Package 'BayesFBHborrow'

Title: Bayesian Dynamic Borrowing with Flexible Baseline Hazard Function
Description: Allows Bayesian borrowing from a historical dataset for time-to- event data. A flexible baseline hazard function is achieved via a piecewise exponential likelihood with time varying split points and smoothing prior on the historic baseline hazards. The method is described in Scott and Lewin (2024) <doi:10.48550/arXiv.2401.06082>, and the software paper is in Axillus et al. (2024) <doi:10.48550/arXiv.2408.04327>.
Authors: Darren Scott [aut, cre], Sophia Axillus [aut]
Maintainer: Darren Scott <[email protected]>
License: Apache License (>= 2)
Version: 2.0.2
Built: 2024-12-16 07:05:26 UTC
Source: CRAN

Help Index


Proposal beta with a Metropolis Adjusted Langevin (MALA)

Description

Proposal beta with a Metropolis Adjusted Langevin (MALA)

Usage

.beta_MH_MALA(df, beta, bp, cprop_beta, beta_count)

Arguments

df

Data frame with indicators

beta

vector of parameters

bp

number of covariates

cprop_beta

proposal variance standard deviation

beta_count

count number of accepts

Value

updated beta vector


Newton Raphson MH move

Description

Sample beta from RW sampler

Usage

.beta_MH_NR(df, beta, bp, cprop_beta, beta_count)

Arguments

df

Data frame with indicators

beta

vector of parameters

bp

number of covariates

cprop_beta

proposal scalar

beta_count

count number of accepts

Value

updated beta


Beta Metropolis-Hastings random walk move

Description

Update beta via a Metropolis-Hastings Random Walk move

Usage

.beta_MH_RW(df, beta, bp, cprop_beta, beta_count)

Arguments

df

data.frame from dataframe_fun()

beta

beta values

bp

number of covariates

cprop_beta

hyperparameter for beta proposal standard deviation

beta_count

number of moves done for beta

Value

beta, either old or new move


Mean for MALA using derivative for beta proposal

Description

Mean for MALA using derivative for beta proposal

Usage

.beta_mom(df, k, beta, bp, cprop_beta)

Arguments

df

Data frame with indicators

k

index for beta

beta

vector of parameters

bp

number of covariates

cprop_beta

proposal standard dev

Value

proposal mean


First and second derivative of target for mode and variance of proposal

Description

First and second derivative of target for mode and variance of proposal

Usage

.beta_mom.NR.fun(df, k, beta, bp, cprop_beta)

Arguments

df

Data frame with indicators

k

index

beta

vector of parameters

bp

number of covariates

cprop_beta

proposal variance standard deviation

Value

First and second derivative mode and variance


Beta MH RW sampler from freq PEM fit

Description

Sample beta from RW sampler

Usage

.beta.MH.RW.glm(df, beta, beta_count, cprop_beta)

Arguments

df

Data frame with indicators

beta

vector of parameters

beta_count

count number of accepted proposals

cprop_beta

proposal scalar

Value

beta, either old or new move


Birth move in RJMCMC

Description

Calculates new values of x when proposing another split point, based on a weighted mean, as x_new/x <- (1-U)/U

Usage

.birth_move(U, sj, s_star, sjm1, x, j)

Arguments

U

uniform random number

sj

upcoming split point location, j

s_star

new split point location, *

sjm1

previous split point location, j-1

x

vector of parameter values, length J + 1

j

split point

Value

vector with adjusted parameter values after additional split point, length J + 2


Create data.frame for piecewise exponential models

Description

Construct a split data.frame for updated split points

Usage

.dataframe_fun(Y, I, X, s, lambda, bp, J)

Arguments

Y

time-to-event

I

censor indicator

X

design Matrix

s

split point locations, including start and end (length J + 2)

lambda

baseline Hazards (length J+1)

bp

number of covariates

J

number of split points

Value

data.frame with columns c(tstart, id, X1,..., Xp, Y, I, lambda)


Death move in RJMCMC

Description

Calculates new values of x when proposing the death of a split point

Usage

.death_move(sjp1, sj, sjm1, x, j)

Arguments

sjp1

upcoming split point location, J + 1

sj

split point location to be removed, j

sjm1

previous split point location, j-1

x

vector of parameter values, length J + 1

j

split point

Value

vector with adjusted parameter values after removal of split point, length J


Fit frequentist piecewise exponential model for MLE and information matrix of beta

Description

Compute MLE for PEM

Usage

.glmFit(df)

Arguments

df

Data frame with time-to-event, censoring indicator and covariates

Value

beta MLE and inverse of information matrix


Calculate covariance matrix in the MVN-ICAR

Description

Calculate covariance matrix in the MVN-ICAR

Usage

.ICAR_calc(s, J, clam)

Arguments

s

split points, J + 2

J

number of split points

clam

controls neighbor interactions, in range (0, 1)

Value

Sigma_s = (I - W)^(-1) * Q, W, Q


Input checker

Description

Checks inputs before Gibbs sampler is run

Usage

.input_check(
  Y,
  Y_0,
  X,
  X_0,
  tuning_parameters,
  initial_values = NULL,
  hyperparameters
)

Arguments

Y

current time-to-event data

Y_0

historical time-to-event data

X

design Matrix

X_0

design Matrix for historical data

tuning_parameters

list of tuning parameters

initial_values

list of initial values (optional)

hyperparameters

list of hyperparameters

Value

a print statement


RJMCMC (with Bayesian Borrowing)

Description

Metropolis-Hastings Green Reversible Jump move, with Bayesian Borrowing

Usage

.J_RJMCMC(
  df_hist,
  df_curr,
  Y,
  Y_0,
  I,
  I_0,
  X,
  X_0,
  lambda,
  lambda_0,
  beta,
  beta_0,
  mu,
  sigma2,
  tau,
  s,
  J,
  Jmax,
  bp,
  bp_0,
  clam_smooth,
  a_tau = NULL,
  b_tau = NULL,
  c_tau = NULL,
  d_tau = NULL,
  type,
  p_0 = NULL,
  phi,
  pi_b,
  maxSj
)

Arguments

df_hist

data_frame containing historical data.

df_curr

data_frame containing current trial data.

Y

data.

Y_0

historical data.

I

censoring indicator.

I_0

historical trial censoring indicator.

X

design matrix.

