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Purpose: CONCORDE is the first phase I drug-radiotherapy (RT) combination platform in non-small-cell lung cancer, designed to assess multiple different DNA damage response inhibitors in combination with radical thoracic RT. Time-to-event continuous reassessment method (TiTE-CRM) methodology will inform dose escalation individually for each different DNA damage response inhibitor-RT combination and a randomized calibration arm will aid attribution of toxicities. We report in detail the novel statistical design and implementation of the TiTE-CRM in the CONCORDE trial., Methods: Statistical parameters were calibrated following recommendations by Lee and Cheung. Simulations were performed to assess the operating characteristics of the chosen models and were written using modified code from the R package dfcrm., Results: The results of the simulation work showed that the proposed statistical model setup can answer the research questions under a wide range of potential scenarios. The proposed models work well under varying levels of recruitment and with multiple adaptations to the original methodology., Conclusion: The results demonstrate how TiTE-CRM methodology may be used in practice in a complex dose-finding platform study. We propose that this novel phase I design has potential to overcome some of the logistical barriers that for many years have prevented timely development of novel drug-RT combinations.