Fast Simulation of Bayesian Optimal Interval Designs for Phase I Trials

Design and evaluate phase I dose-finding trials that use the Bayesian optimal interval (BOIN) design of Liu and Yuan (2015) . Functions are provided to tabulate the decision boundaries, to simulate trials, to estimate the dose-toxicity curve under a monotonicity constraint and to select the maximum tolerated dose. The simulation engine is written in C++ and draws one random variate per patient in enrollment order, which reproduces the reference implementation in the 'BOIN' package trial by trial for a given seed. The traditional 3+3 design is provided as a comparator, with operating characteristics obtained in closed form rather than by simulation.

simFastBOIN

Simulation tools for Bayesian optimal interval (BOIN) designs in phase I dose-finding trials.

Overview

simFastBOIN tabulates the BOIN decision boundaries, simulates the design to obtain operating characteristics, and applies the MTD selection rule used at the end of a trial. The simulation engine is written in C++.

The engine draws one uniform variate per patient, in enrollment order, and applies the decision rules in the same order as BOIN::get.oc(). With the same seed and matching arguments the two implementations agree trial by trial, not merely on average. The test suite checks this directly against the BOIN package rather than relying on a tolerance, so the claim is verifiable rather than asserted. A wider comparison ships with the package as inst/validation/compare-with-BOIN.R, which runs 200 configurations covering every combination of the options the two packages share, including extrasafe and titration.

Installation

install.packages("simFastBOIN")

Or the development version:

# install.packages("devtools")
devtools::install_github("gosukehommaEX/simFastBOIN")

Version 2.0.0 contains compiled code, so a working C++ toolchain is needed to install from source (Rtools on Windows, Xcode command line tools on macOS).

Quick start

library(simFastBOIN)

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 = 10000,
  seed = 123
)

oc

Compare several dose-toxicity scenarios under the same design:

sim_boin_multi(
  target = 0.30,
  scenarios = list(
    "MTD at dose 2"   = c(0.15, 0.30, 0.45, 0.60, 0.75),
    "MTD at dose 4"   = c(0.02, 0.06, 0.15, 0.30, 0.50),
    "All doses toxic" = c(0.40, 0.55, 0.65, 0.75, 0.85)
  ),
  n_cohort = 10,
  cohort_size = 3,
  n_trials = 10000,
  seed = 123
)

Look at the boundaries the design will actually use:

print(boin_boundary(target = 0.30, max_n = 18, extrasafe = TRUE), cohort_size = 3)

Read the dose decisions off a table, or off a figure for a protocol:

decisions <- boin_decision_table(target = 0.30, max_n = 18)

print(decisions, cohort_size = 3)
plot(decisions)                      # needs ggplot2

Functions

Design

Simulation

Design options

Note that n_earlystop defaults to 18 here, whereas BOIN::get.oc() defaults to 100, which in practice switches the rule off. Set it explicitly when comparing the two.

Why the trials stop

boin_simulate() records a reason for every trial, and sim_boin() reports the distribution in stop_reason_percent.

Checking the agreement with the BOIN package yourself

reference <- BOIN::get.oc(
  target = 0.30, p.true = c(0.05, 0.15, 0.25, 0.45, 0.60),
  ncohort = 20, cohortsize = 3, n.earlystop = 18, ntrial = 10000, seed = 6
)

ours <- sim_boin(
  target = 0.30, p_true = c(0.05, 0.15, 0.25, 0.45, 0.60),
  n_cohort = 20, cohort_size = 3, n_earlystop = 18, n_trials = 10000, seed = 6
)

all.equal(unname(ours$sel_percent), reference$selpercent)
all.equal(unname(ours$n_pts_dose), reference$npatients)
all.equal(unname(ours$n_tox_dose), reference$ntox)
all.equal(ours$percent_no_mtd, reference$percentstop)

Speed

Five doses, 20 cohorts of three, n_earlystop = 18 and 10,000 simulated trials, measured on one Windows machine:

That is about two orders of magnitude for this design. The ratio depends on the design and on the machine, so the code below re-measures it rather than asking you to take the table on trust.

scenario <- c(0.05, 0.15, 0.25, 0.45, 0.60)

system.time(
  BOIN::get.oc(target = 0.30, p.true = scenario, ncohort = 20, cohortsize = 3,
               n.earlystop = 18, ntrial = 10000, seed = 6)
)

system.time(
  sim_boin(target = 0.30, p_true = scenario, n_cohort = 20, cohort_size = 3,
           n_earlystop = 18, n_trials = 10000, seed = 6)
)

Comparing with the 3+3 design

The traditional 3+3 design is included as a comparator. Its operating characteristics are obtained in closed form rather than by simulation, so they carry no Monte Carlo error.

oc_3p3(p_true = c(0.30, 0.48, 0.67))

# The other definition of the MTD in common use
oc_3p3(p_true = c(0.30, 0.48, 0.67), mtd_rule = "expand")

sim_3p3() simulates the same design and exists to confirm the closed form. The result of either has the same component names as the result of sim_boin(), so the two designs can be tabulated side by side.

Upgrading from version 1.3.2

Version 2.0.0 renames most functions, changes the argument order of sim_boin() and corrects several defects that affected numerical results. Simulations run with the same seed will not reproduce the version 1.3.2 output. See NEWS.md for the full list and the mapping of old names to new ones.

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.

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.

License

MIT (c) Gosuke Homma