Package 'bayesCT' reference manual

Title:	Simulation and Analysis of Adaptive Bayesian Clinical Trials
Description:	Simulation and analysis of Bayesian adaptive clinical trials for binomial, continuous, and time-to-event data types, incorporates historical data and allows early stopping for futility or early success. The package uses novel and efficient Monte Carlo methods for estimating Bayesian posterior probabilities, evaluation of loss to follow up, and imputation of incomplete data. The package has the functionality for dynamically incorporating historical data into the analysis via the power prior or non-informative priors.
Authors:	Thevaa Chandereng [aut, cre] , Donald Musgrove [aut], Tarek Haddad [aut], Graeme L. Hickey [aut] , Timothy Hanson [aut], Theodore Lystig [aut]
Maintainer:	Thevaa Chandereng <[email protected]>
License:	GPL-3 \| file LICENSE
Version:	0.99.3.9000
Built:	2024-11-09 04:09:18 UTC
Source:	https://github.com/thevaachandereng/bayesct

Analysis wrapper function

Description

Wrapper function to analyze Bayesian trials.

Usage

analysis(
  input,
  type = "binomial",
  N_max_treatment = NULL,
  N_max_control = NULL,
  .data = NULL
)
analysis(
  input,
  type = "binomial",
  N_max_treatment = NULL,
  N_max_control = NULL,
  .data = NULL
)

Arguments

`input`	list. Input function for all the analysis.
`type`	character. Type of analysis to be ran (binomial (default), normal. etc.).
`N_max_treatment`	integer. Maximum allowable sample size for the treatment arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`N_max_control`	integer. Maximum allowable sample size for the control arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`.data`	NULL. Stores the binomial data for analysis. Should not be edited by user.

Value

A list with results of the analysis of Bayesian trial.

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 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 patients 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 patients who had loss to follow up? 1 for yes and 0 for no.

Beta prior for for control and treatment group

Description

Wrapper function for beta prior beta(a0, b0).

Usage

beta_prior(a0 = 1, b0 = 1, .data = NULL)
beta_prior(a0 = 1, b0 = 1, .data = NULL)

Arguments

`a0`	numeric. The first shape parameter in the beta distribution (`beta(a0, b0)`).
`b0`	numeric. The second shape parameter in the beta distribution (`beta(a0, b0)`).
`.data`	NULL. Stores the proportion of control and treatment. Should not be edited by the user.

Value

A list with vector of beta rate for the beta prior for treatment and control group.

Examples

beta_prior(a0 = 1, b0 = 1)

beta_prior(a0 = 1, b0 = 1)

Analyzing a Bayesian trial for binomial counts

Description

Function to analyze a Bayesian trial for binomial count data which allows for early stopping and incorporation of historical data using the discount function approach.

Usage

binomial_analysis(
  treatment,
  outcome,
  complete = NULL,
  p_treatment = 0,
  N_max_treatment = NULL,
  N_max_control = 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"
)
binomial_analysis(
  treatment,
  outcome,
  complete = NULL,
  p_treatment = 0,
  N_max_treatment = NULL,
  N_max_control = 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"
)

Arguments

`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.
`p_treatment`	scalar. Proportion of events under the treatment arm.
`N_max_treatment`	integer. Maximum allowable sample size for the treatment arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`N_max_control`	integer. Maximum allowable sample size for the control arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`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 `"greater"` (default), `"less"` or `"two.sided"`.
`N_impute`	scalar. Number of imputations for Monte Carlo simulation of missing data.
`h0`	scalar. Threshold for comparing two mean values. Default is `h0 = 0`.
`number_mcmc`	scalar. Number of Markov Chain Monte Carlo 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 (`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 maximum 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.
`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 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.
`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 parameter 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.

Details

If the enrollment size is at the final sample size, i.e. the maximum allowable sample size for the trial, then this function is not of practical use since there is no opportunity to stop trial enrollment. In such a case, it is expected that the follow-up will be conducted per the study protocol and a final analysis made.

Value

A list of output for the Bayesian trial for binomial count:

prob_of_accepting_alternative: integer. 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: integer. The number of patients enrolled in the experimental group for each simulation.
N_control: integer. 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: integer. The number of patients who completed the trial and had no loss to follow-up.
N_max_treatment: integer. Maximum allowable sample size for the treatment arm (including the currently enrolled subjects).
N_max_control: integer. Maximum allowable sample size for the control arm (including the currently enrolled subjects).
post_prob_accept_alternative: scalar. 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: integer. 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: integer. Did the trial stop for early success during imputation of patient who had loss to follow up? 1 for yes and 0 for no.

Proportion of an event in control and treatment

Description

Wrapper function for proportion of an event in control and treatment group with binomial outcome.

Usage

binomial_outcome(p_treatment = NULL, p_control = NULL, .data = NULL)
binomial_outcome(p_treatment = NULL, p_control = NULL, .data = NULL)

Arguments

`p_treatment`	numeric. The proportion of an event in the treatment group, 0 < $p_treatment$ < 1.
`p_control`	numeric. The proportion of an event in the control group, 0 < $p_control$ < 1.
`.data`	NULL. Stores the proportion of control and treatment. Should not be edited by the user.

