We selected environmental pollutants for each lipid outcome with adjustment for base covariates and outcome-specific micronutrients. Specifically, for subject i (i = 1, …, N), let Yi represent one given phenotype, Ei be one given environmental pollutant, and Zi (k×1) be the vector of base covariates and micronutrients. The fitted single-pollutant model was(1)where . We adopted a two-stage analyses strategy following Skol et al. [36] using the model in (1). In stage 1, we analyzed the single-pollutant model for every pollutant using stage 1 samples and calculated the standard Wald test statistic z 1 corresponding to . In stage 2, we only included pollutants with |z 1| > C 1 (pre-defined significance threshold). For each of these chosen pollutants, we repeated the same regression analysis using stage 2 samples, and calculated Wald test statistics z 2 corresponding to . Finally, we conducted joint analysis to combine z1 and z2 and get a new statistic that allows for between-stage heterogeneity [36],(2)where was the proportion of samples in stage 1 (0.7 in our case). zjoint was compared with a significance threshold Cjoint.
