Statistics and Its Interface

Volume 5 (2012)

Number 4

A phase I dose-finding study based on polychotomous toxicity responses

Pages: 451 – 461



Xiaobin Yang (Analytic Focus, LLC, San Antonio, Texas, U.S.A.)

Keying Ye (Department of Management Science and Statistics, University of Texas at San Antonio, U.S.A.)


In phase I clinical trials, toxicity study is important and the toxicity level is often categorized into multiple (polychotomous) grades, rather than dichotomous grades. In this paper, we introduce a concept of overall maximum tolerated dose (overall MTD) and we discuss its analytic properties. The traditional definition of the MTD is shown to be a special case of the overall MTD. A dose-finding strategy is also proposed to obtain the overall MTD. Motivated by the continual reassessment method (CRM), a cumulative probit model with latent variables is introduced to fit the data. By introducing latent variables, Markov chain Monte Carlo (MCMC) methods are employed to estimate the model parameters. Simulation studies show that the cumulative probit model, which takes into account the severity level of toxicity, reduces the number of patients allocated to the higher toxicity dose level. This could reduce the risk of toxicity for patients in the phase I study.


phase I clinical trial, polychotomous toxicity responses, dose finding, continual reassessment method (CRM), cumulative probit model, latent variable, Markov chain Monte Carlo (MCMC)

2010 Mathematics Subject Classification

Primary 62F15, 62L05. Secondary 62P10.

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