Joint regression analysis of marginal quantile and quantile association: application to longitudinal body mass index in adolescents

The paper proposes joint regression analysis of the marginal quantiles of longitudinal or clustered outcomes as well as the association between pairs of the outcomes, with the association measuring the tendency of concordance between pairs of the outcomes with respect to their marginal quantiles. The motivation comes from a longitudinal adolescent body mass index (BMI) study where both the marginal quantile regression of BMI and the tendency that an adolescent with BMI higher than the 75th population quantile of the BMI at some age would still have BMI higher than the 75th population quantile of the BMI at some later age are of interest. The new procedure generalizes the alternative logistic regressions' to marginal quantile regression and extends the quantile association regression' to general analysis of longitudinal and clustered data. A novel bivariate induced smoothing technique is proposed for stable and efficient computation. The application to the longitudinal adolescent BMI study reveals the practical utility of our proposal.