Value

A list with proportion of control and treatment group.

Examples

binomial_outcome(p_control = 0.12, p_treatment = 0.08)

binomial_outcome(p_control = 0.12, p_treatment = 0.08)

Binomial counts for Bayesian adaptive trials

Description

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

Usage

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"
)
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"
)

Arguments

`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 proportion 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 Markov Chain Monte Carlo 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 maximum 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 parameter 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.

Value

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.

Binomial dataset for analyzing adaptive Bayesian trials

Description

A dataset containing the results of 300 patients with binomial outcome, the dataset is filled with loss to follow up.

Usage

data(binomialdata)
data(binomialdata)

Format

A data frame with 300 rows and 4 variables:

id: Patient ID in the trial.
treatment: Treatment assignment for patients, 1 for treatment group 0 for control group.
outcome: Binomial outcome of the trial, 1 for response (success or failure), 0 for no response.
complete: 1 for complete outcome, 0 for loss to follow-up.

Examples

data(binomialdata)
data(binomialdata)

Data file for binomial analysis

Description

Wrapper function for data file in binomial analysis.

Usage

data_binomial(treatment, outcome, complete, .data = NULL)
data_binomial(treatment, outcome, complete, .data = NULL)

Arguments

`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.
`.data`	NULL. Stores the binomial data for analysis. Should not be edited by user.

Value

A list with treatment, outcome and loss to follow up vector with binomial outcome.

Examples

data_binomial(treatment = c(0, 1), outcome = c(1, 1), complete = c(1, 1))

data_binomial(treatment = c(0, 1), outcome = c(1, 1), complete = c(1, 1))

Data file for continuous (normally distributed) data analysis

Description

Wrapper function for data file in normal analysis.

Usage

data_normal(treatment, outcome, complete, .data = NULL)
data_normal(treatment, outcome, complete, .data = NULL)

Arguments

`treatment`	vector. Treatment assignment for patients, 1 for treatment group and 0 for control group
`outcome`	vector. Normal outcome of the trial.
`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.
`.data`	NULL. Stores the normal data for analysis. Should not be edited by the user.

Value

a list with treatment, outcome and loss to follow up vector with normal outcome.

Data file for survival analysis

Description

Wrapper function for data file in survival analysis.

Usage

data_survival(time, treatment, event, .data = NULL)
data_survival(time, treatment, event, .data = NULL)

Arguments

`time`	vector. exposure time for the subjects. It must be the same length as the treatment variable.
`treatment`	vector. Treatment assignment for patients, 1 for treatment group and 0 for control group
`event`	vector. The status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2 = death). For censored data, the status indicator is 0 = right censored, 1 = event at time. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.
`.data`	NULL. Stores the survival data for analysis. Should not be edited by the user.

Value

A list with time, treatment, and event with time-to-event outcome.

Examples

data_survival(time      = c(6.2, 8.2, 8.0, 2.3),
                        treatment = c(0, 1, 0, 1),
                        event     = c(1, 1, 1, 1))

data_survival(time      = c(6.2, 8.2, 8.0, 2.3),
                        treatment = c(0, 1, 0, 1),
                        event     = c(1, 1, 1, 1))

Simulating enrollment dates

Description

This function simulates enrollment dates using either Poisson distribution

Usage

enrollment(param, N_total, time = NULL)
enrollment(param, N_total, time = NULL)

Arguments

`param`	vector. Lambda values for Poisson distribution.
`N_total`	integer. Value of total sample size.
`time`	vector. Knots (of `length(param)` - 1) indicating end of time when a specific lambda is used.

Value

A vector of enrollment times (from time of first patient enrollment) in days.

Examples

enrollment(param = c(0.003, 0.7), 100, time = 10)

enrollment(param = c(0.3, 0.5, 0.9, 1.2, 2.1), 200, c(20, 30, 40, 60))

enrollment(param = c(0.003, 0.7), 100, time = 10)

enrollment(param = c(0.3, 0.5, 0.9, 1.2, 2.1), 200, c(20, 30, 40, 60))

Enrollment rate wrapper

Description

Wrapper function for enrollment rate.

Usage

enrollment_rate(lambda = 0.3, time = NULL, .data = NULL)
enrollment_rate(lambda = 0.3, time = NULL, .data = NULL)

Arguments

`lambda`	vector. Vector with different enrollment rate parameters.
`time`	vector. Vector with different cut-off times (knots) for lambda.
`.data`	NULL. This should not be changed by the user.

Value

A list with enrollment rate information.

Examples

enrollment_rate(lambda = c(0.3, 1), time = 25)
enrollment_rate(lambda = c(0.3, 1), time = 25)

Gamma prior for for control and treatment group

Description

Wrapper function for gamma prior Gamma(a0, b0).

