| The reference growth charts are widely used to screen the measurements from an individual subject in the context of population values. The conventional reference growth charts are generated from cross-sectional data and rely on an implicit assumption of normality. More informative screening of individual subjects should be conditioned on their prior growth paths and other relevant covariates. In this thesis, we propose to construct conditional growth charts based on two longitudinal quantile regression models, one parametric and one semi-parametric. Both models incorporate individual prior growth and other covariates without the assumption of normality. The semiparametric model is global in nature and accommodates varying measurement time intervals. Under appropriate Conditions, both models provide consistent estimates for the conditional quantiles. The rank score test, an important inference tool in quantile regression, is extended to testing the effects of covariates in a semiparametric longitudinal model. The functionality of the proposed models is demonstrated with the Finnish growth data, which recorded the heights and weights of 2305 Finnish subjects from birth to 20 years of age. |
