Dose-Finding and Phase I/II Designs
A classical single-agent Bayesian EWOC calculator. Given dose/DLT observations, it updates the posterior distribution of the maximum tolerated dose (MTD) and recommends the posterior α-quantile, explicitly controlling the posterior probability of assigning a dose above the MTD.
EWOC (Escalation With Overdose Control) is a Bayesian adaptive dose-finding design introduced by Babb, Rogatko, and Zacks (1998). Its defining rule is to choose the next dose so that the posterior probability that the dose exceeds the MTD is the feasibility bound α. Thus, if the posterior MTD is Γ, the continuous recommendation xEWOC satisfies:
The calculator uses the classical logistic model parameterized by ρ0, the DLT probability at Xmin, and Γ, the dose at which the DLT probability equals the target θ:
The default priors follow the classical EWOC specification: Γ is uniform on [Xmin, Xmax] and ρ0 is uniform on (0, θ). The posterior is proportional to the Bernoulli likelihood times these priors. The calculator evaluates that posterior numerically on a two-dimensional grid and integrates over ρ0 to obtain the marginal posterior distribution of Γ.
For a continuous dose, the displayed EWOC dose is the posterior α-quantile directly. When a positive minimum dose increment is entered, the continuous recommendation is rounded down to the nearest permitted increment, matching the documented EWOC treatment of discrete dose levels.
Babb, J., Rogatko, A., & Zacks, S. (1998). Cancer phase I clinical trials: efficient dose escalation with overdose control. Statistics in Medicine, 17(10), 1103–1120. doi:10.1002/(SICI)1097-0258(19980530)17:10<1103::AID-SIM793>3.0.CO;2-9.
Zacks, S., Rogatko, A., & Babb, J. (1998). Optimal Bayesian-feasible dose escalation for cancer phase I trials. Statistics & Probability Letters, 38(3), 215–220.
Rogatko, A., Tighiouart, M., Cook-Wiens, G., & Li, Q. (2012). EWOC User Guide, Version 3.1. Samuel Oschin Comprehensive Cancer Institute, Cedars-Sinai Medical Center.