X_0

historical trial design matrix.

lambda

baseline hazard.

lambda_0

historical trial baseline hazard.

beta

current trial parameters.

beta_0

historical trial parameters.

mu

prior mean for baseline hazard.

sigma2

prior variance hyperparameter for baseline hazard.

tau

borrowing parameter.

s

split point locations, J + 2.

J

number of split points.

Jmax

maximum number of split points.

bp

number of covariates in current trial.

bp_0

number of covariates in historical trial.

clam_smooth

neighbor interactions, in range (0, 1), for ICAR update.

a_tau

tau hyperparameter.

b_tau

tau hyperparameter.

c_tau

tau hyperparameter.

d_tau

tau hyperparameter.

type

choice of borrowing, "mix", "uni", or any other string for borrowing on every baseline hazard without mixture.

p_0

mixture ratio.

phi

J hyperparameter.

pi_b

probability of birth move.

maxSj

maximal time point, either current or historic.

Value

list of proposed J and s, with adjusted values of lambda, lambda_0, tau, Sigma_s, and data_frames for historical and current trial data.


RJMCMC (without Bayesian Borrowing)

Description

Metropolis-Hastings Green Reversible Jump move, without Bayesian Borrowing

Usage

.J_RJMCMC_NoBorrow(
  df,
  Y_0,
  I_0,
  X_0,
  lambda_0,
  beta_0,
  mu,
  sigma2,
  s,
  J,
  Jmax,
  bp_0,
  clam_smooth,
  phi,
  pi_b
)

Arguments

df

data_frame

Y_0

data

I_0

censoring indicator

X_0

design matrix

lambda_0

baseline hazard

beta_0

historical trial parameters

mu

prior mean for baseline hazard

sigma2

prior variance hyperparameter for baseline hazard

s

split point locations, J + 2

J

number of split points

Jmax

maximum number of split points

bp_0

number of covariates in historical trial

clam_smooth

neighbor interactions, in range (0, 1), for ICAR update

phi

J hyperparameter

pi_b

probability of birth move

Value

list of proposed J and s, with adjusted values of lambda, lambda_0, tau, Sigma_s, and data_frames for historical and current trial data


Lambda_0 MH step, proposal from conditional conjugate posterior

Description

Lambda_0 MH step, proposal from conditional conjugate posterior

Usage

.lambda_0_MH_cp(
  df_hist,
  Y_0,
  I_0,
  X_0 = NULL,
  s,
  beta_0 = NULL,
  mu,
  sigma2,
  lambda,
  lambda_0,
  tau,
  bp_0 = 0,
  J,
  clam,
  a_lam = 0.01,
  b_lam = 0.01,
  lambda_0_count = 0,
  lambda_0_move = 0
)

Arguments

df_hist

data.frame from dataframe_fun()

Y_0

historical trial data

I_0

historical trial censoring indicator

X_0

historical trial design matrix

s

split point locations, (J+2)

beta_0

parameter value for historical covariates

mu

prior mean for baseline hazard

sigma2

prior variance hyperparameter for baseline hazard

lambda

baseline hazard

lambda_0

historical baseline hazard

tau

borrowing parameter

bp_0

number of covariates, length(beta_0)

J

number of split points

clam

controls neighbor interactions, in range (0, 1)

a_lam

lambda hyperparameter, default is 0.01

b_lam

lambda hyperparameter, default is 0.01

lambda_0_count

number of total moves for lambda_0

lambda_0_move

number of accepted moves for lambda_0

Value

list of updated (if accepted) lambda_0 and data.frames, as well as the number of accepted moves


Lambda_0 MH step, proposal from conditional conjugate posterior

Description

Lambda_0 MH step, proposal from conditional conjugate posterior

Usage

.lambda_0_MH_cp_NoBorrow(
  df_hist,
  Y_0,
  I_0,
  X_0 = NULL,
  s,
  beta_0 = NULL,
  mu,
  sigma2,
  lambda_0,
  bp_0 = 0,
  J,
  clam,
  a_lam = 0.01,
  b_lam = 0.01,
  lambda_0_count = 0,
  lambda_0_move = 0
)

Arguments

df_hist

data.frame from dataframe_fun()

Y_0

historical trial data

I_0

historical trial censoring indicator

X_0

historical trial design matrix

s

split point locations, (J+2)

beta_0

parameter value for historical covariates

mu

prior mean for baseline hazard

sigma2

prior variance hyperparameter for baseline hazard

lambda_0

baseline hazard

bp_0

number of covariates, length(beta_0)

J

number of split points

clam

controls neighbor interactions, in range (0, 1)

a_lam

lambda hyperparameter, default is 0.01

b_lam

lambda hyperparameter, default is 0.01

lambda_0_count

number of total moves for lambda_0

lambda_0_move

number of accepted moves for lambda_0

Value

list of updated (if accepted) lambda_0 and data.frames, as well as the number of accepted moves


Propose lambda from a gamma conditional conjugate posterior proposal

Description

Propose lambda from a gamma conditional conjugate posterior proposal

Usage

.lambda_conj_prop(df, beta, j, bp, alam = 0.01, blam = 0.01)

Arguments

df

data.frame from dataframe_fun()

beta

parameter value for beta

j

current split point

bp

number of covariates

alam

lambda hyperparameter, default set to 0.01

blam

lambda hyperparameter, default set to 0.01

Value

list containing proposed lambda, shape and rate parameters


Lambda MH step, proposal from conditional conjugate posterior

Description

Lambda MH step, proposal from conditional conjugate posterior

Usage

.lambda_MH_cp(
  df_hist,
  df_curr,
  Y,
  I,
  X,
  s,
  beta,
  beta_0 = NULL,
  mu,
  sigma2,
  lambda,
  lambda_0,
  tau,
  bp,
  bp_0 = 0,
  J,
  a_lam = 0.01,
  b_lam = 0.01,
  lambda_move = 0,
  lambda_count = 0,
  alpha = 0.3
)

Arguments

df_hist

data.frame from dataframe_fun()

df_curr

data.frame from dataframe_fun()

Y

data

I

censoring indicator

X

design matrix

s

split point locations, J + 2

beta

parameter value for covariates

beta_0

parameter value for historical covariates

mu

prior mean for baseline hazard

sigma2

prior variance hyperparameter for baseline hazard

lambda

baseline hazard

lambda_0

historical baseline hazard

tau

borrowing parameter

bp

number of covariates, length(beta)

bp_0

number of covariates, length(beta_0)

J

number of split points

a_lam

lambda hyperparameter

b_lam

lambda hyperparameter

lambda_move

number of accepted lambda moves

lambda_count

total number of lambda moves

alpha

power parameter

Value

list of updated (if accepted) lambda and data.frames, as well as the number of accepted moves


