An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts

Abstract

Multivariate quantile contours are useful in numerous applications and have been studied in different contexts. However, no easy solutions exist when dynamic and conditional quantile contours are needed without strong distributional assumptions. In this article we propose a new form of bivariate quantile contours and a two-stage estimation procedure to take time effect into account. The proposed procedure relies on quantile regression for longitudinal data and is flexible to include potentially important covariates as necessary. In addition, we propose a visual model assessment tool and discuss a practical guideline for model selection. The performance of the proposed methodology is demonstrated by a simulation study, as well as an application to joint height–weight screening of young children in the United States. We construct bivariate growth charts by a nested sequence of age-dependent and covariate-varying quantile contours of height and weight, and use it to locate an individual subject's percentile rank with respect to a reference population. Our work shows that the proposed method is valuable for pediatric growth monitoring and provides more informative readings than the conventional approach based on univariate growth charts.