Proportional Relative Hazards Model for Competing Risks Data

In this article, we propose a Proportional Relative Hazards (PRH) model to differentiate subjects according to their risk for a primary event relative to competing events. The model estimates effects on the baseline ratio of the hazard for a primary event, or set of primary events, relative to the hazard for a competing event, or set of competing events ( ω + ratio). An analogous model is presented to estimate effects on the baseline ratio of the hazard for a primary event (or set of events) relative to the hazard for all events ( ω ratio). A weighted regression method is introduced, along with practical presentation of risk-stratification using the PRH model in breast and head and neck cancer data sets. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement Dr. Mell received salary support from National Cancer Institute 1R01CA197059-01. None of the authors or their institutions received other payments related to the work. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: University of California San Diego IRB All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes Clinical trial data available by request from NRG Oncology. Epidemiologic data available from SEER-Medicare. All other data available upon request from the corresponding author.