Usage

gamma_prior(a0 = 0.1, b0 = 0.1, .data = NULL)
gamma_prior(a0 = 0.1, b0 = 0.1, .data = NULL)

Arguments

`a0`	numeric. The shape parameter in the gamma distribution (`beta(a0, b0)`).
`b0`	numeric. The scale parameter in the beta distribution (`beta(a0, b0)`).
`.data`	NULL. Stores the gamma prior rate. Should not be edited by the user.

Value

A list with vector of gamma rate for the gamma prior for treatment and control group.

Examples

gamma_prior(a0 = 0.1, b0 = 0.1)

gamma_prior(a0 = 0.1, b0 = 0.1)

Historical data for binomial distribution

Description

Wrapper function for historical data from binomial outcome.

Usage

historical_binomial(
  y0_treatment = NULL,
  N0_treatment = NULL,
  discount_function = "identity",
  y0_control = NULL,
  N0_control = NULL,
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)
historical_binomial(
  y0_treatment = NULL,
  N0_treatment = NULL,
  discount_function = "identity",
  y0_control = NULL,
  N0_control = NULL,
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)

Arguments

`y0_treatment`	scalar. Number of events for the historical treatment arm.
`N0_treatment`	scalar. Number of observations of the historical treatment group.
`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 maximum 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.
`y0_control`	scalar. Number of events for the historical control arm.
`N0_control`	scalar. Number of observations of the historical control group.
`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 parameter 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.
`.data`	NULL. Stores the proportion of control and treatment. Should not be edited by the user.

Value

A list with historical data for control and treatment group with the discount function.

Examples

historical_binomial(y0_treatment = 5, N0_treatment = 10, y0_control = 15, N0_control = 23)
historical_binomial(y0_treatment = 5, N0_treatment = 10, y0_control = 15, N0_control = 23,
                     discount_function = "weibull", alpha_max = 1, fix_alpha = FALSE,
                     weibull_scale = 0.135, weibull_shape = 3)

historical_binomial(y0_treatment = 5, N0_treatment = 10, y0_control = 15, N0_control = 23)
historical_binomial(y0_treatment = 5, N0_treatment = 10, y0_control = 15, N0_control = 23,
                     discount_function = "weibull", alpha_max = 1, fix_alpha = FALSE,
                     weibull_scale = 0.135, weibull_shape = 3)

Historical data for normal distribution

Description

Wrapper function for historical data from continuous (normally distributed) outcome.

Usage

historical_normal(
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)
historical_normal(
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)

Arguments

`mu0_treatment`	scalar. Mean of the historical treatment group.
`sd0_treatment`	scalar. Standard deviation of the historical treatment group.
`N0_treatment`	scalar. Number of observations of the historical treatment group.
`mu0_control`	scalar. Mean of the historical control group.
`sd0_control`	scalar. Standard deviation of the historical control group.
`N0_control`	scalar. Number of observations of the historical control group.
`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 maximum 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 parameter 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.
`.data`	NULL. Stores the normal data for analysis. Should not be edited by the user.

Value

A list with historical data for control and treatment group with the discount function.

Examples

historical_normal(mu0_treatment = 15, sd0_treatment = 2, N0_treatment = 10,
                  mu0_control = 17, sd0_control = 3, N0_control = 20)

historical_normal(mu0_treatment = 15, sd0_treatment = 2, N0_treatment = 10,
                  mu0_control = 17, sd0_control = 3, N0_control = 20)

Historical data for survival analysis

Description

Wrapper function for historical data from time-to-event outcome.

Usage

historical_survival(
  time = NULL,
  treatment = NULL,
  event = NULL,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)
historical_survival(
  time = NULL,
  treatment = NULL,
  event = NULL,
  discount_function = "identity",
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed",
  .data = NULL
)

Arguments

`time`	vector. exposure time for the subjects. It must be the same length as the treatment variable.
`treatment`	vector. Treatment assignment for patients, 1 for treatment group and 0 for control group
`event`	vector. The status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2 = death). For censored data, the status indicator is 0 = right censored, 1 = event at time. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.
`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 maximum 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 parameter 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.
`.data`	NULL. Stores the historical time, treatment and event. Should not be edited by the user.

Value

A list with historical data for time-to-event outcome with the discount function.

Examples

historical_survival(time      = rexp(10, 0.01),
                    treatment = rep(10, 1),
                    event     = rep(10, 1))

historical_survival(time      = rexp(10, 0.01),
                    treatment = rep(10, 1),
                    event     = rep(10, 1))

Hypothesis wrapper

Description

Wrapper function for the hypothesis in the trial.

Usage

hypothesis(
  delta = 0,
  futility_prob = 0.05,
  prob_accept_ha = 0.95,
  expected_success_prob = 0.9,
  alternative = "greater",
  .data = NULL
)
hypothesis(
  delta = 0,
  futility_prob = 0.05,
  prob_accept_ha = 0.95,
  expected_success_prob = 0.9,
  alternative = "greater",
  .data = NULL
)

Arguments

`delta`	numeric. Threshold set for margin in null hypothesis. The default is set to 0.
`futility_prob`	numeric. Probability of futility. The default is 0.05.
`prob_accept_ha`	numeric. Posterior probability of accepting alternative hypothesis. The default is 0.95.
`expected_success_prob`	numeric. Probability of expected success.
`alternative`	character. The string specifying the alternative hypothesis, must be one of `"greater"` (default), `"less"` or `"two.sided"`.
`.data`	NULL. This should not be changed by the user.

