Dose-Finding and Phase I/II Designs
Monte Carlo simulation of the standard 3+3 Phase I dose-escalation design. Enter the true dose-limiting toxicity probability at each dose level and simulate repeated trials to estimate MTD selection probabilities, patient allocation, DLT burden, and average trial size. Runs entirely in your browser.
The standard 3+3 design is a rule-based Phase I dose-escalation design. Patients are treated in cohorts of three, beginning at the lowest specified dose. Decisions depend only on the number of dose-limiting toxicities (DLTs) observed among the patients treated at the current dose.
When the trial reaches the highest prespecified dose and no stopping rule has been triggered, that highest dose is selected as the MTD under this simulator's convention. If the starting dose produces at least two DLTs among its first three patients, there is no lower dose in the supplied dose grid; the simulator therefore reports that no MTD was identified.
For each simulated patient, the DLT outcome is generated as a Bernoulli random variable with probability equal to the true DLT probability entered for that patient's dose. The simulator then applies the 3+3 algorithm exactly to those simulated outcomes. This process is repeated for the requested number of independent simulated trials.
The principal operating characteristics reported are the probability that each dose is selected as the MTD, the probability that no MTD is identified, the mean number of patients treated at each dose, the mean number of DLTs at each dose, and the mean total sample size.
For a prespecified target DLT rate, the dose whose true DLT probability is closest to the target can be regarded as the scenario's target dose for descriptive purposes. The simulator does not automatically redefine the MTD based on the target; instead, it reports exactly which dose the 3+3 algorithm selected in each simulated trial.
Consequently, the MTD-selection table describes the operating characteristics of the algorithm under the dose-toxicity scenario entered by the user. It should not be interpreted as an estimate of the actual DLT probability in a clinical trial.
A published simulation study by Zhou et al. presents a five-dose scenario with true toxicity probabilities of 0.20, 0.30, 0.40, 0.50, and 0.60 and reports operating characteristics for a 3+3-type design. Those probabilities are used here as a reproducible validation scenario. For an exact deterministic check of this implementation, use the five probabilities above, 100,000 simulations, and random seed 123456789.
The published scenario is used as the substantive test case; the exact percentages above are the deterministic output of this calculator's specified pseudorandom generator and seed, rather than values copied from the publication. This distinction makes the browser implementation independently reproducible.
Storer, B. E. (1989). Design and analysis of phase I clinical trials. Biometrics, 45(3), 925–937. PMID: 2790129.
Chen, Z., Zheng, Y., Wang, Z., Kutner, M., Curran, W. J., & Kowalski, J. (2018). Interactive calculator for operating characteristics of phase I cancer clinical trials using standard 3+3 designs. Contemporary Clinical Trials Communications, 12, 145–153. doi:10.1016/j.conctc.2018.10.006.
Zhou, Y., et al. (2021). Target toxicity design for phase I dose finding. Statistical Theory and Related Fields. The published simulation table includes the five-dose toxicity scenario used for the validation example above.
the relevant methodological literature: the software. this method Sample Size Software Documentation. the relevant methodological literature describes the procedures available in this method and provides technical documentation and validation examples.
documentation: Statistical Solutions. sample-size and clinical-trial design software documentation. is a commercial clinical-trial design package that includes Phase I and dose-finding procedures.