Scaled marginal models for multiple continuous outcomes

In studies that involve multivariate outcomes it is often of interest to test for a common exposure effect. For example, our research is motivated by a study of neurocognitive performance in a cohort of HIV-infected women. The goal is to determine whether highly active antiretroviral therapy affects different aspects of neurocognitive functioning to the same degree and if so, to test for the treatment effect using a more powerful one-degree-of-freedom global test. Since multivariate continuous outcomes are likely to be measured on different scales, such a common exposure effect has not been well defined. We propose the use of a scaled marginal model for testing and estimating this global effect when the outcomes are all continuous. A key feature of the model is that the effect of exposure is represented by a common effect size and hence has a well-understood, practical interpretation. Estimating equations are proposed to estimate the regression coefficients and the outcome-specific scale parameters, where the correct specification of the within-subject correlation is not required. These estimating equations can be solved by repeatedly calling standard generalized estimating equations software such as SAS PROC GENMOD. To test whether the assumption of a common exposure effect is reasonable, we propose the use of an estimating-equation-based score-type test. We study the asymptotic efficiency loss of the proposed estimators, and show that they generally have high efficiency compared to the maximum likelihood estimators. The proposed method is applied to the HIV data.