Integer Decision Boundaries for the BOIN Design

Tabulate, for every attainable number of patients treated at a dose, the number of DLTs that triggers escalation, de-escalation, elimination and, when requested, the stricter safety stopping rule at the lowest dose.

Usage

boin_boundary(
  target,
  max_n,
  p_saf = NULL,
  p_tox = NULL,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  stay_on_1_of_3 = FALSE
)

Arguments

target: Numeric scalar. Target DLT probability, for example 0.30.
max_n: Integer scalar. Largest number of patients that can be treated at a single dose, which is the number of columns of the resulting table. For a trial with n_cohort cohorts of size cohort_size this is n_cohort * cohort_size.
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 above which a dose is eliminated for toxicity. Defaults to 0.95.
extrasafe: Logical scalar. When TRUE, also tabulate the safety stopping boundary applied 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 at the current dose rather than de-escalating. Defaults to FALSE. See the details.

Value

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

lambda_e: Escalation interval boundary.
lambda_d: De-escalation interval boundary.
n: Number of patients, 1 to max_n.
b_esc: Escalate when the number of DLTs is at most this value.
b_deesc: De-escalate when the number of DLTs reaches this value.
b_elim: Eliminate the dose when the number of DLTs reaches this value, NA when no elimination is possible at that sample size.
b_stop: Safety stopping boundary at the lowest dose, all NA unless extrasafe is TRUE.
stay_on_1_of_3: Whether the modification was requested.
stay_on_1_of_3_applied: Whether it changed the boundaries.

together with the design parameters used.

Details

The escalation boundary is floor(lambda_e * n) and the de-escalation boundary is ceiling(lambda_d * n), with the convention that when lambda_d * n is a whole number de-escalation requires one more DLT. The elimination boundary is the smallest positive number of DLTs for which Pr(p > target | data) exceeds cutoff_eli under a uniform Beta(1, 1) prior, and is not evaluated before three patients have been treated. The de-escalation boundary is capped at the elimination boundary.

With the default thresholds these definitions reproduce BOIN::get.boundary() exactly.

Staying on one DLT out of three

For some target rates the optimal BOIN decision after one DLT in three patients is to de-escalate, because the likelihood of overdosing then exceeds the likelihood of proper dosing. Long practice with the 3+3 design has nonetheless made staying at the dose the widely accepted choice, and stay_on_1_of_3 = TRUE aligns the design with that practice by raising the de-escalation boundary at three patients from one DLT to two. Nothing else in the table changes.

The modification is applied only where it is meaningful, that is when one DLT out of three currently triggers de-escalation. It never overrides an escalation, and it never overrides an elimination, which is a safety rule. Whether it took effect is reported in stay_on_1_of_3_applied. With the default thresholds it takes effect for target rates from about 0.098 to 0.279; below that range one DLT out of three already eliminates the dose, and above it the design already stays.

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

bd <- boin_boundary(target = 0.30, max_n = 18)
bd
#> BOIN decision boundaries
#>   target DLT rate : 0.3
#>   p_saf / p_tox   : 0.18 / 0.42
#>   lambda_e        : 0.2365
#>   lambda_d        : 0.3585
#>   cutoff_eli      : 0.95
#> 
#>                                                                          
#> Number of patients treated  1  2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
#> Escalate if # of DLT <=     0  0 0 0 1 1 1 1 2  2  2  2  3  3  3  3  4  4
#> Deescalate if # of DLT >=   1  1 2 2 2 3 3 3 4  4  4  5  5  6  6  6  7  7
#> Eliminate if # of DLT >=   NA NA 3 3 4 4 5 5 5  6  6  7  7  8  8  8  9  9

# At a target of 0.25 one DLT out of three de-escalates by default
boin_boundary(target = 0.25, max_n = 18)$b_deesc[3]
#> [1] 1

# and stays once the modification is switched on
modified <- boin_boundary(target = 0.25, max_n = 18, stay_on_1_of_3 = TRUE)
modified$b_deesc[3]
#> [1] 2
modified$stay_on_1_of_3_applied
#> [1] TRUE

# At a target of 0.30 the design already stays, so nothing changes
boin_boundary(target = 0.30, max_n = 18, stay_on_1_of_3 = TRUE)$stay_on_1_of_3_applied
#> [1] FALSE