Type: Package
Title: Bayesian Regression for Dynamic Treatment Regimes
Version: 1.0.1
Description: Methods to estimate optimal dynamic treatment regimes using Bayesian likelihood-based regression approach as described in Yu, W., & Bondell, H. D. (2023) <doi:10.1093/jrsssb/qkad016> Uses backward induction and dynamic programming theory for computing expected values. Offers options for future parallel computing.
License: GPL (≥ 3)
Imports: Rcpp (≥ 1.0.13-1), mvtnorm, foreach, progressr, stats, future
Depends: doRNG
Suggests: cli, testthat (≥ 3.0.0), doFuture
LinkingTo: Rcpp, RcppArmadillo
Encoding: UTF-8
RoxygenNote: 7.3.2
URL: https://github.com/jlimrasc/BayesRegDTR
BugReports: https://github.com/jlimrasc/BayesRegDTR/issues
Config/testthat/edition: 3
NeedsCompilation: yes
Packaged: 2025-06-24 10:16:44 UTC; jerem
Author: Jeremy Lim [aut, cre], Weichang Yu ORCID iD [aut]
Maintainer: Jeremy Lim <jeremylim23@gmail.com>
Repository: CRAN
Date/Publication: 2025-06-27 13:20:02 UTC

BayesRegDTR: Bayesian Regression for Dynamic Treatment Regimes

Description

Methods to estimate optimal dynamic treatment regimes using Bayesian likelihood-based regression approach as described in Yu, W., & Bondell, H. D. (2023) doi:10.1093/jrsssb/qkad016 Uses backward induction and dynamic programming theory for computing expected values. Offers options for future parallel computing.

Author(s)

Maintainer: Jeremy Lim jeremylim23@gmail.com

Authors:

References

Yu, W., & Bondell, H. D. (2023), “Bayesian Likelihood-Based Regression for Estimation of Optimal Dynamic Treatment Regimes”, Journal of the Royal Statistical Society Series B: Statistical Methodology, 85(3), 551-574. doi:10.1093/jrsssb/qkad016

See Also

generate_dataset() for generating a toy dataset to test the model fitting on

BayesLinRegDTR.model.fit() for obtaining an estimated posterior distribution of the optimal treatment option at a user-specified prediction stage

Useful links:

Main function for fitting a Bayesian likelihood-based linear regression model

Description

Fits the Bayesian likelihood-based linear model to obtain an estimated posterior distribution of the optimal treatment option at a user-specified prediction stage. Uses backward induction and dynamic programming theory for computing expected values.

Usage

BayesLinRegDTR.model.fit(
  Dat.train,
  Dat.pred,
  n.train,
  n.pred,
  num_stages,
  num_treats,
  p_list,
  t,
  R = 30,
  tau = 0.01,
  B = 10000,
  nu0 = 3,
  V0 = mapply(diag, p_list, SIMPLIFY = FALSE),
  alph = 1,
  gam = 1,
  showBar = TRUE
)

Arguments

Dat.train

Training data in format returned by generate_dataset: organised as a list of \{y, X_1, X_2..., X_{num\_stages}, A\} where y is a vector of the final outcomes, X_1, X_2..., X_{num\_stages} is a list of matrices of the intermediate covariates and A is an n.train \times num\_stages matrix of the assigned treatments, where num_stages is the total number of stages

Dat.pred

Prediction data in format returned by generate_dataset: organised as a list of \{X_1, X_2..., X_t, A\} where X_1, X_2..., X_t is a list of matrices of the intermediate covariates and A is an n.pred \times (t-1) matrix of the assigned treatments, where t is the prediction stage

n.train

Number of samples/individuals in the training data

n.pred

Number of samples/individuals in the prediction data

num_stages

Total number of stages

num_treats

Vector of number of treatment options at each stage

p_list

Vector of intermediate covariate dimensions for each stage

t

Prediction stage t, where t \leq num_stages

R

Draw size from distribution of intermediate covariates. default: 30

tau

Normal prior scale parameter for regression coefficients. Should be specified with a small value. default: 0.01

B

Number of MC draws from posterior of regression parameters. default 10000

nu0

Inverse-Wishart prior degrees of freedom for regression error Vcov matrix. Ignored if using a univariate dataset. default: 3

V0

List of Inverse-Wishart prior scale matrix for regression error Vcov matrix. Ignored if using a univariate dataset. default: list of identity matrices

alph

Inverse-Gamma prior shape parameter for regression error variance of y. default: 1

gam

Inverse-Gamma prior rate parameter for regression error variance of y. default: 1

showBar

Whether to show a progress bar. Uses API from progressr and future for parallel integration deafult: TRUE

Details

Utilises a future framework, so to enable parallel processing and register a parallel backend, plan and registerDoFuture must be called first.

