Fast Simulation of Bayesian Optimal Interval Designs for Phase I Trials

Design and evaluate phase I dose-finding trials that use the Bayesian optimal interval (BOIN) design of Liu and Yuan (2015) . Functions are provided to tabulate the decision boundaries, to simulate trials, to estimate the dose-toxicity curve under a monotonicity constraint and to select the maximum tolerated dose. The simulation engine is written in C++ and draws one random variate per patient in enrollment order, which reproduces the reference implementation in the 'BOIN' package trial by trial for a given seed. The traditional 3+3 design is provided as a comparator, with operating characteristics obtained in closed form rather than by simulation. For toxicity that is observed late, the time-to-event BOIN design is provided with the two estimators of Yuan and colleagues (2018) and Lin and Yuan (2020) . Patients who arrive while the dose escalation waits can be backfilled to lower doses with the designs of Zhao and colleagues (2024) and Chen and colleagues (2026) , the latter with the suspension rules of Chen and colleagues (2025) . Trials of two drugs given together are handled by the drug-combination design of Lin and Yin (2017) .

simFastBOIN

Simulation tools for Bayesian optimal interval (BOIN) designs in phase I dose-finding trials. The documentation, with the four vignettes, is also available at https://gosukehommaex.github.io/simFastBOIN/.

Overview

simFastBOIN tabulates the BOIN decision boundaries, simulates the design to obtain operating characteristics, and applies the MTD selection rule used at the end of a trial. The simulation engine is written in C++.

The engine draws one uniform variate per patient, in enrollment order, and applies the decision rules in the same order as BOIN::get.oc(). With the same seed and matching arguments the two implementations agree trial by trial, not merely on average. The test suite checks this directly against the BOIN package rather than relying on a tolerance, so the claim is verifiable rather than asserted. A wider comparison ships with the package as inst/validation/compare-with-BOIN.R, which runs 200 configurations covering every combination of the options the two packages share, including extrasafe and titration.

Version 2.1.0 adds the time-to-event BOIN (TITE-BOIN) design, for toxicity that appears late in the assessment window or accrual that outpaces it. New patients are treated while earlier ones are still being followed, with the pending outcomes handled either by the single mean imputation of Yuan et al. (2018) or by the effective sample size of Lin and Yuan (2020). The decision table reproduces the published tables of Yuan et al. (2018) entry by entry, and whenever no patient is pending the simulated trials are identical to those of sim_boin() with the same seed.

The same version adds backfilling: patients who arrive while the dose escalation waits are treated at a lower dose that is safe and has shown a response. BF-BOIN (Zhao et al., 2024) backfills around the BOIN design, and BE-BOIN (Chen et al., 2026) around the time-to-event design. The operating characteristics of Table 4 of Zhao et al. (2024) are reproduced within simulation error.

For trials of two drugs given together, the same version adds the BOIN drug-combination design of Lin and Yin (2017), which looks for an MTD combination in a matrix of doses. It follows BOIN::get.oc.comb() trial by trial and reproduces the example of Yan et al. (2020) to the printed precision.

Installation

install.packages("simFastBOIN")

Or the development version:

# install.packages("devtools")
devtools::install_github("gosukehommaEX/simFastBOIN")

Since version 2.0.0 the package contains compiled code, so a working C++ toolchain is needed to install from source (Rtools on Windows, Xcode command line tools on macOS).

Quick start

library(simFastBOIN)

oc <- sim_boin(
  target = 0.30,
  p_true = c(0.05, 0.15, 0.30, 0.45, 0.60),
  n_cohort = 10,
  cohort_size = 3,
  n_trials = 10000,
  seed = 123
)

oc

Compare several dose-toxicity scenarios under the same design:

sim_boin_multi(
  target = 0.30,
  scenarios = list(
    "MTD at dose 2"   = c(0.15, 0.30, 0.45, 0.60, 0.75),
    "MTD at dose 4"   = c(0.02, 0.06, 0.15, 0.30, 0.50),
    "All doses toxic" = c(0.40, 0.55, 0.65, 0.75, 0.85)
  ),
  n_cohort = 10,
  cohort_size = 3,
  n_trials = 10000,
  seed = 123
)

Look at the boundaries the design will actually use:

print(boin_boundary(target = 0.30, max_n = 18, extrasafe = TRUE), cohort_size = 3)

