Operating Characteristics of a TITE-BOIN Design

Simulate a time-to-event BOIN (TITE-BOIN) trial many times under one dose-toxicity scenario and summarize how often each dose is selected as the MTD, how many patients are treated and how many DLTs are observed at each dose, how long the trials last and how often accrual is suspended.

Usage

sim_tite_boin(
  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,
  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 0.30.
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.
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("tite_boin_oc", "boin_oc"), which has every component of the result of sim_boin, so that code written for sim_boin() also reads it, and in addition

duration_mean: Average trial duration, from the first arrival until every enrolled patient has completed the 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 accrual was suspended at least once.
avg_n_suspensions: Average number of suspensions per trial.
avg_time_suspended: Average total time with accrual suspended per trial.

The trials component, when kept, also holds duration, n_suspensions and time_suspended for every trial.

Details

The trials are simulated by tite_boin_simulate, whose details describe the conduct of a trial. Once every patient has completed the assessment the MTD is selected from the final data exactly as in sim_boin, with boin_select_mtd, and a trial stopped for safety selects no dose.

When no patient is ever pending at a decision, for example with accrual = "fixed" and window shorter than 1 / accrual_rate, every result agrees with that of sim_boin under the same seed.

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
oc <- 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,
  accrual_rate = 2,
  n_trials = 500,
  seed = 123
)
oc
#> TITE-BOIN operating characteristics
#>   method          : single mean imputation (Yuan et al., 2018)
#>   target DLT rate : 0.3
#>   trials          : 500
#>   cohorts         : 10 of size 3
#>   max sample size : 30
#>   lambda_e / _d   : 0.2365 / 0.3585
#>   window          : 3
#>   accrual         : 2 patients per unit of time (exponential)
#> 
#>                   DL1  DL2  DL3  DL4  DL5 Total / No MTD
#> True DLT rate (%) 5.0 15.0 30.0 45.0 60.0               
#> MTD selected (%)  0.8 28.8 55.0 15.2  0.2            0.0
#> Patients treated  5.6 10.3  9.6  3.4  0.4           29.3
#> Patients with DLT 0.3  1.5  2.9  1.5  0.3            6.6
#> 
#> Doses above a true DLT rate of 0.3: DL4, DL5
#>   Patients treated there              : 13.1%
#>   Trials treating any patient there   : 41.6%
#>   Trials treating over 60% there      : 2.4%
#>   Trials treating over 80% there      : 0%
#>   Trials selecting an MTD there       : 15.4%
#> 
#> Trial duration and suspension of accrual
#>   Average trial duration              : 23.5
#>   Trials with accrual suspended       : 100%
#>   Average number of suspensions       : 3.9
#>   Average time suspended              : 6.5

# \donttest{
# The effective sample size of Lin and Yuan (2020)
oc_ess <- sim_tite_boin(
  target = 0.30,
  p_true = c(0.05, 0.15, 0.30, 0.45, 0.60),
  n_cohort = 12,
  cohort_size = 3,
  window = 3,
  accrual_rate = 2,
  method = "ess",
  n_trials = 10000,
  seed = 123
)
oc_ess
#> TITE-BOIN operating characteristics
#>   method          : effective sample size (Lin and Yuan, 2020)
#>   target DLT rate : 0.3
#>   trials          : 10000
#>   cohorts         : 12 of size 3
#>   max sample size : 36
#>   lambda_e / _d   : 0.2365 / 0.3585
#>   window          : 3
#>   accrual         : 2 patients per unit of time (exponential)
#> 
#>                   DL1  DL2  DL3  DL4  DL5 Total / No MTD
#> True DLT rate (%) 5.0 15.0 30.0 45.0 60.0               
#> MTD selected (%)  1.1 23.5 57.7 16.6  1.1            0.0
#> Patients treated  5.6 10.9 11.7  4.8  0.9           33.9
#> Patients with DLT 0.3  1.6  3.5  2.2  0.5            8.1
#> 
#> Doses above a true DLT rate of 0.3: DL4, DL5
#>   Patients treated there              : 16.7%
#>   Trials treating any patient there   : 55.9%
#>   Trials treating over 60% there      : 3%
#>   Trials treating over 80% there      : 0%
#>   Trials selecting an MTD there       : 17.7%
#> 
#> Trial duration and suspension of accrual
#>   Average trial duration              : 24.1
#>   Trials with accrual suspended       : 99.5%
#>   Average number of suspensions       : 2.9
#>   Average time suspended              : 4.8
# }