Select the MTD Combination from Completed Drug-Combination Trials

Choose the maximum tolerated dose combination for each of a set of completed trials of the BOIN drug-combination design from the final patient and DLT counts.

Usage

comb_boin_select_mtd(
  n_pts,
  n_tox,
  target,
  cutoff_eli = 0.95,
  extrasafe = FALSE,
  offset = 0.05,
  bound_mtd = FALSE,
  p_tox = NULL
)

Arguments

n_pts: Integer matrix giving the number of patients treated at each combination of one trial, with one row per dose level of drug A and one column per dose level of drug B, or an integer array with dimensions trial by level of drug A by level of drug B for several trials, as returned by comb_boin_simulate.
n_tox: Integer matrix or array of the same shape as n_pts, giving the number of DLTs observed.
target: Numeric scalar. Target DLT probability.
cutoff_eli: Numeric scalar. Posterior probability cutoff for eliminating a combination. Defaults to 0.95.
extrasafe: Logical scalar. Apply the stricter safety rule at the lowest combination, in which case no combination is selected when it is judged too toxic. Defaults to FALSE.
offset: Numeric scalar between 0 and 0.5. Amount by which cutoff_eli is relaxed for the safety rule. Defaults to 0.05.
bound_mtd: Logical scalar. Require the isotonic estimate at the selected combination to be below the de-escalation boundary. Defaults to FALSE.
p_tox: Numeric scalar. Lowest DLT probability deemed overly toxic, used to derive the de-escalation boundary when bound_mtd is TRUE. Defaults to 1.4 * target.

Value

A data frame with one row per trial and columns

trial: Trial index.
mtd_a: Dose level of drug A in the selected combination, or NA when none is selected.
mtd_b: Dose level of drug B in the selected combination, or NA.
reason: Why a combination was or was not selected.

Details

The selection follows the reference implementation used by BOIN::get.oc.comb(). Elimination is re-derived from the final data: within each row, the first combination with at least three patients whose posterior probability of a DLT rate above target exceeds cutoff_eli is eliminated together with the rest of its row and the rest of its column. If the lowest combination is eliminated, no combination is selected. Otherwise the estimates (y + 0.05) / (n + 0.1) are smoothed by bivariate isotonic regression with weights n + 0.1, so that they increase along every row and column, and the treated, non-eliminated combination whose estimate is closest to target is selected. A small amount, 1e-5 times the sum of the two dose levels, is added to every estimate first, so that ties go to the lower combination.

The isotonic regression is Iso::biviso(), the routine the reference implementation calls. Combinations that the regression pools together have equal estimates in exact arithmetic but can differ in the last digits, and with the small amount above, these digits decide between combinations on the same anti-diagonal. Another algorithm for the same regression would therefore select differently in a few trials out of a thousand.

The article of Lin and Yin (2017) estimates the DLT rates as y / n and resolves ties differently; the package follows the reference implementation so that the two can be compared trial by trial.

Values of reason are "selected", "lowest_dose_eliminated" and "no_dose_below_bound".

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.

Examples

n_pts <- matrix(c(3, 6, 3,
                  3, 3, 0), nrow = 2, byrow = TRUE)
n_tox <- matrix(c(0, 1, 1,
                  0, 2, 0), nrow = 2, byrow = TRUE)

comb_boin_select_mtd(n_pts, n_tox, target = 0.30)
#>   trial mtd_a mtd_b   reason
#> 1     1     1     3 selected