Read the dose decisions off a table, or off a figure for a protocol:

decisions <- boin_decision_table(target = 0.30, max_n = 18)

print(decisions, cohort_size = 3)
plot(decisions)                      # needs ggplot2

When toxicity can appear late, or patients arrive faster than they can be assessed, use the time-to-event design. Its decisions also depend on how long the pending patients have been followed:

tite <- tite_boin_decision_table(target = 0.30, max_n = 15)
print(tite, cohort_size = 3)

sim_tite_boin(
  target = 0.30,
  p_true = c(0.05, 0.15, 0.30, 0.45, 0.60),
  n_cohort = 10,
  cohort_size = 3,
  window = 3,          # a three month assessment window
  accrual_rate = 2,    # two patients a month
  n_trials = 10000,
  seed = 123
)

To backfill patients to lower doses while the escalation waits, give the response probabilities as well:

sim_bf_boin(
  target = 0.25,
  p_true = c(0.04, 0.12, 0.25, 0.43, 0.63),
  p_resp = c(0.10, 0.20, 0.30, 0.45, 0.58),
  n_cohort = 10,
  cohort_size = 3,
  window = 1,          # a one month assessment window
  accrual_rate = 3,    # three patients a month
  n_earlystop = 9,
  n_trials = 10000,
  seed = 123
)

For two drugs given together, give the true DLT rates as a matrix, with the levels of drug A in the rows and those of drug B in the columns:

sim_comb_boin(
  target = 0.25,
  p_true = matrix(c(0.02, 0.04, 0.08, 0.14,
                    0.08, 0.25, 0.42, 0.48,
                    0.25, 0.45, 0.50, 0.60), nrow = 3, byrow = TRUE),
  n_cohort = 16,
  cohort_size = 3,
  n_trials = 10000,
  seed = 123
)

Functions

Design

Simulation

Time-to-event BOIN (TITE-BOIN)

Backfilling (BF-BOIN and BE-BOIN)

Drug combinations

3+3 design

Design options

Note that n_earlystop defaults to 18 here, whereas BOIN::get.oc() defaults to 100, which in practice switches the rule off. Set it explicitly when comparing the two.

Late-onset toxicity: the TITE-BOIN design

STFT is the total follow-up time of the pending patients divided by the length of the assessment window, and ESS adds to it the number of patients who have completed the assessment. Neither table depends on the length of the window. Both suspension rules can be set for either method with max_pending_ratio and min_completed.

A simulation needs the length of the window and the accrual rate in the same unit of time. Arrivals can be exponential (the default), uniform or fixed, and the time to DLT Weibull, with a share late_fraction of the DLTs in the second half of the window, or uniform. The follow-up of the pending patients can be weighted by a piecewise uniform prior for the time to DLT through prior_weights; both articles evaluate their designs with equal weights, the default.

How the implementation is checked:

• tite_boin_decision_table() reproduces all 640 entries of Table 1 (target 0.2) of Yuan et al. (2018) and of Table S1 (target 0.3) of its supplementary appendix, and the dose decisions of the trial example in Figure 1 of that article. The published tables allow de-escalation when the observed DLT rate equals the target, which equation (5) of the appendix, read literally, does not; the package follows the tables.
• With no patient pending at any decision, the trials of tite_boin_simulate() and the summaries of sim_tite_boin() are identical to those of boin_simulate() and sim_boin() under the same seed.
• The simulated trials agree exactly with a separate implementation written in Python and run on a replica of R's random number stream.

Neither article reports operating characteristics that can be reproduced number for number: Yuan et al. (2018) give them as figures relative to the 3+3 design and as averages over randomly generated scenarios, and the tables of Lin and Yuan (2020) are for the keyboard and mTPI designs.

Backfilling: BF-BOIN and BE-BOIN

In BF-BOIN the dose escalation proceeds in fully staggered cohorts with the BOIN decision table. A patient who arrives while it waits is backfilled to the highest lower dose that has not been eliminated, has fewer than n_cap patients and has a response observed at or below it. Backfilled doses whose DLT rate becomes too high are closed, and when their data conflict with those of the current dose the escalation decides from the pooled data. BE-BOIN applies the same rules around the time-to-event design, with the suspension rules of Chen et al. (2025), and imputes the pending patients in every estimate. The MTD is selected from all patients, backfilled ones included.

