The Extended EWOC Method And Two-dimensional Isotonic Design Of MTD-Finding Trials

The paper investigates designs of dose-finding trials, the purpose of which is to determine the maximum tolerated dose (MTD). Babb et al~[1] proposed a Bayesiau dose escalation scheme referred to as escalation with overdose control (EWOC) for cancer phase I clinical trials. As toxicity is typically measured on a multinomial scale and several distinct types of toxicity in clinical, it is feasible and sometimes even integrant to set multivariate responding measures for toxicity on trials. This paper is devoted to extending the Babb's EWOC method of dose-finding trials to multi-response measures, and conducting simulations to compare the extended EWOC method with CR.M~[3] based on ternary response. Results showed the extended EWOC method is more effective as a means to control the frequency of overdosing than CRM. EWOC method produced a smaller proportion of overdosed patients compared with the CRM method and it estimated the MTD with comparable accuracy. Furthermore, the paper investigates the design of dose-finding trials with two agents. The set of doses for each agent is fixed in advance. The goal of the trial is to find the set of dose combinations with probability of toxicity closest to a pre-specified value. Suppose that each of the two agents is non-decreasing with dose when the dose of the other agent is fixed. Using this assumption we construct a new non-parametric Isotonic design of a two-dimensional grid of all possible dose combinations. We conducted simulations to compare the Isotonic design with several independent dose-finding trials and Narayana design of two-dimension~[5] The Isotonic design is simple to program and very easy to understand, it can be used with any value of the target probability. R.esults showed the Isotonic design is more effective than all one-dimensional methods as a means that the percentage of experimentation at each dose combination and the frequency of overdosing than several independent dose-finding trials. For the estimation of MTD Isotonic design is superior to the Traditional method, and better than Narayana design and Narayana design of two-dimension in most of the cases, the Storer's Up-and-down design 3 is better than Isotonic design in general. Our total isotonic estimator performs better than the two-dimensional estimator proposed by Ivanova and Wang~[5]...