Heterogeneity in phase I clinical trials: prior elicitation and computation using the continual reassessment method

Heterogeneity in a phase I clinical trial patient population may lead to distinctly different dose-response relationships along covariate values. For a given target probability of toxicity, this implies different maximum tolerated doses (MTDs) for each distinct subpopulation. Within the framework of O'Quigley, Pepe and Fisher's (1990) continual reassessment method, we propose the notion of average and patient-specific MTDs by augmenting the dose--response model with other covariates to account for such differences. A method to elicit prior distributions on the dose and other covariate parameters are proposed, based on the predictive approach of Ibrahim and Laud (1994), Laud and Ibrahim (1995), and Ibrahim, Ryan and Chen (1998). This approach relies on prior predictions for the response vector y(0) and a quantity a(0) specifying uncertainty in y(0). Then, y(0) and a(0) are used to specify a prior for the regression coefficients in a semi-automatic fashion. The elicitation scheme for y(0) uses results from previous phase I cancer clinical trials. The average and patient-specific MTDs and an elicitation method are demonstrated in logistic regression examples.