Simulate TITE-BOIN Trials

Run the time-to-event BOIN (TITE-BOIN) design over many simulated trials, in which patients arrive over time and new patients are treated while the DLT assessment of earlier patients is still pending. Return the patient and DLT counts at every dose together with the duration of each trial and the time spent with accrual suspended.

Usage

tite_boin_simulate(
  target,
  p_true,
  n_cohort,
  cohort_size,
  window,
  accrual_rate,
  method = c("imputation", "ess"),
  accrual = c("exponential", "uniform", "fixed"),
  dlt_time = c("weibull", "uniform"),
  late_fraction = 0.5,
  prior_weights = c(1, 1, 1)/3,
  max_pending_ratio = NULL,
  min_completed = NULL,
  min_follow_up = 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,
  n_earlystop_rule = c("with_stay", "simple"),
  seed = 123
)

Arguments

target: Numeric scalar. Target DLT probability, for example 0.30.
p_true: Numeric vector. True DLT probability at each dose level, in increasing dose order. The probability of a DLT within the assessment window.
n_cohort: Integer scalar. Number of cohorts in a trial.
cohort_size: Integer scalar or vector. Number of patients per cohort. 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.
method: Character scalar, "imputation" (the default) or "ess". How the pending patients enter the estimate of the DLT probability. See tite_boin_decision_table.
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), as in the code of Lin and Yuan (2020), or "fixed" for arrivals exactly 1 / accrual_rate apart.
dlt_time: Character scalar. Distribution of the time to DLT within the window: "weibull" (the default), with the share of DLTs in the second half of the window set by late_fraction, 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, the setting of Yuan et al. (2018) and Lin and Yuan (2020).
prior_weights: Numeric vector of three non-negative values. Prior probabilities that a DLT occurs in the first, second and last third of the assessment window, used to weight the follow-up of the pending patients in STFT (Yuan et al., 2018, Supplementary Appendix D) and ESS (Lin and Yuan, 2020, Supplementary S1). They are rescaled to sum to one. Defaults to equal weights, which give the unweighted STFT. The decision table does not change with the weights; only the value compared with its boundaries does. This describes the design and is separate from dlt_time and late_fraction, which describe how the simulated DLTs actually occur.
max_pending_ratio: Numeric scalar or NULL. Suspension rule on the proportion of pending patients. See tite_boin_decision_table.
min_completed: Integer scalar or NULL. Number of completed assessments required for escalation. See tite_boin_decision_table.
min_follow_up: Numeric scalar between 0 and 1. Shortest follow-up, as a fraction of window, that every pending patient at the current dose must have reached before the dose is escalated; accrual is suspended until then. Defaults to 0, which never suspends on this ground. 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 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 tite_boin_trials, which is a list with components

n_pts: Integer matrix, n_trials by number of doses, of patients treated.
n_tox: Integer matrix of the same shape, of DLTs, counted once every patient has completed the assessment.
eliminated: Logical matrix of the same shape, marking doses eliminated during the trial.
cohorts_used: Integer vector of cohorts treated in each trial.
stop_reason: Character vector giving why each trial ended, with the values of boin_simulate.
duration: Numeric vector. Time from the first arrival until every enrolled patient has completed the assessment.
n_suspensions: Integer vector. Number of decisions at which accrual had to be suspended.
time_suspended: Numeric vector. Total time with accrual suspended.
boundary: The boin_boundary object used.
settings: List of the design parameters.

Details

Patients arrive one at a time. The dose for a cohort is decided when its first patient arrives, from the data available at that moment, and the other patients of the cohort receive the same dose. The decision follows tite_boin_decision_table. A patient with a DLT completes the assessment when the DLT occurs, and a patient without one at the end of the window. When the decision is to suspend accrual, the arriving patient waits until the next pending patient at the current dose completes the assessment, or, with a positive min_follow_up, until the last pending patient to arrive at the current dose has been followed for that fraction of the window, whichever comes first, and the decision is taken again at that moment. Later patients arrive after the one who waited.

At every decision the rules are applied in the order used by boin_simulate: elimination at the current dose and the extra safety rule, early stopping on n_earlystop, then the dose transition. Because DLTs can be observed after a dose has been left, the elimination rule is also checked at the other doses; a dose that meets it is eliminated together with all higher doses, and the trial moves below it. Elimination counts every treated patient, the pending ones as without DLT.

One uniform variate is drawn from R's random number stream per patient, in enrollment order and in the cohort blocks of boin_simulate. It decides whether the patient has a DLT and, under the Weibull distribution, gives the time to DLT through the inverse distribution function, which falls inside the window exactly when there is a DLT. The times between arrivals come from a second generator (xoshiro256**) seeded with seed, or with one draw from R's stream when seed is NULL. As a result, whenever no patient is pending at any decision, for example with accrual = "fixed" and window shorter than 1 / accrual_rate, the trials are identical to those of boin_simulate with the same seed.

The follow-up of a pending patient counts towards STFT as the share of the window already covered, or, with prior_weights, as the prior probability that a DLT would have occurred by then. Both articles evaluate their designs with equal weights, the default.

The titration phase and the stay_on_1_of_3 option of boin_simulate are not available, as neither article defines them for the time-to-event design.

References

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.

Examples

# A three month window with two patients a month
trials <- tite_boin_simulate(
  target = 0.30,
  p_true = c(0.05, 0.15, 0.30, 0.45, 0.60),
  n_cohort = 10,
  cohort_size = 3,
  window = 3,
  accrual_rate = 2,
  n_trials = 200,
  seed = 123
)
trials
#> Simulated TITE-BOIN trials
#>   method          : single mean imputation (Yuan et al., 2018)
#>   trials          : 200
#>   doses           : 5
#>   target DLT rate : 0.3
#>   cohorts         : 10 of size 3
#>   max sample size : 30
#>   window          : 3
#>   accrual         : 2 patients per unit of time (exponential)
#> 
#> Average per trial:
#>                   DL1   DL2  DL3  DL4  DL5
#> Patients treated 5.80 10.61 9.12 3.24 0.44
#> DLTs observed    0.32  1.62 2.80 1.46 0.32
#> 
#> Trial duration        : mean 23.55, median 23.44
#> Trials with suspension: 100%
#> Time suspended        : mean 6.19 per trial
#> 
#> Stopping reason (%):
#> 
#> max_sample_size     n_earlystop 
#>            84.5            15.5 

summary(trials$duration)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   14.66   21.40   23.44   23.55   25.93   32.79