Calculate log gamma ratio for two different parameter values

Description

Calculate log gamma ratio for two different parameter values

Usage

.lgamma_ratio(x1, x2, shape, rate)

Arguments

x1

old parameter value

x2

proposed parameter value

shape

shape parameter

rate

rate parameter

Value

log gamma ratio


Loglikelihood ratio calculation for beta parameters

Description

Compute log likelihood for beta update

Usage

.llikelihood_ratio_beta(df, beta, beta_new)

Arguments

df

data.frame from dataframe_fun()

beta

beta values

beta_new

proposed beta values

Value

likelihood ratio


Log likelihood for lambda / lambda_0 update

Description

Log likelihood for lambda / lambda_0 update

Usage

.llikelihood_ratio_lambda(df, df_prop, beta)

Arguments

df

data.frame from dataframe_fun()

df_prop

proposal data.frame

beta

parameter value for beta

Value

log likelihood ratio for lambda


Log likelihood function

Description

Log likelihood function

Usage

.log_likelihood(df, beta)

Arguments

df

data.frame containing data, time split points, and lambda

beta

coefficients for covariates

Value

log likelihood given lambdas and betas


Computes the logarithmic sum of an exponential

Description

Computes the logarithmic sum of an exponential

Usage

.logsumexp(x)

Arguments

x

set of log probabilities

Value

the logarithmic sum of an exponential


Log density of proposal for MALA

Description

Log density of proposal for MALA

Usage

.lprop_density_beta(beta_prop, mu, cprop_beta)

Arguments

beta_prop

proposal beta

mu

mean of proposal distribution

cprop_beta

proposal standard dev

Value

log density


log Gaussian proposal density for Newton Raphson proposal

Description

log Gaussian proposal density for Newton Raphson proposal

Usage

.lprop.dens.beta.NR(beta.prop, mu_old, var_old)

Arguments

beta.prop

beta proposal

mu_old

density mean

var_old

density variance

Value

log Gaussian density


Calculate log density tau prior

Description

Calculate log density tau prior

Usage

.ltau_dprior(tau, a_tau, b_tau, c_tau = NULL, d_tau = NULL, p_0 = NULL, type)

Arguments

tau

current value(s) of tau

a_tau

tau hyperparameter

b_tau

tau hyperparameter

c_tau

tau hyperparameter

d_tau

tau hyperparameter

p_0

mixture ratio

type

choice of borrowing, "mix", "uni", or any other string for borrowing on every baseline hazard without mixture

Value

log density of tau


Calculate mu posterior update

Description

Calculate mu posterior update

Usage

.mu_update(Sigma_s, lambda_0, sigma2, J)

Arguments

Sigma_s

VCV matrix (j + 1) x (j + 1).

lambda_0

Baseline hazard.

sigma2

Scale variance.

J

Number of split point.

Value

mu update from Normal.


Normalize a set of probability to one, using the the log-sum-exp trick

Description

Normalize a set of probability to one, using the the log-sum-exp trick

Usage

.normalize_prob(x)

Arguments

x

set of log probabilities

Value

normalized set of log probabilities


Calculates nu and sigma2 for the Gaussian Markov random field prior, for a given split point j

Description

Calculates nu and sigma2 for the Gaussian Markov random field prior, for a given split point j

Usage

.nu_sigma_update(j, lambda_0, mu, sigma2, W, Q, J)

Arguments

j

current split point

lambda_0

historical baseline hazard

mu

prior mean for baseline hazard

sigma2

prior variance hyperparameter for baseline hazard

W

influence from right and left neighbors

Q

individual effect of neighborhood

J

number of split points

Value

nu and sigma2


Plot histogram from MCMC samples

Description

Plots a histogram of the given discrete MCMC samples

Usage

.plot_hist(
  samples,
  title = "",
  xlab = "Values",
  ylab = "Frequency",
  color = "black",
  fill = "blue",
  binwidth = 0.05,
  scale_x = FALSE
)

Arguments

samples

data.frame containing the discrete MCMC samples

title

title of the plot, default is none

xlab

x-label of the plot, default is "Values"

ylab

y-label of the plot, default is "Frequency"

color

outline color for the bars, default is "black"

fill

fill color, default is "blue"

binwidth

width of the histogram bins, default is 0.5

scale_x

option to scale the x-axis, suitable for discrete samples, default is FALSE

Value

a ggplot2 object


Plot smoothed baseline hazards

Description

Plot mean and given quantiles of a matrix. Can also be used to plot derivatives of the baseline hazard, such as estimated cumulative hazard and survival function.

Usage

.plot_matrix(
  x_lim,
  y,
  percentiles = c(0.05, 0.95),
  title = "",
  xlab = "",
  ylab = "",
  color = "blue",
  fill = "blue",
  linewidth = 1,
  alpha = 0.2,
  y2 = NULL,
  color2 = "red",
  fill2 = "red"
)

Arguments

x_lim

time grid

y

samples

percentiles

percentiles to include in plot, default is c(0.025, 0.975)

title

optional, add title to plot

xlab

optional, add xlabel

ylab

optional, add ylabel

color

color of the mid line, default is blue

fill

color of the percentiles, default is blue

linewidth

thickness of the plotted line, default is 1

alpha

opacity of the percentiles, default is 0.2

y2

(optional) second set of samples for comparison

color2

(optional) color of the mid line, default is red

fill2

(optional) color of the percentiles, default is red

Value

a ggplot2 object


Plot MCMC trace

Description

Creates a trace plot of given MCMC samples.

