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Dose-finding trials for oncology studies are traditionally designed to assess safety in the early stages of drug development. With the rise of molecularly targeted therapies and immuno-oncology compounds, biomarker-driven approaches are increasingly importance. In this article, we propose a novel approach to dose-finding that incorporates biomarkers which predict for the subsequent development of clinical toxicity. The proposed joint model framework, which incorporates repeated biomarker measurements, is compared to the likelihood-based continual reassessment method (CRM) using only binary toxicity data, across various dose-toxicity relationship scenarios. Our findings highlight a critical limitation of likelihood-based approaches in early-phase dose-finding studies with small sample sizes: estimation challenges that have been previously overlooked in the phase I dose-escalation setting. We explore potential remedies to address these challenges and emphasize the appropriate use of likelihood-based methods. Simulation results demonstrate that the proposed joint model framework, by integrating biomarker information, can alleviate estimation problems in the likelihood-based CRM and improve the proportion of correct selection. However, we highlight that the inherent data limitations in early phase dose-finding studies remain a significant challenge that cannot be fully overcome in the frequentist framework.