Where the articles leave a detail of the simulation open, the package offers an argument: no_slot (a patient with nowhere to go waits or is turned away), conflict_dose (which conflicting dose anchors the pooled estimate) and resp_window, resp_late_fraction and resp_cor (the timing of responses and their correlation with DLTs).

How the implementation is checked:

• The operating characteristics of Table 4 of Zhao et al. (2024), twelve scenarios of BF-BOIN and five of BOIN, are reproduced within simulation error, durations included, with stay_on_1_of_3 = TRUE, n_earlystop = 9, accrual = "uniform" and no_slot = "leave". The script inst/validation/compare-with-Zhao2024.R repeats the comparison.
• The trial examples of Zhao et al. (2024) and Chen et al. (2026) are replayed patient by patient.
• When no dose is opened for backfilling the trials are identical to those of boin_simulate() and tite_boin_simulate() under the same seed.
• The simulated trials agree exactly with a separate implementation written in Python and run on a replica of R's random number stream.

See vignette("simFastBOIN-backfill") for the rules, the choices made where the articles are silent, and the comparison with Table 4.

Drug combinations

sim_comb_boin() implements the design of Lin and Yin (2017) as the BOIN package does in BOIN::get.oc.comb() with mtd.contour = FALSE, including the details that the package adds to the article: a candidate's posterior probability is increased by 0.0005 per patient treated there, the trial can stop at n_earlystop, and the MTD is selected from (y + 0.05) / (n + 0.1) smoothed by Iso::biviso(). Note that n_earlystop defaults to 18 here, whereas BOIN::get.oc.comb() defaults to 100.

How the implementation is checked:

• The example of Yan et al. (2020) is reproduced to the printed precision. The one average exactly half-way between two printed values, 1.905 patients at A2B4, is printed 1.90 in the article and 1.91 by R 4.6.0.
• With the same seed, the results equal those of BOIN::get.oc.comb() exactly; the tests check nine settings, and inst/validation/compare-comb-with-BOIN.R 200 configurations.
• The simulated trials agree exactly with a separate implementation written in Python and run on a replica of R's random number stream.
• inst/validation/compare-with-LinYin2017.R sets the results beside Tables 2 and 3 of Lin and Yin (2017), whose rules differ in some details.

To run a trial, comb_boin_next() gives the combination for the next cohort from the numbers of patients and DLTs observed so far. It takes its decision with the same C++ code as the simulations, so the trial follows the rules whose operating characteristics sim_comb_boin() reports. BOIN::next.comb() differs from the simulations of BOIN::get.oc.comb() in a few rules, which the help page of comb_boin_next() lists.

nxt <- comb_boin_next(
  target = 0.25,
  n_pts = matrix(c(6, 6, 0, 0,
                   3, 3, 0, 0,
                   0, 0, 0, 0), nrow = 3, byrow = TRUE),
  n_tox = matrix(c(0, 1, 0, 0,
                   1, 2, 0, 0,
                   0, 0, 0, 0), nrow = 3, byrow = TRUE),
  current = c(2, 2)
)
nxt        # de-escalate to A1B2
plot(nxt)  # the dose matrix with the data and the decision

The waterfall design of Zhang and Yuan (2016), which looks for the MTD contour, is not provided. See vignette("simFastBOIN-combination").

Why the trials stop

boin_simulate() records a reason for every trial, and sim_boin() reports the distribution in stop_reason_percent.

Checking the agreement with the BOIN package yourself

reference <- BOIN::get.oc(
  target = 0.30, p.true = c(0.05, 0.15, 0.25, 0.45, 0.60),
  ncohort = 20, cohortsize = 3, n.earlystop = 18, ntrial = 10000, seed = 6
)

ours <- sim_boin(
  target = 0.30, p_true = c(0.05, 0.15, 0.25, 0.45, 0.60),
  n_cohort = 20, cohort_size = 3, n_earlystop = 18, n_trials = 10000, seed = 6
)

all.equal(unname(ours$sel_percent), reference$selpercent)
all.equal(unname(ours$n_pts_dose), reference$npatients)
all.equal(unname(ours$n_tox_dose), reference$ntox)
all.equal(ours$percent_no_mtd, reference$percentstop)

