Department of Population Health, NYU Langone Health, 180 Madison Avenue, New York, NY, 10016, USA.
Department of Pediatrics, NYU Langone Health, New York, NY, USA.
Environ Health. 2020 Sep 11;19(1):96. doi: 10.1186/s12940-020-00644-4.
Statistical methods to study the joint effects of environmental factors are of great importance to understand the impact of correlated exposures that may act synergistically or antagonistically on health outcomes. This study proposes a family of statistical models under a unified partial-linear single-index (PLSI) modeling framework, to assess the joint effects of environmental factors for continuous, categorical, time-to-event, and longitudinal outcomes. All PLSI models consist of a linear combination of exposures into a single index for practical interpretability of relative direction and importance, and a nonparametric link function for modeling flexibility.
We presented PLSI linear regression and PLSI quantile regression for continuous outcome, PLSI generalized linear regression for categorical outcome, PLSI proportional hazards model for time-to-event outcome, and PLSI mixed-effects model for longitudinal outcome. These models were demonstrated using a dataset of 800 subjects from NHANES 2003-2004 survey including 8 environmental factors. Serum triglyceride concentration was analyzed as a continuous outcome and then dichotomized as a binary outcome. Simulations were conducted to demonstrate the PLSI proportional hazards model and PLSI mixed-effects model. The performance of PLSI models was compared with their counterpart parametric models.
PLSI linear, quantile, and logistic regressions showed similar results that the 8 environmental factors had both positive and negative associations with triglycerides, with a-Tocopherol having the most positive and trans-b-carotene having the most negative association. For the time-to-event and longitudinal settings, simulations showed that PLSI models could correctly identify directions and relative importance for the 8 environmental factors. Compared with parametric models, PLSI models got similar results when the link function was close to linear, but clearly outperformed in simulations with nonlinear effects.
We presented a unified family of PLSI models to assess the joint effects of exposures on four commonly-used types of outcomes in environmental research, and demonstrated their modeling flexibility and effectiveness, especially for studying environmental factors with mixed directional effects and/or nonlinear effects. Our study has expanded the analytical toolbox for investigating the complex effects of environmental factors. A practical contribution also included a coherent algorithm for all proposed PLSI models with R codes available.
研究环境因素联合效应的统计方法对于理解相关暴露可能协同或拮抗作用于健康结果的影响非常重要。本研究在统一的偏线性单指标(PLSI)建模框架下提出了一组统计模型,以评估环境因素对连续、分类、生存和纵向结局的联合效应。所有 PLSI 模型都由暴露因素的线性组合构成单一指标,以便于解释相对方向和重要性,同时采用非参数链接函数来实现建模的灵活性。
我们提出了 PLSI 线性回归和 PLSI 分位数回归用于连续结局,PLSI 广义线性回归用于分类结局,PLSI 比例风险模型用于生存结局,以及 PLSI 混合效应模型用于纵向结局。使用来自 NHANES 2003-2004 调查的 800 名受试者数据集,包括 8 个环境因素,对这些模型进行了演示。血清甘油三酯浓度被分析为连续结局,然后被二分类为二进制结局。进行了模拟来演示 PLSI 比例风险模型和 PLSI 混合效应模型。将 PLSI 模型的性能与它们的参数模型进行了比较。
PLSI 线性、分位数和逻辑回归显示出相似的结果,即 8 个环境因素与甘油三酯既有正相关又有负相关,其中 α-生育酚的相关性最强,反式-β-胡萝卜素的相关性最强。对于生存和纵向设置,模拟表明 PLSI 模型可以正确识别 8 个环境因素的方向和相对重要性。与参数模型相比,当链接函数接近线性时,PLSI 模型可以得到相似的结果,但在具有非线性效应的模拟中,明显表现更好。
我们提出了一个统一的 PLSI 模型家族,用于评估环境研究中四种常用类型结局的暴露联合效应,并展示了它们的建模灵活性和有效性,特别是对于研究具有混合方向效应和/或非线性效应的环境因素。我们的研究扩展了用于研究环境因素复杂效应的分析工具包。一个实际的贡献还包括了一套适用于所有提出的 PLSI 模型的连贯算法,并提供了 R 代码。