Bayesian Benchmark Dose Modeling for Case–Control Studies: Applying Wang (2013) to Effective Counts with an Entropy-Based Extension

Francesco De Pretis, Ph.D.

University of Modena and Reggio Emilia

Benchmark dose (BMD) modeling is increasingly used to quantify dose–response in epidemiology, yet case–control evidence typically arrives as adjusted odds ratios (ORs) rather than raw counts. A practical route is to reconstruct effective case and control counts consistent with the published ORs and confidence intervals, enabling standard dichotomous BBMD pipelines. The approach leverages the Wang (2013) algorithm for converting OR information under partial data into admissible 2×2 contingency tables via constrained optimization, which can admit multiple feasible (near-optimal) solutions. In the present framework (De Pretis, Zhou and Shao, 2025) the Wang algorithm is applied to construct effective counts for Bayesian BMD modeling—as operationalized in recent case–control analyses of arsenic exposure and cancer—thereby harmonizing adjusted epidemiologic summaries with toxicological BMD practice. Beyond published work, current work explores entropy-based criteria as a principled means to guide solution selection when multiple admissible reconstructions arise. These developments represent a natural expansion of the BBMD framework, maintaining the Wang algorithm as its computational foundation while introducing information-theoretic refinements to support future methodological generalization.