Usage

.plot_trace(
  x_lim,
  samples,
  title = "",
  xlab = "",
  ylab = "",
  color = "black",
  linewidth = 1
)

Arguments

x_lim

x-axis of the plot

samples

samples from MCMC

title

optional, add title to plot

xlab

optional, add xlabel

ylab

optional, add ylabel

color

color of the mid line, default is black

linewidth

thickness of the plotted line, default is 1

Value

a ggplot2 object


Predictive hazard from BayesFBHborrow object

Description

Predictive hazard from BayesFBHborrow object

Usage

.predictive_hazard(out_slam, x_pred, beta_samples)

Arguments

out_slam

samples from the smoothed baseline hazard

x_pred

set of predictors to be used for calculating the predictive hazard

beta_samples

samples of the covariates

Value

matrix of the predictive hazard


Predictive hazard ratio (HR) from BayesFBHborrow object

Description

Predictive hazard ratio (HR) from BayesFBHborrow object

Usage

.predictive_hazard_ratio(x_pred, beta_samples)

Arguments

x_pred

set of predictors to be used for calculating the predictive HR

beta_samples

samples of the covariates

Value

posterior samples for expectation and credible intervals


Predictive survival from BayesFBHborrow object

Description

Predictive survival from BayesFBHborrow object

Usage

.predictive_survival(grid_width, out_slam, x_pred, beta_samples)

Arguments

grid_width

size of time step

out_slam

samples from the smoothed baseline hazard

x_pred

set of predictors to be used for calculating the predictive survival

beta_samples

samples of the covariates

Value

matrix of the predictive survival


Set tuning parameters

Description

Set tuning parameters

Usage

.set_hyperparameters(hyperparameters = NULL, model_choice)

Arguments

hyperparameters

list of hyperparameters, could contain any combination of the listed hyperparameters

model_choice

choice of model, could be either of 'mix', 'uni' or 'all'

Value

filled list of tuning_parameters


Set tuning parameters

Description

Set tuning parameters

Usage

.set_tuning_parameters(tuning_parameters = NULL, borrow, X, X_0 = NULL)

Arguments

tuning_parameters

list of tuning_parameters, could contain any combination of the listed tuning parameters

borrow

choice of borrow, could be TRUE or FALSE

X

design matrix for concurrent trial

X_0

design matrix for historical trial

Value

filled list of tuning_parameters


Metropolis Hastings step: shuffle the split point locations (with Bayesian borrowing)

Description

Metropolis Hastings step: shuffle the split point locations (with Bayesian borrowing)

Usage

.shuffle_split_point_location(
  df_hist,
  df_curr,
  Y_0,
  I_0,
  X_0,
  lambda_0,
  beta_0,
  Y,
  I,
  X,
  lambda,
  beta,
  s,
  J,
  bp_0,
  bp,
  clam_smooth,
  maxSj
)

Arguments

df_hist

dataframe containing historical trial data and parmaeters

df_curr

data.frame containing current trial data and parameters

Y_0

historical trial data

I_0

historical trial censoring indicator

X_0

historical trial design matrix

lambda_0

historical baseline hazard

beta_0

historical parameter vector

Y

data

I

censoring indicator

X

design matrix

lambda

baseline hazard

beta

parameter vector

s

split point locations, J + 2

J

number of split points

bp_0

number of covariates in historical trial

bp

number of covariates in current trial

clam_smooth

neighbor interactions, in range (0, 1), for ICAR update

maxSj

the smallest of the maximal time points, min(max(Y), max(Y_0))

Value

list containing new split points, updated Sigma_s and data.frames for historic and current trial data


Metropolis Hastings step: shuffle the split point locations (without Bayesian borrowing)

Description

Metropolis Hastings step: shuffle the split point locations (without Bayesian borrowing)

Usage

.shuffle_split_point_location_NoBorrow(
  df,
  Y_0,
  I_0,
  X_0,
  lambda_0,
  beta_0,
  s,
  J,
  bp_0,
  clam_smooth
)

Arguments

df

dataframe containing trial data and parameters

Y_0

data

I_0

censoring indicator

X_0

design matrix

lambda_0

baseline hazard

beta_0

parameter vector

s

split point locations, J + 2

J

number of split points

bp_0

number of covariates in historical trial

clam_smooth

neighbor interactions, in range (0, 1), for ICAR update

Value

list containing new split points, updated Sigma_s and data.frames for historic and current trial data


Calculate sigma2 posterior update

Description

Calculate sigma2 posterior update

Usage

.sigma2_update(mu, lambda_0, Sigma_s, J, a_sigma, b_sigma)

Arguments

mu

mean.

lambda_0

Baseline hazard.

Sigma_s

VCV matrix (j + 1) x (j + 1).

J

Number of split point.

a_sigma

Hyperparameter a.

b_sigma

Hyperparameter b.

Value

sigma2 draw from IG


Smoothed hazard function

Description

Smoothed hazard function

Usage

.smooth_hazard(out_slam, beta_samples = NULL)

Arguments

out_slam

samples from GibbsMH of the baseline hazard

beta_samples

samples from GibbsMH from the treatment effect

Value

smoothed function for the baseline hazard


Smoothed survival curve

Description

Smoothed survival curve

Usage

.smooth_survival(grid_width, out_slam, beta_samples = NULL)

Arguments

grid_width

step size

out_slam

samples from GibbsMH of the baseline hazard

beta_samples

samples from GibbsMH from the treatment effect

Value

smoothed survival function


Sample tau from posterior distribution

Description

Sample tau from posterior distribution

Usage

.tau_update(
  lambda_0,
  lambda,
  J,
  s,
  a_tau,
  b_tau,
  c_tau = NULL,
  d_tau = NULL,
  p_0 = NULL,
  type
)

Arguments

lambda_0

historical baseline hazard

lambda

baseline hazard

J

number of split points

s

split point locations, J + 2

a_tau

Inverse Gamma hyperparameter

b_tau

Inverse Gamma hyperparameter

c_tau

Inverse Gamma hyperparameter

d_tau

Inverse Gamma hyperparameter

p_0

mixture ratio

type

choice of borrowing, "mix", "uni", or any other string for borrowing on every baseline hazard without mixture

Value

list containing tau and new mixture ratio


BayesFBHborrow: Run MCMC for a piecewise exponential model

Description

Main function of the BayesFBHborrow package. This generic function calls the correct MCMC sampler for time-to-event Bayesian borrowing.

