Theoretical study of the continual reassessment method

Abstract The continual reassessment method (CRM) was first introduced by O’Quigley et al. [1990. Continual reassessment method: a practical design for Phase I clinical trials in cancer. Biometrics 46, 33–48]. Many articles followed adding to the original ideas, among which are articles by Babb et al. [1998 . Cancer Phase I clinical trials: efficient dose escalation with overdose control. Statist. Med. 17, 1103–1120], Braun [2002 . The bivariate-continual reassessment method. Extending the CRM to phase I trials of two competing outcomes. Controlled Clin. Trials 23, 240–256], Chevret [1993 . The continual reassessment method in cancer phase I clinical trials: a simulation study. Statist. Med. 12, 1093–1108], Faries [1994 . Practical modifications of the continual reassessment method for phase I cancer clinical trials. J. Biopharm. Statist. 4, 147–164], Goodman et al. [1995 . Some practical improvements in the continual reassessment method for phase I studies. Statist. Med. 14, 1149–1161], Ishizuka and Ohashi [2001 . The continual reassessment method and its applications: a Bayesian methodology for phase I cancer clinical trials. Statist. Med. 20, 2661–2681], Legedeza and Ibrahim [2002 . Longitudinal design for phase I trials using the continual reassessment method. Controlled Clin. Trials 21, 578–588], Mahmood [2001 . Application of preclinical data to initiate the modified continual reassessment method for maximum tolerated dose-finding trial. J. Clin. Pharmacol. 41, 19–24], Moller [1995. An extension of the continual reassessment method using a preliminary up and down design in a dose finding study in cancer patients in order to investigate a greater number of dose levels. Statist. Med. 14, 911–922], O’Quigley [1992. Estimating the probability of toxicity at the recommended dose following a Phase I clinical trial in cancer. Biometrics 48, 853–862], O’Quigley and Shen [1996. Continual reassessment method: a likelihood approach. Biometrics 52, 163–174], O’Quigley et al. (1999) , O’Quigley et al. [2002. Non-parametric optimal design in dose finding studies. Biostatistics 3, 51–56], O’Quigley and Paoletti [2003. Continual reassessment method for ordered groups. Biometrics 59, 429–439], Piantodosi et al., 1998 . [1998 Practical implementation of a modified continual reassessment method for dose-finding trials. Cancer Chemother. Pharmacol. 41, 429–436] and Whitehead and Williamson [1998. Bayesian decision procedures based on logistic regression models for dose-finding studies. J. Biopharm. Statist. 8, 445–467]. The method is broadly described by Storer [1989. Design and analysis of Phase I clinical trials. Biometrics 45, 925–937]. Whether likelihood or Bayesian based, inference poses particular theoretical difficulties in view of working models being under-parameterized. Nonetheless CRM models have proven themselves to be of practical use and, in this work, the aim is to turn the spotlight on the main theoretical ideas underpinning the approach, obtaining results which can provide guidance in practice. Stemming from this theoretical framework are a number of results and some further development, in particular the way to structure a randomized allocation of subjects as well as a more robust approach to the problem of dealing with patient heterogeneity.