Optimization of dose selection using multiple surrogates of toxicity as a continuous variable in phase I cancer trial

In phase I trials, it is the top priority of clinicians to effectively treat patients and minimize the chance of exposing them to subtherapeutic and overly toxic doses, while exploiting patient information. Motived by this practical consideration, we revive the one parameter linear dose-finder developed in 1970s to accommodate a continuous toxicity response in the phase I cancer clinical trials, which is called the two parameters linear dose-finder (2PLD). The 2PLD is a fully Bayesian model that assumes a linear relationship between toxicity response and dose. We suggest a dose search algorithm based on the 2PLD to exploit the grades of toxicities from multiple adverse events to align with Common Toxicity Criteria for Adverse Events provided by the National Cancer Institute. The proposed search procedure suggests an optimal dose to each patient by using accrued patients' information while controlling the posterior probability of overdose. The heterogeneity of patients in dose reaction is addressed by making a fully Bayesian inference about the standard deviation of toxicity responses. The 2PLD can be an attractive tool for clinical scientists due to its parsimonious description of a toxicity-dose curve and medical interpretation as well as an automatic posterior computation. We illustrate the performance of this design using simulation data to identify the maximum tolerated dose.