Incorporating historical control information into quantal bioassay with Bayesian approach

A comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation

The benchmark dose (BMD) approach has been accepted as a valuable tool for risk assessment but still faces significant challenges associated with combining environmental hazard information from multiple sources and selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose-response models. The main objective of this study is to compare and examine how historical information, especially incompatible data, can impact the Bayesian model averaged BMD estimate through different integration methods. Based on the Bayesian model averaging (BMA) for the benchmark dose estimation, three methods of integration are investigated: (1) pooled data analysis, which combines all dose groups into one dataset; (2) the Bayesian hierarchical model, which takes both between-study and within-study uncertainty into account by building multiple levels of distributions to quantitatively describe parameters in dose-response models; and (3) the power prior method, which allows researchers to weigh the prior information incorporated through a power parameter. Combined historical information can have different levels of impact on the current model weight and BMD estimates depending on the method of integration. The pooled data analysis, which has the largest impact on the current BMA BMD estimate, has limited applicability and might be statistically and biologically flawed. The Bayesian hierarchical model, with a reasonable structure to combine information, can slightly change the current estimates of the model weights and BMD. The power prior method has little influence on current estimates when data are highly incompatible even if the prior information is fully considered.