_followup = 0.1,
  alternative = "greater",
  h0 = 0,
  futility_prob = 0.05,
  expected_success_prob = 0.9,
  prob_ha = 0.95,
  N_impute = 10,
  number_mcmc = 10000,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)

`p_treatment`	scalar. Proportion of events under the treatment arm.
`p_control`	scalar. Proportion of events under the control arm.
`y0_treatment`	scalar. Number of events for the historical treatment arm.
`N0_treatment`	scalar. Sample size of the historical treatment arm.
`y0_control`	scalar. Number of events for the historical control arm.
`N0_control`	scalar. Sample size of the historical control arm.
`N_total`	scalar. Total sample size.
`lambda`	vector. Enrollment rates across simulated enrollment times. See `enrollment` for more details.
`lambda_time`	vector. Enrollment time(s) at which the enrollment rates change. Must be same length as lambda. See `enrollment` for more details.
`interim_look`	vector. Sample size for each interim look. Note: the maximum sample size should not be included.
`EndofStudy`	scalar. Length of the study.
`prior`	vector. Prior values of beta rate, Beta(a0, b0). The default is set to Beta(1, 1).
`block`	scalar. Block size for generating the randomization schedule.
`rand_ratio`	vector. Randomization allocation for the ratio of control to treatment. Integer values mapping the size of the block. See `randomization` for more details.
`prop_loss_to_followup`	scalar. Overall oroportion of subjects lost to follow-up.
`alternative`	character. The string specifying the alternative hypothesis, must be one of `"greater"` (default), `"less"` or `"two.sided"`.
`h0`	scalar. Threshold for comparing two mean values. Default is `h0=0`.
`futility_prob`	scalar. Probability of stopping early for futility.
`expected_success_prob`	scalar. Probability of stopping early for success.
`prob_ha`	scalar. Probability of alternative hypothesis.
`N_impute`	scalar. Number of imputations for Monte Carlo simulation of missing data.
`number_mcmc`	scalar. Number of Monte Carlo Markov Chain draws in sampling posterior.
`discount_function`	character. If incorporating historical data, specify the discount function. Currently supports the Weibull function (`discount_function="weibull"`), the scaled-Weibull function (`discount_function="scaledweibull"`), and the identity function (`discount_function="identity"`). The scaled-Weibull discount function scales the output of the Weibull CDF to have a max value of 1. The identity discount function uses the posterior probability directly as the discount weight. Default value is `"identity"`. See `bdpnormal` for more details.
`alpha_max`	scalar. Maximum weight the discount function can apply. Default is 1. For a two-arm 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.
`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 two-arm 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 two-arm 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 "`mc`" estimates alpha for each Monte Carlo iteration. Alternate value "`fixed`" estimates alpha once and holds it fixed throughout the analysis. See the the `bdpsurvival` vignette `vignette("bdpsurvival-vignette", package="bayesDP")` for more details.

a list of output for a single trial simulation.

p_treatment: scalar. The input parameter of proportion of events in the treatment group.
p_control: scalar. The input parameter of proportion of events in the control group.
prob_of_accepting_alternative: scalar. The input parameter of probability threshold 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.
interim_look: vector. The sample size for each interim look.
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 follow-up.
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.
est_interim: scalar. The interim estimate of the difference in posterior estimate of treatment and posterior estimate of the control group.