Additionally, progress bars use progressr API, and a non-default progress bar (e.g. cli) is recommended. See below or registerDoFuture and handlers for examples.

Note that to have a progress bar for the parallel sections, future must be used. To turn off the immediate warnings, use options(BRDTR_warn_imm = FALSE).

Value

GCV_results

An array of dimension n.pred \times num\_treats[t] \times B, indicating the expected value under each treatment option at stage t.

post.prob

An n.pred \times num\_treats[t] matrix of the posterior probability that each treatment type at stage t is optimal

MC_draws.train

A list of Monte Carlo draws containing:

  • sigmat_B_list - A list of length num_stages with each element a vector of size B \times p\_list[t]

  • Wt_B_list - A list of length num_stages with each element a matrix of size B \times p\_list[t]

  • beta_B - A list of length B

  • sigmay_2B - A list of length B

Examples

# Code does not run within 10 seconds, so don't run

# -----------------------------
# Set Up Parallelism & Progress Bar
# -----------------------------
progressr::handlers("cli")          # Set handler to something with title/text
numCores <- parallel::detectCores() # Detect number of cores, use max
future::plan(future::multisession,  # Or plan(multicore, workers) on Unix
            workers = numCores)     # Set number of cores to use
doFuture::registerDoFuture()        # Or doParallel::registerDoParallel()
                                    # if no progress bar is needed and future
                                    # is unwanted

## UVT
# -----------------------------
# Initialise Inputs
# -----------------------------
num_stages  <- 5
t           <- 3
p_list      <- rep(1, num_stages)
num_treats  <- rep(2, num_stages)
n.train     <- 5000
n.pred      <- 10

# -----------------------------
# Generate Dataset
# -----------------------------
Dat.train  <- generate_dataset(n.train,  num_stages, p_list, num_treats)
Dat.pred  <- generate_dataset(n.pred,  num_stages, p_list, num_treats)
Dat.pred  <- Dat.pred[-1]
Dat.pred[[num_stages+1]]  <- Dat.pred[[num_stages+1]][1:n.pred, 1:(t-1), drop = FALSE]

# -----------------------------
# Main
# -----------------------------
gcv_uvt <- BayesLinRegDTR.model.fit(Dat.train, Dat.pred, n.train, n.pred,
                                    num_stages, num_treats,
                                    p_list, t, R = 30,
                                    tau = 0.01, B = 500, nu0 = NULL,
                                    V0 = NULL, alph = 3, gam = 4)

## MVT
# -----------------------------
# Initialise Inputs
# -----------------------------
num_stages  <- 3
t           <- 2
p_list      <- rep(2, num_stages)
num_treats  <- rep(2, num_stages)
n.train     <- 5000
n.pred      <- 10

# -----------------------------
# Generate Dataset
# -----------------------------
Dat.train <- generate_dataset(n.train, num_stages, p_list, num_treats)
Dat.pred  <- generate_dataset(n.pred,  num_stages, p_list, num_treats)
Dat.pred  <- Dat.pred[-1]
Dat.pred[[num_stages+1]]  <- Dat.pred[[num_stages+1]][1:n.pred, 1:(t-1), drop = FALSE]

# -----------------------------
# Main
# -----------------------------
gcv_res <- BayesLinRegDTR.model.fit(Dat.train, Dat.pred, n.train, n.pred,
                                    num_stages, num_treats,
                                    p_list, t, R = 30,
                                    tau = 0.01, B = 500, nu0 = 3,
                                    V0 = mapply(diag, p_list, SIMPLIFY = FALSE),
                                    alph = 3, gam = 4)

Compute Monte Carlo Draws from Multivariate Dataset

Description

Obtain Monte Carlo draws from posterior distribution of stagewise regression parameters

Usage

compute_MC_draws_mvt(
  Data,
  tau,
  num_treats,
  B,
  nu0 = 3,
  V0 = mapply(diag, p_list, SIMPLIFY = FALSE),
  alph,
  gam,
  p_list,
  showBar = TRUE
)

