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
)
ocCompare 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 ggplot2When 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
| Function | Purpose |
|---|---|
boin_lambda() |
Escalation and de-escalation interval boundaries |
boin_boundary() |
Integer decision boundaries by sample size |
boin_decision_table() |
Decision table indexed by DLTs and patients |
boin_stopping_table() |
Safety stopping boundary as a two-row table |
Simulation
| Function | Purpose |
|---|---|
sim_boin() |
Operating characteristics for one scenario |
sim_boin_multi() |
Operating characteristics across scenarios |
boin_simulate() |
Raw trial data from the engine |
boin_isotonic() |
Isotonic estimates of the dose-toxicity curve |
boin_select_mtd() |
MTD selection from completed trials |
Time-to-event BOIN (TITE-BOIN)
| Function | Purpose |
|---|---|
tite_boin_decision_table() |
Decision table with pending patients, for either method |
sim_tite_boin() |
Operating characteristics, trial duration and suspensions of accrual |
sim_tite_boin_multi() |
The same across scenarios |
tite_boin_simulate() |
Raw trial data from the time-to-event engine |
Backfilling (BF-BOIN and BE-BOIN)
| Function | Purpose |
|---|---|
sim_bf_boin() |
Operating characteristics of BF-BOIN, with backfilled patients, responses and trial duration |
sim_bf_boin_multi() |
The same across scenarios |
bf_boin_simulate() |
Raw trial data from the BF-BOIN engine |
sim_be_boin() |
Operating characteristics of BE-BOIN, backfilling with the time-to-event design |
sim_be_boin_multi() |
The same across scenarios |
be_boin_simulate() |
Raw trial data from the BE-BOIN engine |
Drug combinations
| Function | Purpose |
|---|---|
sim_comb_boin() |
Operating characteristics of the BOIN drug-combination design for one matrix of DLT rates |
sim_comb_boin_multi() |
The same across scenarios |
comb_boin_simulate() |
Raw trial data from the drug-combination engine |
comb_boin_select_mtd() |
MTD combination selection from completed trials |
comb_boin_next() |
Combination for the next cohort of a trial in progress, with print() and plot() methods |
3+3 design
| Function | Purpose |
|---|---|
oc_3p3() |
Operating characteristics in closed form |
sim_3p3() |
The same by simulation, as a check on the closed form |
decision_table_3p3() |
Decision table of the design |
Design options
| Argument | Effect |
|---|---|
titration |
Treat one patient per dose until the first DLT, then switch to full cohorts |
extrasafe |
Add a stopping rule at the lowest dose that triggers before elimination |
bound_mtd |
Refuse to select a dose whose estimate exceeds the de-escalation boundary |
n_earlystop |
Stop once the current dose has accrued this many patients and the design would stay |
start_dose |
Dose level for the first cohort, ignored under titration
|
stay_on_1_of_3 |
Make one DLT out of three a stay rather than a de-escalation |
min_mtd_sample |
Smallest number of patients for a dose to be eligible as the MTD |
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
method |
Pending outcomes handled by | Boundaries refer to | Default suspension rule |
|---|---|---|---|
"imputation" |
Single mean imputation (Yuan et al., 2018) | STFT | Suspend accrual when more than half of the patients at the dose are pending |
"ess" |
Effective sample size (Lin and Yuan, 2020) | ESS | Escalate only once two patients at the dose have completed the assessment |
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 ofsim_tite_boin()are identical to those ofboin_simulate()andsim_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"andno_slot = "leave". The scriptinst/validation/compare-with-Zhao2024.Rrepeats 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()andtite_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, andinst/validation/compare-comb-with-BOIN.R200 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.Rsets 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 decisionThe 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.
| Reason | Meaning |
|---|---|
lowest_dose_eliminated |
The lowest dose was eliminated for toxicity |
lowest_dose_too_toxic |
The extrasafe rule stopped the trial at the lowest dose |
n_earlystop |
Enough patients had accrued at the current dose |
max_sample_size |
The maximum number of patients was reached |
max_cohorts |
All planned cohorts were completed |
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:
| Elapsed | |
|---|---|
BOIN::get.oc() |
9.98 s |
sim_boin() |
0.07 s |
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:
| Elapsed | |
|---|---|
sim_boin() |
0.05 s |
sim_tite_boin(), method = "imputation"
|
0.09 s |
sim_tite_boin(), method = "ess"
|
0.11 s |
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.