Speed

Five doses, 20 cohorts of three, n_earlystop = 18 and 10,000 simulated trials, measured on one Windows machine:

That is about two orders of magnitude for this design. The ratio depends on the design and on the machine, so the code below re-measures it rather than asking you to take the table on trust.

scenario <- c(0.05, 0.15, 0.25, 0.45, 0.60)

system.time(
  BOIN::get.oc(target = 0.30, p.true = scenario, ncohort = 20, cohortsize = 3,
               n.earlystop = 18, ntrial = 10000, seed = 6)
)

system.time(
  sim_boin(target = 0.30, p_true = scenario, n_cohort = 20, cohort_size = 3,
           n_earlystop = 18, n_trials = 10000, seed = 6)
)

The time-to-event engine was timed on a similar design, five doses and 20 cohorts of three with the true DLT rates c(0.05, 0.15, 0.30, 0.45, 0.60), a three month window and two patients a month, 10,000 trials, all three runs together on one Windows machine:

Following patients over time costs about twice as much as the BOIN engine. The BOIN package has no time-to-event design, so there is no reference implementation of TITE-BOIN to time it against.

Comparing with the 3+3 design

The traditional 3+3 design is included as a comparator. Its operating characteristics are obtained in closed form rather than by simulation, so they carry no Monte Carlo error.

oc_3p3(p_true = c(0.30, 0.48, 0.67))

# The other definition of the MTD in common use
oc_3p3(p_true = c(0.30, 0.48, 0.67), mtd_rule = "expand")

sim_3p3() simulates the same design and exists to confirm the closed form. The result of either has the same component names as the result of sim_boin(), so the two designs can be tabulated side by side.

decision_table_3p3() shows the rule itself, with print() and plot() methods like those of the BOIN decision table.

decision_table_3p3(mtd_rule = "expand")

Upgrading from version 1.3.2

Version 2.0.0 renames most functions, changes the argument order of sim_boin() and corrects several defects that affected numerical results. Simulations run with the same seed will not reproduce the version 1.3.2 output. See NEWS.md for the full list and the mapping of old names to new ones.

References

Liu, S. and Yuan, Y. (2015). Bayesian Optimal Interval Designs for Phase I Clinical Trials. Journal of the Royal Statistical Society: Series C, 64, 507-523.

Yan, F., Zhang, L., Zhou, Y., Pan, H., Liu, S. and Yuan, Y. (2020). BOIN: An R Package for Designing Single-Agent and Drug-Combination Dose-Finding Trials Using Bayesian Optimal Interval Designs. Journal of Statistical Software, 94(13), 1-32.

Yuan, Y., Lin, R., Li, D., Nie, L. and Warren, K. E. (2018). Time-to-Event Bayesian Optimal Interval Design to Accelerate Phase I Trials. Clinical Cancer Research, 24(20), 4921-4930.

Lin, R. and Yuan, Y. (2020). Time-to-Event Model-Assisted Designs for Dose-Finding Trials with Delayed Toxicity. Biostatistics, 21(4), 807-824.

Zhao, Y., Yuan, Y., Korn, E. L. and Freidlin, B. (2024). Backfilling Patients in Phase I Dose-Escalation Trials Using Bayesian Optimal Interval Design (BOIN). Clinical Cancer Research, 30(4), 673-679.

Chen, K., Chen, T.-Y., Zhang, Y., Lin, R. and Yuan, Y. (2025). Practical Considerations for Using the TITE-BOIN Design to Handle Late-Onset Toxicity or Fast Accrual in Phase I Trials. Clinical Cancer Research, 31(13), 2573-2580.

Chen, K., Zhao, Y., Takeda, K. and Yuan, Y. (2026). BE-BOIN: A Dose Optimization Design Accommodating Backfill and Late-Onset Toxicity. Therapeutic Innovation and Regulatory Science.

Lin, R. and Yin, G. (2017). Bayesian Optimal Interval Design for Dose Finding in Drug-Combination Trials. Statistical Methods in Medical Research, 26(5), 2155-2167.

Zhang, L. and Yuan, Y. (2016). A Practical Bayesian Design to Identify the Maximum Tolerated Dose Contour for Drug Combination Trials. Statistics in Medicine, 35(27), 4924-4936.

License

MIT (c) Gosuke Homma