A review of practical statistical methods used in epidemiological studies to estimate the health effects of multi-pollutant mixture

Environmental risk factors have been implicated in adverse health effects. Previous epidemiological studies on environmental risk factors mainly analyzed the impact of single pollutant exposure on health, while in fact, humans are constantly exposed to a complex mixture consisted of multiple pollutants/chemicals. In recent years, environmental epidemiologists have sought to assess adverse health effects of exposure to multi-pollutant mixtures based on the diversity of real-world environmental pollutants. However, the statistical challenges are considerable, for instance, multicollinearity and interaction among components of the mixture complicate the statistical analysis. There is currently no consensus on appropriate statistical methods. Here we summarized the practical statistical methods used in environmental epidemiology to estimate health effects of exposure to multi-pollutant mixture, such as Bayesian kernel machine regression (BKMR), weighted quantile sum (WQS) regressions, shrinkage methods (least absolute shrinkage and selection operator, elastic network model, adaptive elastic-net model, and principal component analysis), environment-wide association study (EWAS), etc. We sought to review these statistical methods and determine the application conditions, strengths, weaknesses, and result interpretability of each method, providing crucial insight and assistance for addressing epidemiological statistical issues regarding health effects from multi-pollutant mixture.