Continual Reassessment Method (CRM) Calculator

Methodology

The calculator implements a one-parameter Bayesian Continual Reassessment Method using the power model. The pre-specified skeleton values define the dose-toxicity curve, while observed DLT outcomes update the unknown model parameter through the likelihood and an exponential prior.

Dose-toxicity model

For patient i treated at dose level j(i), with DLT indicator y_i, the likelihood is the product of Bernoulli probabilities. The prior is g(a) = exp(−a), a ≥ 0. The calculator obtains the posterior mean of a numerically and plugs that value into the dose-toxicity model.

Choosing the next dose

The model-based MTD is the dose level whose posterior-mean toxicity probability is closest to the target toxicity probability. If the optional one-level escalation restriction is enabled, an upward recommendation is capped at one dose level above the current dose. The unrestricted model-based candidate remains visible in the results.

Safety check

The calculator also evaluates the posterior probability that the lowest dose exceeds the target toxicity probability. If that probability exceeds the user-specified safety cutoff, the result is flagged as a safety-stop signal. This is an explicit safety augmentation and should be prespecified and calibrated by simulation before use in an actual clinical trial.

Worked validation example

The validation example reproduces the published Table 1 patient sequence from O'Quigley, Pepe & Fisher (1990), as reproduced in the CRAN CRM package documentation. Use target = 0.20 and skeleton = 0.05, 0.10, 0.20, 0.30, 0.50, 0.70, then enter these 25 records:

The validated implementation gives a posterior mean parameter of approximately 0.060434, with estimated toxicity probabilities of approximately 0.04149, 0.08664, 0.18092, 0.27832, 0.47887, and 0.68462 across the six dose levels. The model-based candidate closest to the 0.20 target is dose level 3.

References

O'Quigley, J., Pepe, M., & Fisher, L. (1990). Continual reassessment method: a practical design for phase 1 clinical trials in cancer. Biometrics, 46(1), 33–48. DOI: 10.2307/2531628.

Garrett-Mayer, E. (2006). The continual reassessment method for dose-finding studies: a tutorial. Clinical Trials, 3(1), 57–71. DOI: 10.1191/1740774506cn134oa.

CRAN CRM package documentation, version 1.2.4. The crm() documentation specifies the target, skeleton, patient-level dose/DLT data, exponential prior, dose-toxicity models, and the O'Quigley et al. Table 1 example used for validation.

lists Bayesian Continual Reassessment Method among its Bayesian procedures. The implementation here is explicitly the published Bayesian CRM formulation described above rather than a claim to reproduce proprietary internals.