Simulate BE-BOIN Trials

Run the BOIN design with backfilling and late-onset toxicity (BE-BOIN) of Chen et al. (2026) over many simulated trials. Dose escalation follows TITE-BOIN, which decides while some patients are still pending; patients who arrive while the escalation is suspended are backfilled to a lower dose that is safe and has shown a response. Every estimate imputes the pending patients, backfilled ones included. Return the patient, DLT, backfill and response counts at every dose together with the duration of each trial.

Usage

be_boin_simulate(
  target,
  p_true,
  p_resp,
  n_cohort,
  cohort_size,
  window,
  accrual_rate,
  n_cap = 12,
  backfill_dose = c("highest", "lowest"),
  conflict_dose = c("lowest", "highest"),
  no_slot = c("wait", "leave"),
  accrual = c("exponential", "uniform", "fixed"),
  dlt_time = c("weibull", "uniform"),
  late_fraction = 0.5,
  resp_window = window,
  resp_late_fraction = 0.5,
  resp_cor = 0,
  max_pending_ratio = 0.49,
  min_completed = 0,
  min_follow_up = 0.25,
  n_trials = 10000,
  start_dose = 1,
  n_earlystop = 18,
  p_saf = NULL,
  p_tox = NULL,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  n_earlystop_rule = c("with_stay", "simple"),
  seed = 123
)

Arguments

target: Numeric scalar. Target DLT probability, for example 0.25.
p_true: Numeric vector. True DLT probability at each dose level, in increasing dose order. The probability of a DLT within the assessment window.
p_resp: Numeric vector of the same length as p_true. True probability of a response within the response window at each dose. A response at or below a dose is what makes the dose eligible for backfilling.
n_cohort: Integer scalar. Number of cohorts in the dose escalation.
cohort_size: Integer scalar or vector. Number of patients per cohort of the dose escalation. A scalar is used for every cohort. A vector shorter than n_cohort is padded with its last element and a longer one is truncated.
window: Numeric scalar. Length of the DLT assessment window.
accrual_rate: Numeric scalar. Average number of patients arriving per unit of time, in the same unit as window.
n_cap: Integer scalar. A dose is no longer backfilled once this many patients, from the dose escalation and from backfilling together, have been treated at it. The dose escalation can still treat patients at the dose. Defaults to 12.
backfill_dose: Character scalar. Which dose receives a backfill patient when several are open: "highest" (the default, as in both articles) or "lowest".
conflict_dose: Character scalar. When the data of several backfilled doses conflict with those of the current dose, which of them anchors the pooled estimate: "lowest" (the default here, following Chen et al., 2026) or "highest" (the default of bf_boin_simulate, following Zhao et al., 2024).
no_slot: Character scalar. What happens to a patient who arrives when neither the dose escalation nor any backfill dose can take a patient: "wait" (the default), the patient waits and is treated as soon as one can, as in tite_boin_simulate; or "leave", the patient is turned away and the trial waits for the next arrival.
accrual: Character scalar. Distribution of the times between arrivals: "exponential" (the default) for a Poisson process, "uniform" for a uniform distribution on (0, 2 / accrual_rate), or "fixed" for arrivals exactly 1 / accrual_rate apart.
dlt_time: Character scalar. Distribution of the time to DLT within the window, and of the time to response within the response window: "weibull" (the default) or "uniform".
late_fraction: Numeric scalar strictly between 0 and 1. Share of the DLTs that occur in the second half of the assessment window under the Weibull distribution. Defaults to 0.5.
resp_window: Numeric scalar. Length of the window within which a response is observed. Defaults to window.
resp_late_fraction: Numeric scalar strictly between 0 and 1. Share of the responses that occur in the second half of the response window under the Weibull distribution. Defaults to 0.5.
resp_cor: Numeric scalar strictly between -1 and 1. Correlation of the Gaussian copula that links the DLT and the response of a patient; a positive value makes a response more likely in a patient with a DLT. Defaults to 0, independence.
max_pending_ratio: Numeric scalar greater than 0 and at most 1. Rule 1 of the design: the escalation is suspended when the proportion of pending patients at the current dose exceeds this value, unless the dose is de-escalated whatever their outcomes. Defaults to 0.49, which suspends when fewer than 51 percent have completed the assessment, as in Chen et al. (2026). See tite_boin_decision_table.
min_completed: Integer scalar. While some patients are pending, escalation requires at least this many patients with a completed assessment. Defaults to 0, which the design does not use. See tite_boin_decision_table.
min_follow_up: Numeric scalar between 0 and 1. Rule 2 of the design: escalation requires every pending patient at the current dose to have been followed for at least this fraction of the window. Defaults to 0.25, as in Chen et al. (2026). See tite_boin_decision_table.
n_trials: Integer scalar. Number of trials to simulate. Defaults to 10000.
start_dose: Integer scalar. Dose level for the first cohort. Defaults to 1.
n_earlystop: Integer scalar. The trial stops once this many patients, backfilled ones included, have been treated at the current dose and the design would stay there. Defaults to 18.
p_saf: Numeric scalar. Highest DLT probability deemed subtherapeutic. Defaults to 0.6 * target.
p_tox: Numeric scalar. Lowest DLT probability deemed overly toxic. Defaults to 1.4 * target.
cutoff_eli: Numeric scalar. Posterior probability cutoff for dose elimination. Defaults to 0.95.
extrasafe: Logical scalar. Apply the stricter safety stopping rule at the lowest dose. Defaults to FALSE.
offset: Numeric scalar between 0 and 0.5. Amount by which cutoff_eli is relaxed for the safety stopping rule. Defaults to 0.05.
n_earlystop_rule: Character scalar, either "with_stay" or "simple". See boin_simulate.
seed: Integer scalar or NULL. Random seed. When NULL the current state of the random number generator is used. The state of the calling session is restored on exit. Defaults to 123.

