Chemical mixtures modeling

在对化学品暴露和健康结果之间的关联进行建模时，通常希望能够估计出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中提供了最佳的能力。然而，文献中的标准方法仅限于几次曝光。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。本质上，这相当于从可用于最佳组合的大量潜在敞口开始，将那些影响较小的潜在敞口缩减至零系数，并将它们从最终的最佳组合中剔除。陈博士还将探索使用等级似然法的可能性，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，如检测极限和过多的零点，可以在相同的框架内考虑。 虽然惩罚最大似然法在同时进行参数估计和模型选择时很有用，但与健康结果非零相关的浓度可能仍然很多，即使在正则化之后，系数也很小。这些小系数很难估计，并且会在估计中造成计算稳定性问题。由于这些原因，在这些分析中探索同时正则化和平滑是有意义的。正则化部分将使用惩罚最大似然法进行，以便将系数非常小的那些从最终模型中剔除；平滑将通过使用适当的相关结构的分层建模实现，类似于空间建模中使用的想法。

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.