Value

A list with information of hypothesis testing (threshold, futility probability, probability of accepting the alternative hypothesis, and probability of expected success).

Examples

hypothesis(delta = 0, futility_prob = 0.05, prob_accept_ha = 0.95,
           expected_success_prob = 0.90, alternative = "greater")
hypothesis(delta = 0.2, futility_prob = 0.1, prob_accept_ha = 0.975,
           expected_success_prob = 0.80, alternative = "less")
hypothesis(delta = 0, futility_prob = 0.05, prob_accept_ha = 0.95,
           expected_success_prob = 0.90, alternative = "greater")
hypothesis(delta = 0.2, futility_prob = 0.1, prob_accept_ha = 0.975,
           expected_success_prob = 0.80, alternative = "less")

Imputation wrapper

Description

Wrapper function for no_of_impute.

Usage

impute(no_of_impute = 10000, number_mcmc = 10000, .data = NULL)
impute(no_of_impute = 10000, number_mcmc = 10000, .data = NULL)

Arguments

`no_of_impute`	integer. Number of Monte Carlo imputations for missing data.
`number_mcmc`	scalar. Number of Markov Chain Monte Carlo (MCMC) draws from posterior distribution.
`.data`	NULL. This should not be changed by the user.

Value

A list with number of imputation.

Examples

impute(no_of_impute = 100, number_mcmc = 1000)
impute(no_of_impute = 100, number_mcmc = 1000)

Analyzing Bayesian trial for continuous (normally distributed) data

Description

Function to analyze Bayesian trial for continuous (normally distributed) data, which allows early stopping and incorporation of historical data using the discount function approach.

Usage

normal_analysis(
  treatment,
  outcome,
  complete = NULL,
  N_max_treatment = NULL,
  N_max_control = NULL,
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  alternative = "greater",
  N_impute = 100,
  h0 = 0,
  number_mcmc = 10000,
  prob_ha = 0.95,
  futility_prob = 0.1,
  expected_success_prob = 0.9,
  discount_function = "identity",
  fix_alpha = FALSE,
  alpha_max = 1,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)
normal_analysis(
  treatment,
  outcome,
  complete = NULL,
  N_max_treatment = NULL,
  N_max_control = NULL,
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  alternative = "greater",
  N_impute = 100,
  h0 = 0,
  number_mcmc = 10000,
  prob_ha = 0.95,
  futility_prob = 0.1,
  expected_success_prob = 0.9,
  discount_function = "identity",
  fix_alpha = FALSE,
  alpha_max = 1,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)

Arguments

`treatment`	vector. Treatment assignment for patients, 1 for treatment group and 0 for control group.
`outcome`	vector. Normal outcome of the trial.
`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.
`N_max_treatment`	integer. Maximum allowable sample size for the treatment arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`N_max_control`	integer. Maximum allowable sample size for the control arm (including the currently enrolled subjects). Default is NULL, meaning we are already at the final analysis.
`mu0_treatment`	scalar. Mean of the historical treatment group.
`sd0_treatment`	scalar. Standard deviation of the historical treatment group.
`N0_treatment`	scalar. Number of observations of the historical treatment group.
`mu0_control`	scalar. Mean of the historical control group.
`sd0_control`	scalar. Standard deviation of the historical control group.
`N0_control`	scalar. Number of observations of the historical control group.
`alternative`	character. The string specifying the alternative hypothesis, must be one of `"greater"` (default), `"less"` or `"two.sided"`.
`N_impute`	scalar. Number of imputations for Monte Carlo simulation of missing data.
`h0`	scalar. Threshold for comparing two mean values. Default is `h0 = 0`.
`number_mcmc`	scalar. Number of Markov Chain Monte Carlo 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.
`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 maximum 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.
`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 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.
`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 parameter 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.

Details

Value

A list of output for the analysis of Bayesian trial for normal mean:

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 follow-up.
N_max_treatment: integer. Maximum allowable sample size for the treatment arm (including the currently enrolled subjects).
N_max_control: integer. Maximum allowable sample size for the control arm (including the currently enrolled subjects).
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.

Parameters for treatment and control in continuous (normally distributed) data case

Description

Wrapper function for mean and standard deviation with continuous (normally distributed) outcome.

Usage

normal_outcome(
  mu_control = NULL,
  sd_control = NULL,
  mu_treatment = NULL,
  sd_treatment = NULL,
  .data = NULL
)
normal_outcome(
  mu_control = NULL,
  sd_control = NULL,
  mu_treatment = NULL,
  sd_treatment = NULL,
  .data = NULL
)

Arguments

`mu_control`	numeric. The mean for the control group.
`sd_control`	numeric. The standard deviation for the control group.
`mu_treatment`	numeric. The mean for the treatment group.
`sd_treatment`	numeric. The standard deviation for the treatment group.
`.data`	NULL. Stores the normal data for analysis. Should not be edited by the user.

