Estimating the dose-toxicity curve in completed phase I studies.

While there is an extensive amount of literature covering prospective designs for phase I trials, the methodology for analyzing these data is limited. Prospective designs select the maximum tolerated dose (MTD) through a dose escalation scheme based on a model or on empirical rules. For example, the '3 + 3' method (standard method: SM) assigns patients in cohorts of three and expands to six if one toxicity is observed. It has been shown previously that the MTD chosen by the SM may be low, possibly leading to a non-efficacious dose. Additionally, when deviation from the original trial design occurs, the rules for determining MTD might not be applicable. We hypothesize that a retrospective analysis would suggest an MTD that is more accurate than the one obtained by the SM. A weighted Continual Reassessment Method (CRM-w) has been suggested (Biometrics 2005; 61:749-756) for analyzing data obtained from designs other than the prospective Continual Reassessment Method (CRM). However, CRM-w has not been evaluated in trials that follow the SM design. In this study, we propose a method to analyze completed phase I trials and possibly confirm or amend the recommended phase II dose, based on a constrained maximum likelihood estimation (CMLE). A comparison of CRM-w, isotonic regression, and CMLE in analyzing simulated SM trials shows that CMLE more accurately selects the true MTD than SM, and is better or comparable to isotonic regression and CRM-w. Confidence intervals around the toxicity probabilities at each dose level are estimated using the cumulative toxicity data. A programming code is included.