Multc Lean

This page implements a special case of the clinical trial method of Thall, Simon, and Estey.* Toxicity and response are modeled using a Dirichlet distribution with elementary events the four possible combinations of (response, toxicity). The two compound events we are monitoring are response (with or without toxicity) and toxicity (with or without response). In other words, we are monitoring the marginals.

The marginal probabilities of response and toxicity on both the standard and experimental treatments therefore have beta distributions. Trials are stopped when the marginal posterior probability of the experimental arm being worse than standard (either less effective or more toxic) exceeds specified thresholds. Since only marginal probabilities are being monitored, the association between toxicity and response does not impact the operating characteristics. A tutorial stepping through a trial design in detail is available here. Also, a commandline application implementing the full Thall-Simon-Estey method is available here.

Maximum sample size

Maximum number of patients in trial if no stopping rule applies:

Marginal response parameters

Standard treatment response distribution	a:	b:	help
Experimental treatment response prior distribution	a:	b:	help
Stop if the posterior probability of the experimental treatment being less responsive is greater than	π*		help

Marginal toxicity parameters

Standard treatment toxicity distribution	a:	b:	help
Experimental treatment toxicity prior distribution	a:	b:	help
Stop if the posterior probability of the experimental treatment being more toxic is greater than	π_*		help

*Peter F. Thall, Richard M. Simon, and Elihu H. Estey, Bayesian sequential monitoring designs for single-arm clinical trials with multiple outcomes, Statistics in Medicine, vol 14, 357-379 (1995).

Multc Lean

The Department of Biostatistics & Applied Mathematics