Kim Steven B, Sanders Nathan
Department of Mathematics and Statistics, California State University, Monterey Bay, Seaside, CA, USA.
Dose Response. 2017 Jun 29;15(2):1559325817715314. doi: 10.1177/1559325817715314. eCollection 2017 Apr-Jun.
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 values from averaged semiparametric models are more credible than 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.
对于许多剂量反应研究而言，无法获得大样本。特别是，当感兴趣的结果是二元而非连续的时，需要大样本量才能为低剂量时的 hormesis 提供证据。在小样本或中等样本中，我们可以通过使用参数模型来提高统计功效。如果正确设定，这是一种有效的方法，但否则可能会产生误导。本研究的动机是，当参数模型设定错误时，高实验剂量的数据点在假设检验中贡献过大。在剂量反应分析中，为了考虑模型不确定性并减少模型设定错误的影响，文献中广泛讨论了对多个模型进行平均的方法。在本文中，我们建议在低剂量时检验 hormesis 时对半参数模型进行平均。我们通过模拟展示了平均参数模型和平均半参数模型的不同特征。我们将所提出的方法应用于实际数据，并表明平均半参数模型的值比平均参数方法的值更可信。当真实的剂量反应关系不遵循参数假设时，所提出的方法可以是一种替代的稳健方法。