Value

A list with means and standard deviations for control and treatment groups.

Examples

normal_outcome(mu_control = 12, mu_treatment = 8,
               sd_treatment = 2.2, sd_control = 1.6)

normal_outcome(mu_control = 12, mu_treatment = 8,
               sd_treatment = 2.2, sd_control = 1.6)

Normal distribution for Bayesian Adaptive trials

Description

Simulation of continuous (normally distributed) data for Bayesian adaptive trials with various inputs to control for power, sample size, type I error rate, etc.

Usage

normalBACT(
  mu_treatment,
  sd_treatment,
  mu_control = NULL,
  sd_control = NULL,
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  N_total,
  lambda = 0.3,
  lambda_time = NULL,
  interim_look = NULL,
  EndofStudy,
  block = 2,
  rand_ratio = c(1, 1),
  discount_function = "identity",
  alternative = "greater",
  prop_loss_to_followup = 0.15,
  h0 = 0,
  futility_prob = 0.05,
  expected_success_prob = 0.9,
  prob_ha = 0.95,
  N_impute = 10,
  number_mcmc = 10000,
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)
normalBACT(
  mu_treatment,
  sd_treatment,
  mu_control = NULL,
  sd_control = NULL,
  mu0_treatment = NULL,
  sd0_treatment = NULL,
  N0_treatment = NULL,
  mu0_control = NULL,
  sd0_control = NULL,
  N0_control = NULL,
  N_total,
  lambda = 0.3,
  lambda_time = NULL,
  interim_look = NULL,
  EndofStudy,
  block = 2,
  rand_ratio = c(1, 1),
  discount_function = "identity",
  alternative = "greater",
  prop_loss_to_followup = 0.15,
  h0 = 0,
  futility_prob = 0.05,
  expected_success_prob = 0.9,
  prob_ha = 0.95,
  N_impute = 10,
  number_mcmc = 10000,
  alpha_max = 1,
  fix_alpha = FALSE,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)

Arguments

`mu_treatment`	scalar. Mean outcome in the treatment arm.
`sd_treatment`	scalar. Standard deviation of outcome in the treatment.
`mu_control`	scalar. Mean outcome in the control arm.
`sd_control`	scalar. Standard deviation of outcome in the control arm. arm.
`mu0_treatment`	scalar. Mean of the historical treatment group.
`sd0_treatment`	scalar. Standard deviation of the historical treatment group.
`N0_treatment`	scalar. Number of observations of the historical treatment group.
`mu0_control`	scalar. Mean of the historical control group.
`sd0_control`	scalar. Standard deviation of the historical control group.
`N0_control`	scalar. Number of observations of the historical control group.
`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.
`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.
`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 maximum 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.
`alternative`	character. The string specifying the alternative hypothesis, must be one of `"greater"` (default), `"less"` or `"two.sided"`.
`prop_loss_to_followup`	scalar. Overall proportion of subjects lost to follow-up.
`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 Markov Chain Monte Carlo draws in sampling posterior.
`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 parameter 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.

Value

A list of output for a single trial simulation:

mu_treatment: scalar. The input parameter of mean value of the outcome in the treatment group.
p_control: scalar. The input parameter of mean value of the outcome in the control group.
sd_treatment: scalar. The input parameter of standard deviation of the outcome in the control group.
sd_control: scalar. The input parameter of standard deviation of the outcome 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.

Gaussian dataset for analyzing adaptive Bayesian trials

Description

A dataset containing the results of 300 patients with continuous (normal) outcome, the dataset is filled with loss to follow up.

Usage

data(normaldata)
data(normaldata)

Format

A data frame with 300 rows and 4 variables:

id: Patient ID in the trial.
treatment: Treatment assignment for patients, 1 for treatment group 0 for control group.
outcome: Continuous outcome of the trial (Gaussian distributed).
complete: 1 for complete outcome, 0 for loss to follow-up.

Examples

data(normaldata)
data(normaldata)

Imputes time-to-event outcomes.

Description

Imputation of time-to-event outcomes using the piecewise constant hazard exponential function.

Usage

pw_exp_impute(time, hazard, maxtime = NULL, cutpoint = NULL)
pw_exp_impute(time, hazard, maxtime = NULL, cutpoint = NULL)

Arguments

`time`	vector. The observed time for patient that have had no event or passed maxtime.
`hazard`	vector. The constant hazard rates for exponential failures.
`maxtime`	scalar. maximum time before end of study.
`cutpoint`	vector. The change-point vector indicating time when the hazard rates change.

