A joint marginal-conditional model for multivariate longitudinal data

Multivariate longitudinal data frequently arise in biomedical applications; however, their analyses are often performed one outcome at a time, or jointly using existing software in an ad hoc fashion. A main challenge in the proper analysis of such data is the fact that the different outcomes are measured on different unknown scales. Methodology for handling the scale problem has been previously proposed for cross-sectional data, and here we extend it to the longitudinal setting. We consider modeling the longitudinal data using random effects, while leaving the joint distribution of the multiple outcomes unspecified. We propose an estimating equation together with an expectation-maximization-type (expectation-substitution) algorithm. The consistency and the asymptotic distribution of the parameter estimates are established. The method is evaluated using extensive simulations and applied to a longitudinal nutrition data set from a large dietary intervention trial on breast cancer survivors, the Women's Healthy Eating and Living Study.