A Multivariate Multiple Third-Variable Effect Analysis with an Application to Explore Racial and Ethnic Disparities in Obesity.

Third-Variable effect refers to the intervening effect from a third variable (called mediators or confounders) to the observed relationship between an exposure and an outcome. The general multiple third-variable effect analysis method (TVEA) allows consideration of multiple mediators/confounders (MC) simultaneously and the use of linear and non-linear predictive models for estimating MC effects. Previous studies have found that compared with non-Hispanic White population, Blacks and Hispanic Whites suffered disproportionally more with obesity and related chronic diseases. In this paper, we extend the general TVEA to deal with multivariate/multicategorical predictors and multivariate response variables. We designed algorithms and an R package for this extension and applied MMA on the NHANES data to identify MCs and quantify the indirect effect of each MC in explaining both racial and ethnic disparities in obesity and the body mass index (BMI) simultaneously. We considered a number of socio-demographic variables, individual factors, and environmental variables as potential MCs and found that some of the ethnic/racial differences in obesity and BMI were explained by the included variables.