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Properties of Model-Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation


*Address correspondence to Matthew W. Wheeler, National Institute for Occupational Safety and Health, Risk Evaluation Branch, MS C-15, 4676 Columbia Parkway, Cincinnati, OH 45226, USA; tel: 513-533-8195; fax: 513-533-8224;


Model averaging (MA) has been proposed as a method of accounting for model uncertainty in benchmark dose (BMD) estimation. The technique has been used to average BMD dose estimates derived from dichotomous dose-response experiments, microbial dose-response experiments, as well as observational epidemiological studies. While MA is a promising tool for the risk assessor, a previous study suggested that the simple strategy of averaging individual models' BMD lower limits did not yield interval estimators that met nominal coverage levels in certain situations, and this performance was very sensitive to the underlying model space chosen. We present a different, more computationally intensive, approach in which the BMD is estimated using the average dose-response model and the corresponding benchmark dose lower bound (BMDL) is computed by bootstrapping. This method is illustrated with TiO2 dose-response rat lung cancer data, and then systematically studied through an extensive Monte Carlo simulation. The results of this study suggest that the MA-BMD, estimated using this technique, performs better, in terms of bias and coverage, than the previous MA methodology. Further, the MA-BMDL achieves nominal coverage in most cases, and is superior to picking the “best fitting model” when estimating the benchmark dose. Although these results show utility of MA for benchmark dose risk estimation, they continue to highlight the importance of choosing an adequate model space as well as proper model fit diagnostics.