Usage

BayesFBHborrow(
  data,
  data_hist = NULL,
  borrow = TRUE,
  model_choice,
  tuning_parameters,
  hyperparameters,
  lambda_hyperparameters,
  iter,
  warmup_iter,
  refresh,
  verbose,
  max_grid
)

Arguments

data

data.frame containing atleast three vectors of "tte" (time-to-event) and "event" (censoring), and covariates "X_i" (where i should be a number/ indicator of the covariate)

data_hist

data.frame containing atleast two vectors of "tte" (time-to-event) and "event" (censoring), with the option of adding covariates named "X_0_i" (where i should be a number/indicator of the covariate), for historical data

borrow

TRUE (default), will run the model with borrowing

model_choice

choice of which borrowing model to use out of "mix", "uni" or "all"

tuning_parameters

list of "cprop_beta" ("cprop_beta_0" for historical data), "alpha", "Jmax", and "pi_b". Default is list("Jmax" = 5, "clam_smooth" = 0.8, "cprop_beta" = 0.5, "cprop_beta_0" = 0.5, "pi_b" = 0.5, "alpha" = 0.4)

hyperparameters

list containing the hyperparameters ("a_tau", "b_tau", "c_tau", "d_tau","type", "p_0", "a_sigma", "b_sigma"). Default is list("a_tau" = 1, "b_tau" = 1,"c_tau" = 1, "d_tau" = 0.001, "type" = "mix", "p_0" = 0.5, "a_sigma" = 2, "b_sigma" = 2, "phi" = 3)

lambda_hyperparameters

contains two hyperparameters (a_lambda and b_lambda) used for the update of lambda and lambda_0. Default is c(0.01, 0.01)

iter

number of iterations for MCMC sampler

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler.

refresh

number of iterations between printed screen updates

verbose

FALSE (default), choice of output, if TRUE will output intermittent results into console

max_grid

grid size for the smoothed baseline hazard

Value

a nested list of two items, 'out' and 'plots'. The list 'out' will contain all the samples of the MCMC chain, as well as acceptance ratios. The latter, 'plots', contains plots (and data) of the smoothed baseline hazard, smoothed survival, a histogram of the sampled number of split points, and the trace plot of the treatment effect beta_1

Examples

set.seed(123)
# Load the example data
data(piecewise_exp_cc, package = "BayesFBHborrow")
data(piecewise_exp_hist, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 3.25,
                          "alpha" = 0.4)
                          
# Set hyperparameters to default, with the borrowing model "mix"
out <- BayesFBHborrow(data = piecewise_exp_cc, data_hist = piecewise_exp_hist,
                      model_choice = 'mix', tuning_parameters = tuning_parameters,
                      iter = 2, warmup_iter = 0)

# Create a summary of the output
summary(out$out, estimator = "out_fixed")

# Plot the predictive curves for the treatment group
plots <- plot(out$out, out$out$time_grid, x_pred = c(1))

Run the MCMC sampler without Bayesian Borrowing

Description

Main function of the BayesFBHborrow package. This generic function calls the correct MCMC sampler for time-to-event without Bayesian borrowing.

Usage

## S3 method for class 'NoBorrow'
BayesFBHborrow(
  data,
  data_hist = NULL,
  borrow = FALSE,
  model_choice = "no_borrow",
  tuning_parameters = NULL,
  hyperparameters = NULL,
  lambda_hyperparameters = list(a_lambda = 0.01, b_lambda = 0.01),
  iter = 2000,
  warmup_iter = 2000,
  refresh = 0,
  verbose = FALSE,
  max_grid = 2000
)

Arguments

data

data.frame containing atleast three vectors of "tte" (time-to-event) and "event" (event indicator), and covariates "X_i" (where i should be a number/ indicator of the covariate)

data_hist

NULL (not used)

borrow

FALSE (default), will run the model with borrowing

model_choice

'no_borrow' (default), for no borrowing

tuning_parameters

list of "cprop_beta", "Jmax", and "pi_b". Default is ("Jmax" = 5, "cprop_beta" = 0.5, "pi_b" = 0.5)

hyperparameters

list containing the hyperparameters c("a_sigma", "b_sigma", "phi", clam_smooth"). Default is list("a_sigma" = 2, "b_sigma" = 2, "phi" = 3 , "clam_smooth" = 0.8)

lambda_hyperparameters

contains two hyperparameters ("a_lambda" and "b_lambda") used for the update of lambda, default is c(0.01, 0.01)

iter

number of iterations for MCMC sampler. Default is 2000

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler. Default is 2000

refresh

number of iterations between printed console updates. Default is 0

verbose

FALSE (default), choice of output, if TRUE will output intermittent results into console

max_grid

grid size for the smoothed baseline hazard. Default is 2000

Value

a nested list of two items, 'out' and 'plots'. The list 'out' will contain all the samples of the MCMC chain, as well as acceptance ratios. The latter, 'plots', contains plots (and data) of the smoothed baseline hazard, smoothed survival, a histogram of the sampled number of split points, and the trace plot of the treatment effect beta_1

Examples

set.seed(123)
# Load the example data
data(piecewise_exp_cc, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "cprop_beta" = 3.25)
                          
# Set initial values to default
out <- BayesFBHborrow(piecewise_exp_cc, NULL, borrow = FALSE, 
                      tuning_parameters = tuning_parameters,
                      iter = 2, warmup_iter = 0)

Run the MCMC sampler with Bayesian Borrowing

Description

Main function of the BayesFBHborrow package. This generic function calls the correct MCMC sampler for time-to-event Bayesian borrowing.

Usage

## S3 method for class 'WBorrow'
BayesFBHborrow(
  data,
  data_hist,
  borrow = TRUE,
  model_choice = "mix",
  tuning_parameters = NULL,
  hyperparameters = NULL,
  lambda_hyperparameters = list(a_lambda = 0.01, b_lambda = 0.01),
  iter = 2000,
  warmup_iter = 2000,
  refresh = 0,
  verbose = FALSE,
  max_grid = 2000
)

Arguments

data

data.frame containing atleast three vectors called "tte" (time-to-event), "event" (censoring), and covariates "X_i" (where i should be a number/indicator of the covariate)

data_hist

data.frame containing atleast two vectors called "tte" (time-to-event) and "event" (censoring), with the option of adding covariates named "X_0_i" (where i should be a number/indicator of the covariate) for the historical data

borrow

TRUE (default), will run the model with borrowing

model_choice

choice of which borrowing model to use out of 'mix', 'uni' or 'all'

tuning_parameters

list of "cprop_beta" ("cprop_beta_0" for historical data), "alpha", "Jmax", and "pi_b". Default is list("Jmax" = 5, "clam_smooth" = 0.8, "cprop_beta" = 0.5, cprop_beta_0" = 0.5, "pi_b" = 0.5, "alpha" = 0.4)

hyperparameters

list containing the hyperparameters ("a_tau", "b_tau", "c_tau", "d_tau","type", "p_0", "a_sigma", "b_sigma"). Default is list("a_tau" = 1, "b_tau" = 1,"c_tau" = 1, "d_tau" = 0.001, "type" = "mix", "p_0" = 0.5, "a_sigma" = 2, "b_sigma" = 2, "phi" = 3)

lambda_hyperparameters

contains three hyperparameters (a_lambda, b_lambda) used for the update of lambda and lambda_0. Default is c(0.01, 0.01)

iter

number of iterations for MCMC sampler. Default is 2000

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler. Default is 2000

refresh

number of iterations between printed console updates. Default is 0

verbose

FALSE (default), choice of output, if TRUE will output intermittent results into console

max_grid

grid size for the smoothed baseline hazard. Default is 2000

Value

a nested list of two items, 'out' and 'plots'. The list 'out' will contain all the samples of the MCMC chain, as well as acceptance ratios. The latter, 'plots', contains plots (and data) of the smoothed baseline hazard, smoothed survival, a histogram of the sampled number of split points, and the trace plot of the treatment effect beta_1