Arguments

Data

Observed data organised as a list of \{y, X, A\} where y is a vector of the final outcomes, X is a list of matrices of the intermediate covariates and A is a matrix of the assigned treatments

tau

Prior precision scale. Should be specified with a small value

num_treats

Vector of number of treatment options at each stage

B

Number of MC draws

nu0

Inverse-Wishart degres of freedom. default: 3

V0

Inverse-Wishart scale matrix. default: diagonalisation of p_list

alph

Inverse-Gamma prior shape parameter for regression error variance of y. default: 1

gam

Inverse-Gamma prior rate parameter for regression error variance of y. default: 1

p_list

Vector of dimension for each stage

showBar

Whether to show a progress bar. Uses bar from progress_bar deafult: TRUE

Value

Monte Carlo draws??? A list containing:

  1. sigmat_B_list: Desc. A list of length num_stages with each element a vector of size B x p_t

  2. Wt_B_list: Desc. A list of length num_stages with each element a matrix of size B x p_t

  3. beta_B: Desc. A list of length B

  4. sigmay_2B: Desc. A list of length B

Compute Monte Carlo Draws from Univariate Dataset

Description

Obtain Monte Carlo draws from posterior distribution of stagewise regression parameters

Usage

compute_MC_draws_uvt(
  Data,
  tau,
  num_treats,
  B,
  alph,
  gam,
  p_list,
  showBar = TRUE
)

Arguments

Data

Observed data organised as a list of \{y, X, A\} where y is a vector of the final outcomes, X is a list of matrices of the intermediate covariates and A is a matrix of the assigned treatments

tau

Prior precision scale. Should be specified with a small value

num_treats

Vector of number of treatment options at each stage

B

Number of MC draws

alph

Inverse-Gamma prior shape parameter for regression error variance of y. default: 1

gam

Inverse-Gamma prior rate parameter for regression error variance of y. default: 1

p_list

Vector of dimension for each stage

showBar

Whether to show a progress bar. Uses bar from progress_bar deafult: TRUE

Value

Monte Carlo draws??? A list containing:

  1. thetat_B_list: Desc. A list of length num_stages with each element a vector of length B

  2. sigmat_2B_list: Desc. A list of length num_stages with each element a vector of length B

  3. beta_B: Desc. A list of length B

  4. sigmay_2B: Desc. A list of length B

Generate a toy dataset in the right format for testing BayesLinRegDTR.model.fit

Description

Generates a toy dataset simulating observed data of treatments over time with final outcomes and intermediate covariates. Follows the method outlined in Toy-Datagen on Github

Usage

generate_dataset(n, num_stages, p_list, num_treats)

Arguments

n

Number of samples/individuals to generate

num_stages

Total number of stages per individual

p_list

Vector of dimension for each stage

num_treats

Vector of number of treatment options at each stage

Value

Observed data organised as a list of \{y, X_1, X_2..., X_{num\_stages}, A\} where y is a vector of the final outcomes, X_1, X_2..., X_{num\_stages} is a list of matrices of the intermediate covariates and A is an n \times num\_stages matrix of the assigned treatments

Examples

# -----------------------------
# Initialise Inputs
# -----------------------------
n           <- 5000
num_stages  <- 3
p_list_uvt  <- rep(1, num_stages)
p_list_mvt  <- c(1, 3, 3)
num_treats  <- rep(3, num_stages)

# -----------------------------
# Main
# -----------------------------
Data_uvt    <- generate_dataset(n, num_stages, p_list_uvt, num_treats)
Data_mvt    <- generate_dataset(n, num_stages, p_list_mvt, num_treats)

Generate Multivariate dataset

Description

Generate Multivariate dataset

Usage

generate_dataset_mvt(n, num_stages, p_list, num_treats)

Arguments

n

Number of samples/individuals to generate

num_stages

Total number of stages per individual

p_list

Vector of dimension for each stage

num_treats

Vector of number of treatment options at each stage

Value

Observed data organised as a list of \{y, X, A\} where y is a vector of the final outcomes, X is a list of matrices of the intermediate covariates and A is a matrix of the assigned treatments

Generate Univariate Dataset

Description

Generate Univariate Dataset

Usage

generate_dataset_uvt(n, num_stages, num_treats)

Arguments

n

Number of samples/individuals to generate

num_stages

Total number of stages per individual

num_treats

Vector of number of treatment options at each stage

Value

Observed data organised as a list of \{y, X, A\} where y is a vector of the final outcomes, X is a list of matrices of the intermediate covariates and A is a matrix of the assigned treatments

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