ABSTRACT
In the third-variable analysis, we often have to deal with multiple exposures or multivariate outcomes. For example, when the exposure is a categorical variable with K levels, we can create K-1 dummy variables as the exposures. In such situations, we need to make inferences on the third-variable effects for each pair of the exposure-outcome relationship, while taking into account of the covariance among the multi-variables. We provide the algorithms for the multivariate method in third-variable effect analysis and give examples on how to make inferences and interpret results. In addition, a new method to create confidence intervals of multivariate third-variable effects that controls for the overall Type-I error is proposed in the chapter. With the method, multiple comparisons are considered without inflating the familywise Type-I error rate. Simulations are provided to compare the new method with traditional methods. The multivariate third-variable analysis is then used on a real data analysis to explore the racial and ethnic disparities in BMI and overweight rates.
