Model Averaging with AIC Weights for Hypothesis Testing of Hormesis at Low Doses

Abstract

For many dose–response studies, large samples are not available. Particularly, when the outcome of interest is binary rather than continuous, a large sample size is required to provide evidence for hormesis at low doses. In a small or moderate sample, we can gain statistical power by the use of a parametric model. It is an efficient approach when it is correctly specified, but it can be misleading otherwise. This research is motivated by the fact that data points at high experimental doses have too much contribution in the hypothesis testing when a parametric model is misspecified. In dose–response analyses, to account for model uncertainty and to reduce the impact of model misspecification, averaging multiple models have been widely discussed in the literature. In this article, we propose to average semiparametric models when we test for hormesis at low doses. We show the different characteristics of averaging parametric models and averaging semiparametric models by simulation. We apply the proposed method to real data, and we show that P values from averaged semiparametric models are more credible than P values from averaged parametric methods. When the true dose–response relationship does not follow a parametric assumption, the proposed method can be an alternative robust approach.

Calculations of the Radiation Dose for the Maximum Hormesis Effect

“…In addition to LNT and hormesis, some possible models in the low-dose range (supra-linear, linear-quadratic, threshold, sigmoidal threshold, and hyper-radiosensitivity) have been proposed [52,56]. Biological findings and mathematical models at the molecular-cellular level have been studied to unravel the mysteries of low-dose exposure [32,[43][44][45][46][47][48][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68], and we have previously proposed a linear-hormesis coupling theory.…”

The Radiation-Specific Components Generated in the Second Step of Sequential Reactions Have a Mountain-Shaped Function

“…However, there are doubts as to whether the LNT model is valid at low doses, and the phenomenon of radiation hormesis, in which radiation is beneficial to living organisms, has also been reported [11][12][13]. Therefore, it may be possible to clarify the truth at low doses by adding biological findings at the molecular-cellular level and mathematical models [11,[14][15][16][17][18][19][20][21][22].…”

The Theoretical Dose That Exerts the Maximum Hormesis Effect Is 20 mSv When the Risk Is Approximately Proportional to Dose above 100 mSv.

“…Radiation adaptation responses have been reported as a phenomenon associated with low doses [11][12][13][14][15][16][17][18][19] and are closely related to radiation hormesis [20][21][22][23][24][25][26][27][28], the hypothesis that low-dose radiation is beneficial to an organism. Thus, biological findings and mathematical models at the molecular-cellular level have been studied to unravel the mysteries of low-dose exposure [20,[29][30][31][32][33][34][35][36][37], and we have previously proposed a linear-hormesis coupling theory.…”