Operating Characteristics of a BF-BOIN Design

Simulate the BOIN design with backfilling (BF-BOIN) of Zhao et al. (2024) many times under one scenario of DLT and response probabilities, and summarize how often each dose is selected as the MTD, how many patients are treated and backfilled at each dose, how many DLTs and responses occur, and how long the trials last.

Usage

sim_bf_boin(
  target,
  p_true,
  p_resp,
  n_cohort,
  cohort_size,
  window,
  accrual_rate,
  n_cap = 12,
  backfill_dose = c("highest", "lowest"),
  conflict_dose = c("highest", "lowest"),
  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,
  n_trials = 10000,
  start_dose = 1,
  n_earlystop = 18,
  p_saf = NULL,
  p_tox = NULL,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  stay_on_1_of_3 = FALSE,
  bound_mtd = FALSE,
  mtd_max_estimate = NULL,
  min_mtd_sample = 1,
  overdose_cutoff = NULL,
  n_earlystop_rule = c("with_stay", "simple"),
  keep_trials = FALSE,
  verbose = FALSE,
  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: "highest" (the default here, following Zhao et al., 2024) or "lowest" (the default of be_boin_simulate, following Chen et al., 2026). See the details.
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.
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.
stay_on_1_of_3: Logical scalar. When TRUE, one DLT out of three patients leads to staying rather than de-escalating, in every use of the decision table. Zhao et al. (2024) use this modification in their main simulation. Defaults to FALSE. See boin_boundary.
bound_mtd: Logical scalar. Require the isotonic estimate at the selected dose to be at or below the de-escalation boundary. Defaults to FALSE.
mtd_max_estimate: Numeric scalar or NULL. Largest isotonic estimate a dose may have and still be selected as the MTD. See sim_boin.
min_mtd_sample: Integer scalar. Smallest number of patients a dose must have received to be eligible as the MTD. Defaults to 1.
overdose_cutoff: Numeric scalar or NULL. Doses whose true DLT probability exceeds this value count as overdoses in the overdose component of the result. Defaults to NULL, which uses target.
n_earlystop_rule: Character scalar, either "with_stay" or "simple". See boin_simulate.
keep_trials: Logical scalar. Keep the full trial by trial data in the result. Defaults to FALSE.
verbose: Logical scalar. Report progress while the simulation runs. Defaults to FALSE.
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("bf_boin_oc", "backfill_oc", "boin_oc"), which has every component of the result of sim_boin, so that code written for sim_boin() also reads it, counting backfilled patients among the patients treated, and in addition

n_bf_dose: Average number of backfilled patients at each dose.
total_n_bf: Average number of backfilled patients per trial.
pct_trials_backfill: Percentage of trials with at least one backfilled patient.
n_resp_dose: Average number of patients with a response at each dose.
total_n_resp: Average number of patients with a response per trial.
duration_mean: Average trial duration, from the first arrival until every enrolled patient has completed the DLT assessment, in the time unit of window and accrual_rate.
duration_sd: Standard deviation of the trial duration.
pct_trials_suspended: Percentage of trials in which the dose escalation had to wait at least once.
avg_n_suspensions: Average number of decisions per trial at which the dose escalation had to wait.
avg_time_suspended: Average total time per trial during which the dose escalation waited.
avg_n_turned_away: Average number of patients turned away per trial, which is zero unless no_slot = "leave".
p_resp: The true response probabilities.

The trials component, when kept, holds the trial by trial data of bf_boin_simulate together with the selected MTD.

Details

The trials are simulated by bf_boin_simulate, whose details describe the conduct of a trial. Once every patient has completed the assessment the MTD is selected from the data of all patients, backfilled ones included, exactly as in sim_boin, and a trial stopped for safety selects no dose. The overdose cutoffs of 60 and 80 percent refer to the size of the dose escalation, n_cohort cohorts.

When no dose is ever opened for backfilling, for example with every p_resp equal to 0, the selection and the patient counts agree with those of sim_boin under the same seed.

To reproduce Table 4 of Zhao et al. (2024), use target = 0.25, n_cohort = 10, cohort_size = 3, window = 1, accrual_rate = 3, n_earlystop = 9, stay_on_1_of_3 = TRUE, accrual = "uniform" and no_slot = "leave".

References

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

# Scenario 3 of Zhao et al. (2024)
oc <- 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,
  accrual_rate = 3,
  n_earlystop = 9,
  stay_on_1_of_3 = TRUE,
  accrual = "uniform",
  no_slot = "leave",
  n_trials = 500,
  seed = 123
)
oc
#> BF-BOIN operating characteristics (Zhao et al., 2024)
#>   target DLT rate : 0.25
#>   trials          : 500
#>   cohorts         : 10 of size 3
#>   escalation size : 30
#>   backfill cap    : 12 patients per dose
#>   lambda_e / _d   : 0.1968 / 0.2984
#>   window          : 1 (DLT), 1 (response)
#>   accrual         : 3 patients per unit of time (uniform)
#> 
#>                         DL1  DL2  DL3  DL4  DL5 Total / No MTD
#> True DLT rate (%)       4.0 12.0 25.0 43.0 63.0               
#> True response rate (%) 10.0 20.0 30.0 45.0 58.0               
#> MTD selected (%)        2.6 30.0 57.8  9.6  0.0            0.0
#> Patients treated        6.0 10.8  9.8  3.7  0.4           30.7
#>   of which backfilled   1.8  3.3  1.9  0.2  0.0            7.2
#> Patients with DLT       0.3  1.3  2.4  1.6  0.3            5.9
#> 
#> Doses above a true DLT rate of 0.25: DL4, DL5
#>   Patients treated there              : 13.3%
#>   Trials treating any patient there   : 49.2%
#>   Trials selecting an MTD there       : 9.6%
#> 
#> Backfilling and timing
#>   Trials with backfilled patients     : 86.4%
#>   Average trial duration              : 14.3
#>   Trials in which the escalation waited: 100%
#>   Average time the escalation waited  : 6.2
#>   Average patients turned away        : 11.1