Borrowing Historical Information Across All Concentration Groups with an Application of Potency Estimation in Aquatic Toxicity Assessment

Aquatic toxicity tests assess the negative impact of toxicants on survival, reproduction, and growth of organisms. Since the tests are often repeated in the same laboratory, borrowing historical experimental outcomes that are congruent would increase the precision of potency estimation with current data. In this paper, we extend the historical borrowing from control only to historical data from all concentration levels in toxicity assessments with current data using the calibrated power prior. We assume the transportability (i.e., identical concentration-response relationship) between historical and current experimental outcomes while penalizing the historical data borrowing in each concentration group independently with a modified distribution-informed calibration process. This modified calibration process prevents the over/underfitting issues by sufficiently exploring the distribution of congruence level and allows researchers to determine the level of historical information borrowing, either conservatively or aggressively, from a data-driven perspective. The effectiveness and flexibility of our proposed method are demonstrated via simulation studies. As shown in the simulation study, in scenarios when the transportability assumption fails, the proposed method still tremendously aids in the precision of toxicity assessment. The proposed method is applied in a Ceriodaphnia dubia \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textit{Ceriodaphnia dubia}$$\end{document} test.