Commensurate prior models with random effects for interval-censored data to accommodate historical controls.

Using historical controls for clinical trial data analysis may increase statistical power and reduce required sample sizes when studying rare diseases. Most existing literature on borrowing information from historical controls with survival outcomes studied right-censored data. However, events of interest are often confirmed during routine follow-up visits or when patients display symptoms, leading to the recording of events after their occurrence. Treating these recorded events as an exact time rather than as interval-censored data may introduce bias into the assessment of treatment effect. When combining data sources, differential patterns of assessment timing may impact the comparability of the data and contribute to bias unless properly accounted for. Additionally, historical controls are often obtained by matching with clinical trial data, or which existing commensurate prior models have not been explored. To address these issues, we propose commensurate prior models with random effects for matched interval-censored survival data. These models effectively borrow information based on the degree of comparability between historical controls and clinical trial data. Simulation studies demonstrate the model's ability to control Type I error well, where the two data sources exhibit exchangeability or non-exchangeability. We apply our proposed methods by reanalyzing data from BMT CTN 1101 and BMT CTN 0901, incorporating corresponding historical datasets.