A study of the probit model with latent variables in Phase I clinical trials

Abstract

In recent years, the continual reassessment method (CRM) has gained considerable popularity in Phase I cancer studies. In this article, we propose a two-parameter probit model with latent variables. Introducing the latent variables enables exact Bayesian inference in the sense that conditional posterior distributions of all the parameters, including the latent variables, are known. Such inference can be more accurate than the maximum likelihood inference and can also alleviate the estimation issue due to small sample size [Albert J, Chib S. Bayesian analysis of binary and polychotomous response data. J Amer Statist Assoc. 1993;88:669–679] in Phase I studies. Simulation studies demonstrated that the proposed method compares favourably to the one-parameter CRM.

Keywords:

• Bayesian method
• continual reassessment method
• dose finding
• latent variable
• Markov chain Monte Carlo
• Phase I clinical trial
• probit model

Funding

Keying Ye's research was partially supported by a grant from the College of Business of the University of Texas at San Antonio.