Value

a dataset with simulated follow-up time (time) and respective event indicator (1 = event, 0 = censoring)

Examples

pw_exp_impute(time = c(120), c(0.005, 0.001), 110, 40)
          pw_exp_impute(time = c(10, 20, 30), c(0.005, 0.01, 0.02), 100, c(40, 80))
          pw_exp_impute(time = c(40, 30), c(0.005, 0.01), 120, c(50))


pw_exp_impute(time = c(120), c(0.005, 0.001), 110, 40)
          pw_exp_impute(time = c(10, 20, 30), c(0.005, 0.01, 0.02), 100, c(40, 80))
          pw_exp_impute(time = c(40, 30), c(0.005, 0.01), 120, c(50))

Simulates time-to-event outcomes.

Description

Simulation of time-to-event outcomes using the piecewise constant hazard exponential function.

Usage

pw_exp_sim(hazard, n, maxtime = NULL, cutpoint = NULL)
pw_exp_sim(hazard, n, maxtime = NULL, cutpoint = NULL)

Arguments

`hazard`	vector. The constant hazard rates for exponential failures.
`n`	scalar. The number of outcomes for simulation.
`maxtime`	scalar. maximum time before end of study.
`cutpoint`	vector. The change-point vector indicating time when the hazard rates change.

Value

a dataset with simulated follow-up time (time) and respective event indicator (1 = event, 0 = censoring)

Examples

pw_exp_sim(c(0.02, 0.01, 0.005), 100, 100, c(10, 20))
          pw_exp_sim(0.015, 100, 100)


pw_exp_sim(c(0.02, 0.01, 0.005), 100, 100, c(10, 20))
          pw_exp_sim(0.015, 100, 100)

Randomization allocation

Description

Implements a randomization allocation for control and treatment arms with different randomization ratios and block sizes.

Usage

randomization(N_total, block = 2, allocation = c(1, 1))
randomization(N_total, block = 2, allocation = c(1, 1))

Arguments

`N_total`	an integer value of total sample size for randomization allocation.
`block`	a vector value of the block size for randomization. Note that it needs to be a multiple of the sum of `allocation`.
`allocation`	a numeric vector of the randomization allocation in the order `c(control, treatment)`.

Value

the randomization allocation with 0, 1 for control and treatment

Examples

# Implementing treatment allocation for control to treatment with 1:1.5
# randomization ratio
randomization(N_total = 100, block = 5, allocation = c(2, 3))

# Treatment allocation with 2:1 for control to treatment
randomization(N_total = 70, block = 9, allocation = c(2, 1))

# Treatment allocation for control to treatment with 1:2 for control
# to treatment with multiple block sizes c(3, 9, 6)
randomization(N_total = 100, block = c(3, 9, 6), allocation = c(1, 2))

# For complete randomization set the N_total to block size
randomization(N_total = 100, block = 100, allocation = c(1, 1))

# Implementing treatment allocation for control to treatment with 1:1.5
# randomization ratio
randomization(N_total = 100, block = 5, allocation = c(2, 3))

# Treatment allocation with 2:1 for control to treatment
randomization(N_total = 70, block = 9, allocation = c(2, 1))

# Treatment allocation for control to treatment with 1:2 for control
# to treatment with multiple block sizes c(3, 9, 6)
randomization(N_total = 100, block = c(3, 9, 6), allocation = c(1, 2))

# For complete randomization set the N_total to block size
randomization(N_total = 100, block = 100, allocation = c(1, 1))

Randomization scheme wrapper

Description

Wrapper function for the randomization scheme in the trial.

Usage

randomize(block_size = 2, randomization_ratio = c(1, 1), .data = NULL)
randomize(block_size = 2, randomization_ratio = c(1, 1), .data = NULL)

Arguments

`block_size`	integer. Block size for the complete randomization in a block.
`randomization_ratio`	vector. The randomization allocation for control to treatment.
`.data`	NULL. This should not be changed by the user.

Value

A list with randomization details (block size and ratio).

Examples

randomize(block_size = 100, randomization_ratio = c(2, 3))
randomize(block_size = 10, randomization_ratio = c(1, 4))
randomize(block_size = 100, randomization_ratio = c(2, 3))
randomize(block_size = 10, randomization_ratio = c(1, 4))

Simulation wrapper for binomial and normal

Description

Wrapper function for complete binomial and normal function to compute power and type I error.

Usage

simulate(input, no_of_sim = 10000, .data = NULL)
simulate(input, no_of_sim = 10000, .data = NULL)

Arguments

`input`	list. Input function for all inputs in binomial, normal, and survival.
`no_of_sim`	numeric. Number of simulations to run.
`.data`	NULL. Stores the proportion of control and treatment, please do not fill it in.

Value

A list with results of the simulation (power and type I error) and the input.

input: A list of input values used in the trial simulation.
power: data frame. A data frame with the interim look and power at each look.
type1_error: scalar. The type I error or the proportion of times the trial rejects the null when the parameters are simulated under the null hypothesis.
est_final: vector. The final estimate of the difference in posterior estimate of treatment and posterior estimate of the control group for all the simulations.
post_prob_accept_alternative: vector. The final probability of accepting the alternative for the simulations.
N_enrolled: vector. The number of patients enrolled in the trial (sum of control and experimental group for each simulation).
stop_futility: vector. 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: vector. Did the trial stop for early success during imputation of patient who had loss to follow up? 1 for yes and 0 for no.