Examples

set.seed(123)
# Load the example data
data(piecewise_exp_cc, package = "BayesFBHborrow")
data(piecewise_exp_hist, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 3.25,
                          "alpha" = 0.4)
                          
# Set hyperparameters to default, with the borrowing model "mix"
out <- BayesFBHborrow(data = piecewise_exp_cc, data_hist = piecewise_exp_hist,
                      model_choice = 'mix', tuning_parameters = tuning_parameters,
                      iter = 2, warmup_iter = 0)

# Create a summary of the output
summary(out$out, estimator = "out_fixed")

# Plot the predictive curves for the treatment group
plots <- plot(out$out, out$out$time_grid, x_pred = c(1))

Extract mean posterior values

Description

S3 method for class "BayesFBHborrow", returns the mean posterior values for the fixed parameters

Usage

## S3 method for class 'BayesFBHborrow'
coef(object, ...)

Arguments

object

MCMC sample object from BayesFBHborrow()

...

other arguments, see coef.default()

Value

mean values of given samples

Examples

data(weibull_cc, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5)
                          
# run the MCMC sampler
out <- BayesFBHborrow(weibull_cc, NULL, tuning_parameters = tuning_parameters,
                      iter = 3, warmup_iter = 1)

# Plot the posterior mean values of the fixed parameters
coef(out$out)

S3 generic, calls the correct GibbsMH sampler

Description

An MCMC sampler for Bayesian borrowing with time-to-event data. We obtain a flexible baseline hazard function by making the split points random within a piecewise exponential model and using a Gaussian Markov random field prior to smooth the baseline hazards. Only calls the sampler and does not run any input checks. Best practice is to call BayesFBHborrow(), if the user is not familiar with the model at hand.

Usage

GibbsMH(
  Y,
  I,
  X,
  Y_0 = NULL,
  I_0 = NULL,
  X_0 = NULL,
  tuning_parameters,
  hyperparameters,
  lambda_hyperparameters,
  iter,
  warmup_iter,
  refresh,
  max_grid
)

Arguments

Y

data

I

event indicator

X

design matrix

Y_0

historical data, default is NULL

I_0

historical event indicator, default is NULL

X_0

historical design matrix, default is NULL

tuning_parameters

list of "cprop_beta", "cprop_beta_0", "alpha", "Jmax", and "pi_b"

hyperparameters

list containing the hyperparameters c("a_tau", "b_tau", "c_tau", "d_tau","type", "p_0", "a_sigma", "b_sigma", "Jmax", "clam_smooth", "cprop_beta", "phi", "pi_b"). Default is list("a_tau" = 1,"b_tau" = 1,"c_tau" = 1, "d_tau" = 0.001, "type" = "mix", "p_0" = 0.5, "a_sigma" = 2, "b_sigma" = 2, "Jmax" = 20, "clam_smooth" = 0.8, "cprop_beta" = 0.5, "phi" = 3, "pi_b" = 0.5)

lambda_hyperparameters

contains two hyperparameters (a_lambda and b_lambda) used for the update of lambda and lambda_0

iter

number of iterations for MCMC sampler, excluding warmup, default is 2000

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler, default is 2000

refresh

number of iterations between printed screen updates, default is 500

max_grid

grid size for the smoothed baseline hazard, default is 2000

Value

depending on if the user wishes to borrow; returns a list with values after each iteration for parameters: out_fixed (J, mu, sigma2, beta), lambda, lambda_0, tau, s, as well as tuning values of the total number of accepts: lambda_move, lambda_0_move and beta_move. Also included is the out_slam which contains the shrunk estimate of the baseline hazard.

Examples

set.seed(123)
# Load example data and set your initial values and hyper parameters
data(weibull_cc, package = "BayesFBHborrow")
data(weibull_hist, package = "BayesFBHborrow")

# The datasets consists of 3 (2) columns named "tte", "event" and "X" 
# (only for concurrent). To explicitly run the sampler, extract the samples as
# following
Y <- weibull_cc$tte
I <- weibull_cc$event
X <- matrix(weibull_cc$X_trt)

Y_0 <- weibull_hist$tte
I_0 <- weibull_hist$event
X_0 <- NULL

# Specify hyperparameters and tuning parameters
hyper <-  list("a_tau" = 1, 
               "b_tau" = 0.001,
               "c_tau" = 1,
               "d_tau" = 1, 
               "type" = 'all',
               "p_0" = 0.5, 
               "a_sigma" = 2,
               "b_sigma" = 2,
               "clam_smooth" = 0.5,
               "phi" = 3)

tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5,
                          "alpha" = 0.4)
                          
output <- GibbsMH(Y, I, X, Y_0, I_0, X_0,
                  tuning_parameters, hyper, 
                  iter = 5, warmup_iter = 1)

GibbsMH sampler, without Bayesian Borrowing

Description

An MCMC sampler for time-to-event data, without Bayesian Borrowing. We obtain a flexible baseline hazard function by making the split points random within a piecewise exponential model and using a Gaussian Markov random field prior to smooth the baseline hazards. Only calls the sampler and does not run any input checks. Best practice is to call BayesFBHborrow(), if the user is not familiar with the model at hand.

