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Title: A weighted quantile sum regression with penalized weights and two indices Authors:  Stefano Renzetti - Università degli Studi di Brescia (Italy) [presenting]
Chris Gennings - Icahn School of Medicine at Mount Sinai (United States)
Stefano Calza - Universita degli Studi di Brescia (Italy)
Abstract: An extension of Weighted Quantile Sum (WQS) regression is proposed which estimates the double effect of a mixture of chemicals on a health outcome in the same model through the inclusion of two indices, one in the positive and one in the negative direction, with the introduction of a penalization term. To evaluate the performance of this new model in terms of the estimation of the regression parameters and the weights we performed both a simulation study and a real case study where we assessed the effects of nutrients on obesity among adults. The results showed good performance of the method in estimating both the regression parameter and the weights associated with the single elements when the penalized term was set equal to the magnitude of the AIC of the unpenalized WQS regression. The two indices further helped to give a better estimate of the parameters (Positive direction Median Error (PME): 0.017; Negative direction Median Error (NME): -0.023) compared to the standard WQS (PME: -0.141; NME: 0.078). In the case study, WQS with two indices was able to find a significant effect of nutrients on obesity in both directions identifying caffeine and magnesium as the main actors in the positive and negative association respectively. We introduce an extension of the WQS regression that showed how to improve the accuracy of the parameter estimates when considering a mixture of elements that can have both a protective and a harmful effect on the outcome