Details of the clinical study

Description

Wrapper function for details of the clinical trial simulation.

Usage

study_details(
  total_sample_size,
  study_period,
  interim_look = NULL,
  prop_loss_to_followup = 0.1,
  .data = NULL
)
study_details(
  total_sample_size,
  study_period,
  interim_look = NULL,
  prop_loss_to_followup = 0.1,
  .data = NULL
)

Arguments

`total_sample_size`	integer. The total sample size.
`study_period`	integer. The length of the study (in days).
`interim_look`	vector. Vector with interim looks (sample sizes).
`prop_loss_to_followup`	integer. The proportion of loss to follow-up.
`.data`	NULL. This should not be changed by the user.

Value

A list with sample size, length of the study, interim looks and proportion loss to follow up.

Examples

study_details(total_sample_size = 300, study_period = 50,
                        interim_look = c(210, 240, 270))
study_details(total_sample_size = 300, study_period = 50,
                        interim_look = c(210, 240, 270))

Analyzing Bayesian trial for time-to-event data

Description

Function to analyze Bayesian trial for time-to-event data which allows early stopping and incorporation of historical data using the discount function approach.

Usage

survival_analysis(
  time,
  treatment,
  event = NULL,
  time0 = NULL,
  treatment0 = NULL,
  event0 = NULL,
  surv_time = NULL,
  h0 = 0,
  breaks = NULL,
  alternative = "greater",
  N_impute = 10,
  number_mcmc = 10000,
  prob_ha = 0.95,
  futility_prob = 0.1,
  expected_success_prob = 0.9,
  prior = c(0.1, 0.1),
  discount_function = "identity",
  fix_alpha = FALSE,
  alpha_max = 1,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)
survival_analysis(
  time,
  treatment,
  event = NULL,
  time0 = NULL,
  treatment0 = NULL,
  event0 = NULL,
  surv_time = NULL,
  h0 = 0,
  breaks = NULL,
  alternative = "greater",
  N_impute = 10,
  number_mcmc = 10000,
  prob_ha = 0.95,
  futility_prob = 0.1,
  expected_success_prob = 0.9,
  prior = c(0.1, 0.1),
  discount_function = "identity",
  fix_alpha = FALSE,
  alpha_max = 1,
  weibull_scale = 0.135,
  weibull_shape = 3,
  method = "fixed"
)

Arguments

`time`	vector. exposure time for the subjects. It must be the same length as the treatment variable.
`treatment`	vector. Treatment assignment for patients, 1 for treatment group and 0 for control group
`event`	vector. The status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2 = death). For censored data, the status indicator is 0 = right censored, 1 = event at time. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.
`time0`	vector. Historical exposure time for the subjects. It must be the same length as the treatment variable.
`treatment0`	vector. the historical treatment assignment for patients, 1 for treatment group and 0 for control group.
`event0`	vector. Historical status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2 = death). For censored data, the status indicator is 0 = right censored, 1 = event at time. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.
`surv_time`	scalar. scalar. Survival time of interest for computing the probability of survival for a single arm (OPC) trial. Default is overall (pooled), i.e. current and historical, median survival time.
`h0`	scalar. Threshold for comparing two mean values. Default is `h0 = 0`.
`breaks`	vector. Breaks (interval starts) used to compose the breaks of the piecewise exponential model. Do not include zero. Default breaks are the quantiles of the input times.
`alternative`	character. The string specifying the alternative hypothesis, must be one of `"greater"` (default), `"less"` or `"two.sided"`.
`N_impute`	scalar. Number of imputations for Monte Carlo simulation of missing data.
`number_mcmc`	scalar. Number of Markov Chain Monte Carlo 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 the gamma rate, Gamma(a0, b0). The default is set to Gamma(0.1, 0.1).
`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 maximum 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.
`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 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.
`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 parameter 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.

Value

A list of output for the Bayesian trial for time-to-event:

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.
alpha_max: scalar. The alpha_max input.
N_treatment: scalar. The number of patients enrolled in the experimental group for each simulation.
event_treatment: scalar. The number of events in the experimental group for each simulation.
N_control: scalar. The number of patients enrolled in the control group for each simulation.
event_control: scalar. The number of events in the control group for each simulation.
N_enrolled: scalar. The number of patients enrolled in the trial (sum of control and experimental group for each simulation).
N_complete: scalar. The number of patients whose time passes the surv_time.
alpha_discount: vector. The alpha discount function used for control and treatment.
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.

Piecewise constant hazard rates and the cutpoint for control and treatment group

Description

Wrapper function for the piecewise constant hazard rates and the cutpoint for control and treatment group.

