Operating Characteristics of the BOIN Drug-Combination Design

Simulate a trial of two drugs given together, run with the BOIN drug-combination design of Lin and Yin (2017), many times under one matrix of true DLT probabilities, and summarize how often each dose combination is selected as the MTD, how many patients are treated at each combination and how many DLTs are observed.

Usage

sim_comb_boin(
  target,
  p_true,
  n_cohort,
  cohort_size,
  n_trials = 10000,
  start_dose = c(1, 1),
  n_earlystop = 18,
  p_saf = NULL,
  p_tox = NULL,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  titration = FALSE,
  bound_mtd = FALSE,
  overdose_cutoff = NULL,
  keep_trials = FALSE,
  verbose = FALSE,
  seed = 123
)

Arguments

target: Numeric scalar. Target DLT probability, for example 0.30.
p_true: Numeric matrix. True DLT probability of each dose combination, with one row per dose level of drug A and one column per dose level of drug B, both 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 vector of length two. Dose levels of drug A and drug B for the first cohort. Defaults to c(1, 1).
n_earlystop: Integer scalar. The trial stops once this many patients have been treated at the current combination and the design would neither escalate nor de-escalate, or cannot. 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 eliminating a combination. Defaults to 0.95.
extrasafe: Logical scalar. Apply the stricter safety stopping rule at the lowest combination. 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. Treat one patient per combination, moving up one level of either drug, until the first DLT. Ignored when the first cohort size is one. Defaults to FALSE.
bound_mtd: Logical scalar. Require the isotonic estimate at the selected combination to be below the de-escalation boundary. Defaults to FALSE.
overdose_cutoff: Numeric scalar or NULL. Combinations whose true DLT probability exceeds this value count as overdoses in the overdose component of the result. Defaults to NULL, which uses target.
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 comb_boin_oc, which is a list with components

sel_percent: Matrix of the percentage of trials selecting each combination as the MTD.
percent_no_mtd: Percentage of trials ending without an MTD.
n_pts_dose: Matrix of the average number of patients treated at each combination.
n_tox_dose: Matrix of the average number of DLTs observed at each combination.
total_n_pts: Average total number of patients per trial.
total_n_tox: Average total number of DLTs per trial.
true_mtd: Two-column matrix of the dose levels of drug A and drug B of the combinations whose true DLT probability is closest to target.
pct_true_mtd_selected: Percentage of trials selecting one of these combinations.
pct_patients_true_mtd: Percentage of all patients treated at one of them.
overdose: List describing the exposure to combinations above overdose_cutoff, with the components of the same list returned by sim_boin; combinations gives the dose levels of the combinations above the cutoff.
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 trials are simulated with comb_boin_simulate and the MTD is selected with comb_boin_select_mtd. A trial stopped for safety at the lowest combination selects none. Both follow BOIN::get.oc.comb() with mtd.contour = FALSE: with the same seed and matching arguments the two implementations agree trial by trial. pct_true_mtd_selected and pct_patients_true_mtd are the quantities that the reference implementation reports as the selection percentage of the MTD and the percentage of patients treated at the MTD.

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

Only the design that searches for a single MTD combination is provided; the waterfall design of Zhang and Yuan (2016), which searches for the MTD contour, is not.

References

Lin, R. and Yin, G. (2017). Bayesian Optimal Interval Design for Dose Finding in Drug-Combination Trials. Statistical Methods in Medical Research, 26(5), 2155-2167.

Yan, F., Zhang, L., Zhou, Y., Pan, H., Liu, S. and Yuan, Y. (2020). BOIN: An R Package for Designing Single-Agent and Drug-Combination Dose-Finding Trials Using Bayesian Optimal Interval Designs. Journal of Statistical Software, 94(13), 1-32.

Zhang, L. and Yuan, Y. (2016). A Practical Bayesian Design to Identify the Maximum Tolerated Dose Contour for Drug Combination Trials. Statistics in Medicine, 35(27), 4924-4936.

Examples

# The example of Yan and colleagues (2020): three levels of drug A, four of
# drug B and a target DLT rate of 0.25
p_true <- matrix(c(0.02, 0.04, 0.08, 0.14,
                   0.08, 0.25, 0.42, 0.48,
                   0.25, 0.45, 0.50, 0.60), nrow = 3, byrow = TRUE)

oc <- sim_comb_boin(
  target = 0.25,
  p_true = p_true,
  n_cohort = 16,
  cohort_size = 3,
  n_trials = 500,
  seed = 123
)
oc
#> BOIN drug-combination operating characteristics
#>   target DLT rate : 0.25
#>   dose levels     : 3 of drug A, 4 of drug B
#>   trials          : 500
#>   cohorts         : 16 of size 3
#>   max sample size : 48
#>   lambda_e / _d   : 0.1968 / 0.2984
#> 
#>               Item Drug A   B1   B2   B3   B4
#>  True DLT rate (%)     A1  2.0  4.0  8.0 14.0
#>                        A2  8.0 25.0 42.0 48.0
#>                        A3 25.0 45.0 50.0 60.0
#>   MTD selected (%)     A1  0.0  1.0  5.0 16.0
#>                        A2  4.2 35.4  8.6  1.0
#>                        A3 23.8  4.8  0.2  0.0
#>   Patients treated     A1  4.0  3.6  3.0  2.9
#>                        A2  5.8  8.4  4.0  1.5
#>                        A3  5.0  3.9  1.0  0.3
#>  Patients with DLT     A1  0.1  0.2  0.2  0.4
#>                        A2  0.4  2.1  1.6  0.7
#>                        A3  1.2  1.8  0.5  0.2
#> 
#> No MTD selected                      : 0%
#> Average number of patients           : 43.4
#> Average number of DLTs               : 9.4
#> 
#> True MTD (closest to the target)     : A3B1, A2B2
#>   Selected as the MTD                : 59.2%
#>   Patients treated there             : 30.9%
#> 
#> Combinations above a true DLT rate of 0.25: 5 of 12
#>   Patients treated there             : 24.6%
#>   Trials treating any patient there  : 82%
#>   Trials treating over 60% there     : 3%
#>   Trials treating over 80% there     : 0.2%
#>   Trials selecting an MTD there      : 14.6%

# \donttest{
# The settings of the article, which turn early stopping off
oc_jss <- sim_comb_boin(
  target = 0.25,
  p_true = p_true,
  n_cohort = 16,
  cohort_size = 3,
  n_earlystop = 100,
  n_trials = 1000,
  seed = 6
)
oc_jss$pct_true_mtd_selected
#> [1] 59.4
# }