This article considers the concept of designing Phase I clinical trials using both clinician- and patient-reported outcomes to adaptively allocate study participants to tolerable doses and determine the maximum tolerated dose (MTD) at the study conclusion. We describe a new isotonic patient-reported outcome (PRO-ISO) Phase I design with the flexibility of allocating patients to lower, more tolerable regimens if a large number of PRO-DLT events are seen at higher doses. We conduct simulation studies of the operating characteristics of the design and compared them to the patient-reported outcomes continual reassessment method (PRO-CRM). We illustrate that the PRO-ISO makes appropriate dose assignments during the study to give investigators and reviewers an idea of how the method behaves. In simulation studies, the PRO-ISO demonstrates comparable performance to the PRO-CRM in terms of recommending target doses and allocating patients to these doses. It also performs well relative to a nonparametric optimal benchmark applied to the PRO setting. Finally, we extend our methodology to account for the problem of late-onset toxicities.