Usage

survival_outcome(
  hazard_treatment = NULL,
  cutpoint = NULL,
  hazard_control = NULL,
  .data = NULL
)
survival_outcome(
  hazard_treatment = NULL,
  cutpoint = NULL,
  hazard_control = NULL,
  .data = NULL
)

Arguments

`hazard_treatment`	vector. Constant hazard rates under the treatment arm.
`cutpoint`	vector. The change-point vector indicating time when the hazard rates change.
`hazard_control`	vector. Constant hazard rates under the control arm.
`.data`	NULL. Stores the hazard rates and cutpoint. Should not be edited by the user.

Value

A list with hazard rates and cutpoint for control and treatment group.

Examples

survival_outcome(hazard_treatment = 0.06,
                           hazard_control   = 0.08,
                           cutpoint         = NULL)
survival_outcome(hazard_treatment = 0.06,
                           hazard_control   = 0.08,
                           cutpoint         = NULL)

Time-to-event outcome for Bayesian Adaptive trials

Description

Simulation for time-to-event outcome for Bayesian Adaptive trial with different inputs to control for power, sample size, type 1 error rate, etc.

Usage

survivalBACT(
  hazard_treatment,
  cutpoint = NULL,
  hazard_control = NULL,
  N_total,
  breaks = NULL,
  time0 = NULL,
  treatment0 = NULL,
  event0 = NULL,
  lambda = 0.3,
  lambda_time = NULL,
  interim_look = NULL,
  EndofStudy,
  prior = c(0.1, 0.1),
  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"
)
survivalBACT(
  hazard_treatment,
  cutpoint = NULL,
  hazard_control = NULL,
  N_total,
  breaks = NULL,
  time0 = NULL,
  treatment0 = NULL,
  event0 = NULL,
  lambda = 0.3,
  lambda_time = NULL,
  interim_look = NULL,
  EndofStudy,
  prior = c(0.1, 0.1),
  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"
)

Arguments

`hazard_treatment`	vector. Constant hazard rates under the treatment arm.
`cutpoint`	vector. The change-point vector indicating time when the hazard rates change.
`hazard_control`	vector. Constant hazard rates under the control arm.
`N_total`	scalar. Total sample size.
`breaks`	vector. Breaks (interval starts) used to compose the breaks of the piecewise exponential model. Do not include zero. Default breaks are the quantiles of the input times.
`time0`	vector. Historical exposure time for the subjects. It must be the same length as the treatment variable.
`treatment0`	vector. the historical treatment assignment for patients, 1 for treatment group and 0 for control group.
`event0`	vector. Historical status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE = death) or 1/2 (2 = death). For censored data, the status indicator is 0 = right censored, 1 = event at time. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have an event.
`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 the gamma rate, Gamma(a0, b0). The default is set to Gamma(0.1, 0.1).
`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 proportion 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 Markov Chain Monte Carlo 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 maximum 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 parameter 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.

Value

A list of output for a single trial simulation.

lambda_treatment: vector. The input parameter of constant hazard rates in the treatment group.
cutpoint_treatment: vector. The change-point vector when the constant hazard rate(s) changes for the treatment group.
lambda_control: vector. The input parameter of constant hazard rates in the control group.
cutpoint_control: vector. The change-point vector when the constant hazard rate(s) changes for 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 treatment group for each simulation.
event_treatment: scalar. The number of events in the treatment group for each simulation.
N_control: scalar. The number of patients enrolled in the control group for each simulation.
event_control: scalar. The number of events 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.

Time-to-event dataset for analyzing adaptive Bayesian trials

Description

A dataset containing the results of 100 patients with time-to-event outcome, the dataset is filled with treatment assignment and status (0 = censored, 1 = not censored).

Usage

data(survivaldata)
data(survivaldata)

Format

A data frame with 100 rows and 4 variables:

id: Patient ID in the trial.
treatment: Treatment assignment for patients, 1 for treatment group 0 for control group.
time: The follow up time for patients.
event: The status indicator, normally 0=alive, 1=dead or 0 = no event, 1 = event occurred.

Examples

data(survivaldata)
data(survivaldata)

Package 'bayesCT'

Help Index

Analysis wrapper function

Description

Usage

Arguments

Value

Beta prior for for control and treatment group

Description

Usage

Arguments

Value

Examples

Analyzing a Bayesian trial for binomial counts

Description

Usage

Arguments

Details

Value

Proportion of an event in control and treatment

Description

Usage

Arguments

Value

Examples

Binomial counts for Bayesian adaptive trials

Description

Usage

Arguments

Value

Binomial dataset for analyzing adaptive Bayesian trials

Description

Usage

Format

Examples

Data file for binomial analysis

Description

Usage

Arguments

Value

Examples

Data file for continuous (normally distributed) data analysis

Description

Usage

Arguments

Value

Data file for survival analysis

Description

Usage

Arguments

Value

Examples

Simulating enrollment dates

Description

Usage

Arguments

Value

Examples

Enrollment rate wrapper

Description

Usage

Arguments

Value

Examples

Gamma prior for for control and treatment group

Description

Usage

Arguments

Value

Examples

Historical data for binomial distribution

Description

Usage

Arguments

Value

Examples

Historical data for normal distribution

Description

Usage

Arguments