The aim of a phase I oncology trial is to identify a dose with an acceptable safety level. Most phase I designs use the Dose-Limiting Toxicity (DLT), a binary endpoint, to assess the level of toxicity. DLT might be an incomplete endpoint for investigating molecularly targeted therapies as a lot of useful toxicity information is discarded.In this work, we propose a quasi-continuous toxicity score, the Total Toxicity Profile (TTP), to measure quantitatively and comprehensively the overall burden of multiple toxicities. The TTP is defined as the Euclidean norm of the weights of toxicities experienced by a patient, where the weights reflect the relative clinical importance of each type and grade of toxicity.We propose then a dose-finding design, the Quasi-Likelihood Continual Reassessment Method (QLCRM), incorporating the TTP-score into the CRM, with a logistic model for the dose-toxicity relationship in a frequentist framework. Using simulations, we compare our design to three existing designs for quasi-continuous toxicity scores: i) the QCRM design, proposed by Yuan et al., with an empiric model for the dose-toxicity relationship in a Bayesian framework, ii) the UA design of Ivanova and Kim derived from the "up-and-down" methods for the dose-escalation process and using an isotonic regression to estimate the recommended dose at the end of the trial, and iii) the EID design of Chen et al. using the isotonic regression for the dose-escalation process and for the identification of the recommended dose.We also perform a simulation study to evaluate the TTP-driven methods in comparison to the classical DLT-driven CRM. We then evaluate the robustness of these designs in a setting where grades can be misclassified.In the last part of this work, we illustrate the process of building the TTP-score and the application of the QLCRM method through the example of a paediatric trial. In this study, we have used the Delphi method to elicit the weights and the target toxicity-score considered as an acceptable toxicity measure.All designs using the TTP-score to identify the recommended dose had good performance characteristics for most scenarios, with good overdosing control. For a sample size of 36, the percentage of correct selection for the QLCRM ranged from 80 to 90%, with similar results for the QCRM design. Simulation study demonstrates also that score-driven designs present an improved performance and robustness compared to conventional DLT-driven designs. In the retrospective application of erlotinib trial, the consensus weights as well as the target-TTP were easily obtained, confirming the feasibility of the process. Some guidelines to facilitate the process in a real clinical trial for a better practice of this approach are suggested.The QLCRM method based on the TTP-endpoint combining multiple graded toxicities is an appealing alternative to the conventional dose-finding designs, especially in the context of molecularly targeted agents.