Data-driven prior elicitation for Bayes factors in Cox regression for nine subfields in biomedicine

Abstract

Biomedical research often utilizes Cox regression for the analysis of time-to-event data. The pervasive use of frequentist inference for these analyses implicates that the evidence for or against the presence (or absence) of an effect cannot be directly compared and that researchers must adhere to a predefined sampling plan. As an alternative, the use of Bayes factors improves upon these limitations, which is especially important for costly and time-consuming biomedical studies. However, Bayes factors involve their own difficulty of specifying priors for the parameters of the statistical model. In this article, we develop data-driven priors centered around zero for Cox regression tailored to nine subfields in biomedicine. To this end, we extracted hazard ratios and associated x % confidence intervals from the abstracts of large corpora of already existing studies within the nine biomedical subfields. We used these extracted data to inform priors for the nine subfields. All of our suggested priors are Normal distributions with means of 0 and standard deviations closely scattered around 1. We propose that researchers use these priors as reasonable starting points for their analyses.