Operating Characteristics of a BOIN Design

Simulate a BOIN dose-finding trial many times under one dose-toxicity scenario and summarize how often each dose is selected as the MTD, how many patients are treated at each dose and how many DLTs are observed.

Usage

sim_boin(
  target,
  p_true,
  n_cohort,
  cohort_size,
  n_trials = 10000,
  start_dose = 1,
  n_earlystop = 18,
  p_saf = NULL,
  p_tox = NULL,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  titration = FALSE,
  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 0.30.
p_true: Numeric vector. True DLT probability at each dose level, in increasing dose order.
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.
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. It is ignored when titration is TRUE, because the titration phase always begins at the lowest dose.
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. Set it to a value above the maximum sample size to switch this rule off.
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.
titration: Logical scalar. Start with single patient cohorts until the first DLT is seen. Ignored when the first cohort size is one. Defaults to FALSE.
stay_on_1_of_3: Logical scalar. When TRUE, one DLT out of three patients leads to staying at the current dose rather than de-escalating. 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. Supplying it bounds the selection whatever bound_mtd says, and unlike bound_mtd it can be set at or below the target rate. It changes only the selection, never the dose-finding itself. Defaults to NULL.
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. The state of the calling session is restored on exit. Defaults to 123.

Value

An object of class boin_oc, which is a list with components

sel_percent: Percentage of trials selecting each dose as the MTD.
percent_no_mtd: Percentage of trials ending without an MTD.
n_pts_dose: Average number of patients treated at each dose.
n_tox_dose: Average number of DLTs observed at each dose.
total_n_pts: Average total number of patients per trial.
total_n_tox: Average total number of DLTs per trial.
overdose: List describing the design's relationship with doses above overdose_cutoff. Two questions are answered separately. How far were patients exposed during the trial: pct_patients (the percentage of all simulated patients treated at such a dose, that is the probability that a patient is dosed above the cutoff), pct_patients_by_trial (the same percentage computed within each trial and then averaged), avg_n_patients, pct_trials_any, pct_trials_over_60 and pct_trials_over_80. And how often did the design end up recommending such a dose: pct_trials_mtd_above (the percentage of all trials whose selected MTD is above the cutoff) and pct_mtd_above_when_selected (the same among the trials that selected an MTD at all). The cutoff and the dose levels doses that exceed it are also returned.
stop_reason_percent: Percentage of trials by reason for stopping.
trials: Trial level data when keep_trials is TRUE, otherwise NULL.

together with the design parameters and the call.

Details

The engine draws one uniform variate per patient, in enrollment order, and applies the decision rules in the order used by BOIN::get.oc(). See boin_simulate for the two places where a variate is drawn but not used. With the same seed and matching arguments the two implementations agree trial by trial, not merely on average.

Note that n_earlystop defaults to 18 here, whereas the reference implementation defaults to 100, which in practice switches the rule off.

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.

Examples

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 = 500,
  seed = 123
)
oc
#> BOIN operating characteristics
#>   target DLT rate : 0.3
#>   trials          : 500
#>   cohorts         : 10 of size 3
#>   max sample size : 30
#>   lambda_e / _d   : 0.2365 / 0.3585
#> 
#>                   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 24.8 54.2 19.0  1.2            0.0
#> Patients treated  4.0  8.9 10.9  4.6  0.7           29.1
#> Patients with DLT 0.2  1.4  3.2  2.1  0.4            7.3
#> 
#> Doses above a true DLT rate of 0.3: DL4, DL5
#>   Patients treated there              : 18.1%
#>   Trials treating any patient there   : 56%
#>   Trials treating over 60% there      : 1.4%
#>   Trials treating over 80% there      : 0%
#>   Trials selecting an MTD there       : 20.2%

# \donttest{
# A larger run with the safety options switched on
oc_safe <- sim_boin(
  target = 0.30,
  p_true = c(0.30, 0.40, 0.50, 0.60, 0.70),
  n_cohort = 20,
  cohort_size = 3,
  n_trials = 10000,
  extrasafe = TRUE,
  bound_mtd = TRUE,
  titration = TRUE,
  seed = 123
)
oc_safe
#> BOIN operating characteristics
#>   target DLT rate : 0.3
#>   trials          : 10000
#>   cohorts         : 20 of size 3
#>   max sample size : 60
#>   lambda_e / _d   : 0.2365 / 0.3585
#> 
#>                    DL1  DL2  DL3  DL4  DL5 Total / No MTD
#> True DLT rate (%) 30.0 40.0 50.0 60.0 70.0               
#> MTD selected (%)  40.1 20.8  2.7  0.1  0.0           36.2
#> Patients treated  12.3  9.8  3.9  1.2  0.3           27.5
#> Patients with DLT  3.7  3.9  2.0  0.7  0.2           10.5
#> 
#> Doses above a true DLT rate of 0.3: DL2, DL3, DL4, DL5
#>   Patients treated there              : 55.4%
#>   Trials treating any patient there   : 78.7%
#>   Trials treating over 60% there      : 7.6%
#>   Trials treating over 80% there      : 1.2%
#>   Trials selecting an MTD there       : 23.7%

# How often are patients dosed above a true DLT rate of 0.33?
oc_cut <- sim_boin(
  target = 0.30,
  p_true = c(0.10, 0.20, 0.30, 0.42, 0.55),
  n_cohort = 20,
  cohort_size = 3,
  n_trials = 10000,
  overdose_cutoff = 0.33,
  seed = 123
)
oc_cut$overdose$pct_patients            # patients dosed above 0.33
#> [1] 21.38077
oc_cut$overdose$pct_trials_mtd_above     # trials recommending a dose above 0.33
#> [1] 15.89
# }