Usage

## S3 method for class 'NoBorrow'
GibbsMH(
  Y,
  I,
  X = NULL,
  Y_0 = NULL,
  I_0 = NULL,
  X_0 = NULL,
  tuning_parameters,
  hyperparameters = list(a_sigma = 1, b_sigma = 1, phi = 3, clam_smooth = 0.8),
  lambda_hyperparameters = list(a_lambda = 0.01, b_lambda = 0.01),
  iter = 1500L,
  warmup_iter = 10L,
  refresh = 0,
  max_grid = 2000L
)

Arguments

Y

data

I

event indicator

X

design matrix

Y_0

historical data, default is NULL

I_0

historical event indicator, default is NULL

X_0

historical design matrix, default is NULL

tuning_parameters

list of "cprop_beta", "Jmax", and "pi_b"

hyperparameters

list containing the hyperparameters c("a_sigma", "b_sigma", "Jmax", "clam_smooth", "cprop_beta", "phi"). Default is list("a_sigma" = 2, "b_sigma" = 2, "Jmax" = 20, "clam_smooth" = 0.8, "cprop_beta" = 0.5, "phi" = 3)

lambda_hyperparameters

contains two hyperparameters ("a" and "b") used for the update of lambda, default is c(0.01, 0.01)

iter

number of iterations for MCMC sampler, excluding warmup, default is 2000

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler, default is 2000

refresh

number of iterations between printed screen updates, default is 500

max_grid

grid size for the smoothed baseline hazard, default is 2000

Value

list with values after each iteration for parameters: out_fixed (J, mu, sigma2, beta), lambda, s, as well as tuning values of the total number of accepts: lambda_move and beta_move. Also included is the out_slam which contains the shrunk estimate of the baseline hazard.

Examples

set.seed(123)
# Load example data and set your hyper parameters
data(weibull_cc, package = "BayesFBHborrow")
data(weibull_hist, package = "BayesFBHborrow")

# The datasets consists of 3 (2) columns named "tte", "event" and "X".
# To explicitly run the sampler, extract the samples as following
Y <- weibull_cc$tte
I <- weibull_cc$event
X <- matrix(weibull_cc$X_trt)

# Specify hyperparameters and tuning parameters
hyper <-  list("a_sigma" = 2,
               "b_sigma" = 2,
               "clam_smooth" = 0.5,
               "phi" = 3)

tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5)
                          
# Set initial values to 'NULL' for default settings
output <- GibbsMH(Y, I, X, NULL, NULL, NULL,
                  tuning_parameters = tuning_parameters, hyperparameters = hyper, 
                  iter = 5, warmup_iter = 1)

GibbsMH sampler, with Bayesian Borrowing

Description

An MCMC sampler for Bayesian borrowing with time-to-event data. We obtain a flexible baseline hazard function by making the split points random within a piecewise exponential model and using a Gaussian Markov random field prior to smooth the baseline hazards. Only calls the sampler and does not run any input checks. Best practice is to call BayesFBHborrow(), if the user is not familiar with the model at hand.

Usage

## S3 method for class 'WBorrow'
GibbsMH(
  Y,
  I,
  X,
  Y_0,
  I_0,
  X_0,
  tuning_parameters = NULL,
  hyperparameters = list(a_tau = 1, b_tau = 0.001, c_tau = 1, d_tau = 1, type = "mix",
    p_0 = 0.8, a_sigma = 1, b_sigma = 1, phi = 3, clam_smooth = 0.8),
  lambda_hyperparameters = list(a_lambda = 0.01, b_lambda = 0.01),
  iter = 150L,
  warmup_iter = 10L,
  refresh = 0,
  max_grid = 2000L
)

Arguments

Y

data

I

event indicator

X

design matrix

Y_0

historical data

I_0

historical event indicator

X_0

historical design matrix

tuning_parameters

list of "cprop_beta", "cprop_beta_0", "alpha", "Jmax", and "pi_b"

hyperparameters

list containing the hyperparameters c("a_tau", "b_tau", "c_tau", "d_tau","type", "p_0", "a_sigma", "b_sigma", "Jmax", "clam_smooth", "cprop_beta", "phi", "pi_b"). Default is list("a_tau" = 1,"b_tau" = 1,"c_tau" = 1, "d_tau" = 0.001, "type" = "mix", "p_0" = 0.5, "a_sigma" = 2, "b_sigma" = 2, "Jmax" = 20, "clam_smooth" = 0.8, "cprop_beta" = 0.5, "phi" = 3, "pi_b" = 0.5)

lambda_hyperparameters

contains two hyperparameters (a_lambda and b_lambda) used for the update of lambda and lambda_0. Default is c(0.01, 0.01)

iter

number of iterations for MCMC sampler, excluding warmup, default is 2000

warmup_iter

number of warmup iterations (burn-in) for MCMC sampler, default is 2000

refresh

number of iterations between printed screen updates, default is 500

max_grid

grid size for the smoothed baseline hazard, default is 2000

Value

list with values after each iteration for parameters: out_fixed (J, mu, sigma2, beta), lambda, lambda_0, tau, s, as well as tuning values of the total number of accepts: lambda_move, lambda_0_move and beta_move. Also included is the out_slam which contains the shrunk estimate of the baseline hazard.

Examples

set.seed(123)
# Load example data and set your initial values and hyper parameters
data(weibull_cc, package = "BayesFBHborrow")
data(weibull_hist, package = "BayesFBHborrow")

# The datasets consists of 3 (2) columns named "tte", "event" and "X" 
# (only for concurrent). To explicitly run the sampler, extract the samples as
# following
Y <- weibull_cc$tte
I <- weibull_cc$event
X <- matrix(weibull_cc$X_trt)

Y_0 <- weibull_hist$tte
I_0 <- weibull_hist$event
X_0 <- NULL

# Specify hyperparameters and tuning parameters
hyper <-  list("a_tau" = 1, 
               "b_tau" = 0.001,
               "c_tau" = 1,
               "d_tau" = 1, 
               "type" = "all",
               "p_0" = 0.5, 
               "a_sigma" = 2,
               "b_sigma" = 2,
               "clam_smooth" = 0.5,
               "phi" = 3)

tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5,
                          "alpha" = 0.4)
          
output <- GibbsMH(Y, I, X, Y_0, I_0, X_0, tuning_parameters = tuning_parameters,
                  hyperparameters = hyper, iter = 5, warmup_iter = 1)

Create group level data

Description

Aggregate individual level data into group level data

Usage

group_summary(Y, I, X, s)

Arguments

Y

data

I

censoring indicator

X

design matrix

s

split points, J + 2

Value

list of group level data

Examples

set.seed(111)
# Load example data and set your initial values and hyper parameters
data(weibull_cc, package = "BayesFBHborrow")
data(weibull_hist, package = "BayesFBHborrow")

Y <- weibull_cc$tte
I <- weibull_cc$event
X <- weibull_cc$X_trt

# Say we want to know the group level data for the following split points
s <- quantile(Y, c(0, 0.45, 0.65, 1), names = FALSE)

group_summary(Y, I, X, s)

Initialize lambda hyperparameters

Description

Propose lambda hyperparameters for the choice of initial values for lambda

Usage

init_lambda_hyperparameters(group_data, s, w = 0.5)

Arguments

group_data

group level data

s

split points

w

weight

Value

shape and rate for the estimated lambda distribution

Examples

set.seed(111)
# Load example data and set your initial values and hyper parameters
data(weibull_cc, package = "BayesFBHborrow")
data(weibull_hist, package = "BayesFBHborrow")

Y <- weibull_cc$tte
I <- weibull_cc$event
X <- weibull_cc$X_trt

# Say we want to know the group level data for the following split points
s <- quantile(Y, c(0, 0.45, 0.65, 1), names = FALSE)

group_data <- group_summary(Y, I, NULL, s)
init_lambda_hyperparameters(group_data, s)

Example data, simulated from a piecewise exponential model.