Value

An object of class c("be_boin_trials", "backfill_trials"), with the components described in bf_boin_simulate.

Details

Dose escalation. The dose for a cohort is decided when its first patient arrives, with the rules of tite_boin_decision_table for method = "imputation" and the suspension rules max_pending_ratio and min_follow_up; every patient at the current dose counts, backfilled ones included. A suspension lasts until a decision can be taken again, as in tite_boin_simulate. Elimination counts every treated patient, the pending ones as without DLT, and is checked at every dose.

Estimates. The DLT rate at a dose is the single mean imputation estimate of TITE-BOIN, equation (1) of Chen et al. (2026), and the rate pooled over several doses adds up the observed and imputed DLTs of each dose, each imputed with its own posterior mean, and divides by the number of treated patients, equation (2). Both enter the opening and closing of backfill doses and the resolution of conflicts, which otherwise follow bf_boin_simulate. The categories of a backfilled dose for the conflicts compare its estimate with the escalation and de-escalation boundaries directly.

End of the trial, arrivals and random numbers are as in bf_boin_simulate. When no dose is ever opened for backfilling, for example with every p_resp equal to 0, and with no_slot = "wait", the trials are identical to those of tite_boin_simulate with method = "imputation", the same suspension rules and the same seed.

Chen et al. (2026) report their operating characteristics for scenarios that are given only as figures, so they cannot be reproduced. The decision table of their supplementary materials is reproduced by tite_boin_decision_table, and their trial example is replayed patient by patient in the tests of the package.

References

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. doi:10.1007/s43441-026-00994-0

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.

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.

Examples

# A three month window with two patients a month
trials <- be_boin_simulate(
  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 = 3,
  accrual_rate = 2,
  n_earlystop = 9,
  n_trials = 200,
  seed = 123
)
trials
#> Simulated BE-BOIN (Chen et al., 2026) trials
#>   trials          : 200
#>   doses           : 5
#>   target DLT rate : 0.25
#>   cohorts         : 10 of size 3
#>   escalation size : 30
#>   backfill cap    : 12 patients per dose
#>   window          : 3 (DLT), 3 (response)
#>   accrual         : 2 patients per unit of time (exponential)
#> 
#> Average per trial:
#>                        DL1   DL2  DL3  DL4  DL5
#> Patients treated      7.38 10.96 8.47 2.98 0.30
#>   of which backfilled 2.08  2.82 1.20 0.07 0.00
#> DLTs observed         0.30  1.31 2.16 1.26 0.22
#> Responses             0.66  2.22 2.58 1.30 0.20
#> 
#> Patients per trial    : mean 30.09, of which backfilled 6.16
#> Trials with backfill  : 71.5%
#> Trial duration        : mean 22.72, median 23.19
#> Escalation waiting    : 100% of trials, mean time 7.93 per trial
#> 
#> Stopping reason (%):
#> 
#> max_sample_size     n_earlystop 
#>              35              65 

summary(trials$duration)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   6.904  19.473  23.188  22.716  26.263  33.632