The Study And Application Of Nonparametric Bayesian Methods For Benchmark Dose Estimation

Objective:This paper will introduce two nonparametric Bayesian methods for benchmark dose estimating. First is the nonparametric Bayesian method based on the weighting process and second is the nonparametric Bayesian method based on stochastic process. The methodology is compared with traditional parametric methods available in standard benchmark dose estimation software, then we analysis their performance under different dose response data.Methods:Introduce the basic principle of the traditional parametric models, nonparametric Bayesian method based on weighted process and nonparametric Bayesian method based on stochastic process separately. We constituted eight kinds of dose response data through different parameter configurations. R software is used to simulate the data and the parameters are estimated by the two proposed NPB procedures. The performance of the two NPB procedures is compared through the difference between the BMD estimate and the true value, and the coverage of BMDL. To illustrate and compare the proposed methods with existing methods in the EPA Benchmark Dose Software, we selected nine of the cancer bioassay data sets previously analyzed by Nitcheva et al.(2007).Results:The posterior estimates were reasonably close to the target true BMD value for the two nonparametric methods. The NPB1 coverage was well below the nominal level for six dose logarithmic spacing case for MS(0, 1, 1, 3), as a result of the upward bias in BMD estimation. The upward bias was due to oversmoothing by a relatively higher posterior bandwidth. The RMSE values of the two methods are both small. For the chosen parameter configurations, only NPB2 had coverage that always met the nominal levels. Although somewhat conservative, that may be a desirable feature for NBP2 compared to NPB1.The nine examples indicate that the BMD estimates from the nonparametric approaches generally fall into or very near the interval of BMD estimates obtained from BMDS. In terms of BMDLs, nonparametric approaches tend to produce lower BMDLs than the parametric modeling approaches.Conclusions:The posterior estimates were reasonably close to the target true BMD value for the two nonparametric methods, especially when standard parametric models fail to fit to the data adequately. The NPB2 method is slightly better than the NPB1 method in the aspect of estimation result and the software operation speed. The nonparametric methods provide a lot of flexibility in terms of model fit and are widely used. It can be a very useful tool in benchmark dose estimation studies.