Cancer Clinical Trials with Efficacy and Toxicity Endpoints: A Simulation Study to Compare Two Nonparametric Methods

Abstract

Few methods for cancer clinical trials have been proposed in the past decade to evaluate treatments on the basis of joint efficacy and toxicity endpoints. The primary goal of a new cancer treatment is to improve efficacy. Because of the antagonist relationship between efficacy and toxicity, a critical question is to achieve this improvement without increasing unacceptably the risk of a severe toxicity. In this paper, two methods due to Letierce et al. (2003) and Tubert-Bitter et al. (2005) are compared in a simulation study. They are both nonparametric and, besides the joint approach of efficacy and toxicity, they consider the cumulative doses at which efficacy and toxicity occur, with the idea that it is better for the patient to attain efficacy at a small dose and to experience toxicity, if it happens, at the highest dose possible. These methods are detailed in the same framework. For the simulation study, the two true correlated doses at which efficacy and toxicity occur are generated from a Clayton model with Weibull marginal distributions. A fixed censoring value is considered, corresponding to the total dose of drug received at the end of the trial by the patients. Treatment groups of size 50 and 100 patients were simulated with 50%, 65%, and 80% of efficacy and 20%, 35%, and 50% of toxicity. Two values for the correlation of the variables were considered. One thousand simulations were run to estimate the type I error rate and the power of the tests. A few features were observed depending on the sample size, the correlation of the variables, and whether the difference between the two simulated treatments concerned efficacy, toxicity, or both.