Description

Data is simulated for a concurrent trial with three columns named "tte" (time-to-event), "event" (event indicator), and "X_trt" (treatment indicator). It was simulated using the following parameters:

Usage

data(piecewise_exp_cc)

Format

An object of class tbl_df (inherits from tbl, data.frame) with 250 rows and 3 columns.

Examples

data(piecewise_exp_cc)
survival_model <- survival::survfit(survival::Surv(tte, event) ~ X_trt, data = piecewise_exp_cc)
line_colors <- c("blue", "red")  # Adjust colors as needed
line_types <- 1:length(unique(piecewise_exp_cc$X_trt))
plot(survival_model, col = line_colors, lty = line_types, 
     xlab = "Time (tte)", ylab = "Survival Probability", 
     main = "Kaplan-Meier Survival Curves by Treatment")

Example data, simulated from a piecewise exponential model.

Description

Data is simulated for a historical trial with two columns named "tte" (time-to-event) and "event" (event indicator). It was simulated using the following parameters:

Usage

data(piecewise_exp_hist)

Format

An object of class tbl_df (inherits from tbl, data.frame) with 100 rows and 2 columns.

Examples

data(piecewise_exp_cc)
data(piecewise_exp_hist)
piecewise_exp_hist$X_trt <- 0
survival_model <- survival::survfit(survival::Surv(tte, event) ~ X_trt, 
                                    data = rbind(piecewise_exp_cc, 
                                    piecewise_exp_hist))
line_colors <- c("blue", "red", "green")  # Adjust colors as needed
line_types <- 1:length(unique(piecewise_exp_cc$X_trt))
plot(survival_model, col = line_colors, lty = line_types, 
     xlab = "Time (tte)", ylab = "Survival Probability", 
     main = "Kaplan-Meier Survival Curves by Treatment")

Plot the MCMC results

Description

S3 object which produces predictive probabilities of the survival, hazard, and hazard ratio for a given set of predictors

Usage

## S3 method for class 'BayesFBHborrow'
plot(x, x_lim, x_pred = NULL, ...)

Arguments

x

object of class "BayesFBHborrow" to be visualized

x_lim

x-axis to be used for plot, set to NULL to use default from MCMC sampling

x_pred

vector of chosen predictors

...

other plotting arguments, see .plot_matrix() for more information

Value

nested list of 'plots' (posterior predictive hazard, survival, and hazard ratio) as well as their samples.

Examples

data(weibull_cc, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5)
                          
# run the MCMC sampler
out <- BayesFBHborrow(weibull_cc, NULL, tuning_parameters = tuning_parameters,
                      iter = 3, warmup_iter = 1)

# for the treatment group
plots <- plot(out$out, out$out$time_grid, x_pred = c(1))

Summarize fixed MCMC results

Description

S3 method for with borrowing. Returns summary of mean, median and given percentiles for the one dimensional parameters.

Usage

## S3 method for class 'BayesFBHborrow'
summary(
  object,
  estimator = NULL,
  percentiles = c(0.025, 0.25, 0.75, 0.975),
  ...
)

Arguments

object

MCMC sample object from BayesFBHborrow()

estimator

The type of estimator to summarize, could be "fixed", "lambda", "lambda_0" or "s". The default is NULL and will print a summary of the output list.

percentiles

Given percentiles to output, default is c(0.025, 0.25, 0.75, 0.975)

...

other arguments, see summary.default

Value

summary of the given estimator

Examples

data(piecewise_exp_cc, package = "BayesFBHborrow")

# Set your tuning parameters
tuning_parameters <- list("Jmax" = 5,
                          "pi_b" = 0.5,
                          "cprop_beta" = 0.5)
                          
# run the MCMC sampler
out <- BayesFBHborrow(piecewise_exp_cc, NULL, tuning_parameters = tuning_parameters,
                      iter = 3, warmup_iter = 1)

# Create a summary of the output
summary(out$out, estimator = "out_fixed")

Example data, simulated from a Weibull distribution.

Description

Data is simulated for a concurrent trial with three columns named "tte" (time-to-event), "event" (event indicator), and "X_trt" (treatment indicator). It was simulated by drawing samples from a Weibull with kappa = 1.5 (shape) and nu = 0.4 (scale)

Usage

data(weibull_cc)

Format

An object of class tbl_df (inherits from tbl, data.frame) with 250 rows and 3 columns.

Examples

data(weibull_cc)
survival_model <- survival::survfit(survival::Surv(tte, event) ~ X_trt, data = weibull_cc)
line_colors <- c("blue", "red")  # Adjust colors as needed
line_types <- 1:length(unique(weibull_cc$X_trt))
plot(survival_model, col = line_colors, lty = line_types, 
     xlab = "Time (tte)", ylab = "Survival Probability", 
     main = "Kaplan-Meier Survival Curves by Treatment")

Example data, simulated from a Weibull distribution

Description

Data is simulated for a historical trial with two columns named "tte" (time-to-event) and "event" (event indicator). It was simulated using the following parameters:

Usage

data(weibull_hist)

Format

An object of class tbl_df (inherits from tbl, data.frame) with 100 rows and 2 columns.

Examples

data(weibull_cc)
data(weibull_hist)
weibull_hist$X_trt <- 0
survival_model <- survival::survfit(survival::Surv(tte, event) ~ X_trt, 
                                    data = rbind(weibull_cc, 
                                    weibull_hist))
line_colors <- c("blue", "red", "green")  # Adjust colors as needed
line_types <- 1:length(unique(weibull_cc$X_trt))
plot(survival_model, col = line_colors, lty = line_types, 
     xlab = "Time (tte)", ylab = "Survival Probability", 
     main = "Kaplan-Meier Survival Curves by Treatment")