A wrapper function supporting exact simulation of dose-escalation trials.

Implemented currently only for the (most?) common variant of the 3+3 design, which requires that at least 6 patients be treated at a dose before it may be declared as ‘the’ MTD.

exact(selector_factory)

Arguments

selector_factory: An object of type three_plus_three_selector_factory, with allow_deescalation = TRUE.

Details

In any given realization of a 3+3 design, each of the $D$ prespecified doses will enroll 0, 1 or 2 cohorts, each with 3 patients. Each cohort will result in a tally of 0--3 dose-limiting toxicities (DLTs), and these may be recorded in a $2 \times D$ matrix. Moreover, the 3+3 dose-escalation rules allow for only one path through any such matrix. For example, the matrix


   d
c   D1 D2 D3 D4
  1  0  1  2 NA
  2 NA  0 NA NA

represents the path in a 4-dose 3+3 trial, where the following events occur:

Initial cohort at $d=1$ results 0/3
Escalation to $d=2$ results 1/3
Additional cohort at $d=2$ results 0/3 for net 1/6 at this dose
Escalation to $d=3$ results 2/3; MTD declared as $d=1$.

(Indeed, as you may verify at the R prompt, the above matrix is the 262nd of 442 such paths enumerated comprehensively in the $2 \times 4 \times 442$ array precautionary:::T[[4]].)

As detailed in Norris 2020c (below), these matrices may be used to construct simple matrix computations that altogether eliminate the need for discrete-event simulation of the 3+3 design. For each $D = 2,...,8$, the precautionary package has pretabulated a $J \times 2D$ matrix precautionary:::U[[D]] and $J$-vector precautionary:::b[[D]] such that the $J$-vector $\pi$ of path probabilities is given by: $$ log(\pi) = b + U [log(p), log(q)]', $$ where $p$ is the $D$-vector of DLT probabilities at the prespecified doses, and $q \equiv 1-p$ is its complement. See Eq. (4) of Norris (2020c).

For details on the enumeration itself, please see the Prolog code in directory exec/ of the installed package.

References

Norris DC. What Were They Thinking? Pharmacologic priors implicit in a choice of 3+3 dose-escalation design. arXiv:2012.05301 [stat.ME]. December 2020. https://arxiv.org/abs/2012.05301

Examples

# Run an exact version of the simulation from FDA-proactive vignette
design <- get_three_plus_three(
  num_doses = 6
, allow_deescalate = TRUE)
old <- options(
  dose_levels = c(2, 6, 20, 60, 180, 400)
, ordinalizer = function(MTDi, r0 = 1.5)
    MTDi * r0 ^ c(Gr1=-2, Gr2=-1, Gr3=0, Gr4=1, Gr5=2)
)
mtdi_gen <- hyper_mtdi_lognormal(CV = 0.5
                                ,median_mtd = 180
                                ,median_sdlog = 0.6
                                ,units="ng/kg/week")
exact(design) %>% simulate_trials(
  num_sims = 1000
, true_prob_tox = mtdi_gen) -> EXACT
summary(EXACT)$safety
#>                             None        Gr1        Gr2       Gr3       Gr4
#> Expected participants 12.9746375 1.96895576 1.81297882 1.3603539 0.8611740
#> MCSE                   0.0566762 0.02322388 0.02283031 0.0117814 0.0111036
#>                              Gr5      Total
#> Expected participants 0.61216947 19.5902694
#> MCSE                  0.01210457  0.0527376
if (interactive()) { # runs too long for CRAN servers
  # Compare with discrete-event-simulation trials
  design %>% simulate_trials(
    num_sims = 1000
  , true_prob_tox = mtdi_gen) -> DISCRETE
  summary(DISCRETE)$safety[,]
  # Note the larger MCSEs in this latter simulation, reflecting combined noise
  # from hyperprior sampling and the nested discrete-event trial simulations.
  # The MCSE of the former simulation is purely from the hyperprior sampling,
  # since the nested trial simulation is carried out by an exact computation.
}
options(old)