Chemical mixtures modeling

在对化学品接触与健康结果之间的关联进行建模时，通常希望能够估计所考虑的化学品浓度的最佳组合，因为这种组合在疾病检测和预测方面提供了最佳能力。然而，文献中的标准方法仅限于几种暴露。陈博士计划在最佳暴露组合的背景下探索稀疏估计。特别是，他将研究在最优组合估计中使用惩罚最大似然的可能性。从本质上讲，这相当于从可用于最优组合的大量潜在风险开始，将影响较小的风险缩减为零系数，并将其从最终的最优组合中剔除。陈博士还将探讨使用秩似然的可能性，因为它允许对浓度进行更灵活的分布假设。浓度的其他特征，如检测限和过零，可以在同一框架内考虑。

In modeling association between chemical exposures and health outcomes, it is often desired that an optimal combination of the chemical concentrations under consideration can be estimated, in the sense that this combination provides the best power in disease detection and prediction. However, standard approaches in the literature have been limited to several exposures. Dr. Chen plans to explore sparse estimation in the context of optimal exposure combinations. In particular, he will investigate the possibility of using penalized maximum likelihood in optimal combination estimation. In essence, this amounts to starting with a large number of potential exposures that can be used in the optimal combination, shrinking those with small effects to have zero coefficients, and dropping them out of the final optimal combination. Dr. Chen will also explore the possibility of using rank likelihood, as it allows more flexible distributional assumptions of the concentrations. Other features of the concentrations, such as limit of detection and excessive zeros, can be considered in the same framework. Although penalized maximal likelihood approaches are useful in simultaneous parameters estimation and model selection, it is possible that concentrations with nonzero associations with the health outcome can still be numerous and have small coefficients even after regularization. These small coefficients are difficult to estimate and can create computational stability problems in estimation. For these reasons, it is of interest to explore simultaneous regularization and smoothing in these analyses. The regularization part will be carried out using penalized maximum likelihood so that those with very small coefficients will be dropped out of the final models; the smoothing will be achieved through hierarchical modeling using appropriate correlation structure, similar to ideas used in spatial modeling.