A systematic comparison of statistical methods to detect interactions in exposome-health associations

Abstract

Background: There is growing interest in examining the simultaneous effects of multiple exposures and, more generally, the effects of mixtures of exposures, as part of the exposome concept (being defined as the totality of human environmental exposures from conception onwards). Uncovering such combined effects is challenging owing to the large number of exposures, several of them being highly correlated. We performed a simulation study in an exposome context to compare the performance of several statistical methods that have been proposed to detect statistical interactions.

Methods: Simulations were based on an exposome including 237 exposures with a realistic correlation structure. We considered several statistical regression-based methods, including two-step Environment-Wide Association Study (EWAS₂), the Deletion/Substitution/Addition (DSA) algorithm, the Least Absolute Shrinkage and Selection Operator (LASSO), Group-Lasso INTERaction-NET (GLINTERNET), a three-step method based on regression trees and finally Boosted Regression Trees (BRT). We assessed the performance of each method in terms of model size, predictive ability, sensitivity and false discovery rate.

Results: GLINTERNET and DSA had better overall performance than the other methods, with GLINTERNET having better properties in terms of selecting the true predictors (sensitivity) and of predictive ability, while DSA had a lower number of false positives. In terms of ability to capture interaction terms, GLINTERNET and DSA had again the best performances, with the same trade-off between sensitivity and false discovery proportion. When GLINTERNET and DSA failed to select an exposure truly associated with the outcome, they tended to select a highly correlated one. When interactions were not present in the data, using variable selection methods that allowed for interactions had only slight costs in performance compared to methods that only searched for main effects.

Conclusions: GLINTERNET and DSA provided better performance in detecting two-way interactions, compared to other existing methods.

Keywords: Exposome; Interactions; Variable selection.

Fig. 1

Performance of the compared methods in terms of number of variables in the fitted model and predictive ability. a Relative number of variables (RNV), in log scale, and b Relative out-of-sample R ² ($R_{\text{rel}}^2$). Both measures are relative such that the true model corresponds to the value 1. Mean values based on 100 simulations. The vertical line separates scenarios according to the pairwise correlation between the true predictors as “Mixed” (any exposure can be selected as a true predictor regardless of correlation), or “High” (exposures are chosen so that all their pairwise correlations are above 0.6). Scenarios 1, 2 and 3 involve no interactions, one two-way interaction, and two two-way interactions, respectively

Fig. 2

Performance of the compared methods in terms of sensitivity. a Sensitivity for variables (Sensvar), b Alternative sensitivity (AltSens), and c Sensitivity for interactions terms (Sens₂). Mean values based on 100 simulations. The vertical line separates scenarios according to the pairwise correlation between the true predictors as “Mixed” (any exposure can be selected as a true predictor regardless of correlation), or “High” (exposures are chosen so that all their pairwise correlations are above 0.6). Scenarios 1, 2 and 3 involve no interactions, one two-way interaction, and two two-way interactions, respectively

Fig. 3

Performance of the compared methods in terms of specificity. a False discovery proportion for variables (FDPvar), b Alternative false discovery proportion (AltFDP), and c False discovery proportion for interaction terms (FDP₂). Mean values based on 100 simulations. The vertical line separates scenarios according to the pairwise correlation between the true predictors as “Mixed” (any exposure can be selected as a true predictor regardless of correlation), or “High” (exposures are chosen so that all their pairwise correlations are above 0.6). Scenarios 1, 2 and 3 involve no interactions, one two-way interaction, and two two-way interactions, respectively