title: Flexible quantile regression and Bayesian quantile modelling for longitudinal child growth data
Creators: name: Channgam, Taweesak
Publisher: name: University of Glasgow
Year: 2024

description: Numerous studies have been conducted to understand the comprehensive mechanisms of child growth and development. Among these, the longitudinal study is a key approach that can provide a complete characterisation of these aspects. However, the greater benefits of this approach often come with increased complexities inherent in the data from such studies. These complexities include non-linear trajectories, within-subject correlation, heterogeneity of individual baseline and dynamic growth characteristics, and autocorrelation within individuals. Moreover, given the diverse range of growth patterns in children, it is particularly relevant to evaluate risk factors that exhibit significant associations with growth measurements across different locations in the distribution, rather than focusing solely on the central location, such as the mean or median. This thesis aims to address these complexities by examining longitudinal child growth data (LCGD) through appropriate statistical models. In order to characterise LCGD and describe the entire distribution of growth, the additive quantile mixed model (AQMM) has been reviewed. This approach has been incorporated into both the mixed-effects model framework and the additive model, enabling the analysis of longitudinal data. Simulation studies conducted within this thesis assess the performance of AQMM under various experimental designs in the context of LCGD. Overall, AQMM performed well in predicting simulated data. Subsequently, the LCGD in Scotland was used to construct reference growth curves and identify risk factors associated with physical growth measurements. However, AQMM lacks a method for determining appropriate random effects to capture individual variability.

To address this limitation, a Bayesian variable selection method within quantile mixed models (QMMs) is proposed. This novel methodology combines several key components: the Bayesian sparse group LASSO method with spike and slab priors, a likelihood function based on the scale mixture representation of the asymmetric Laplace (AL) distribution, and the utilisation of mixed models based on a decomposition for the covariance matrix of random effects. By incorporating these elements, the methodology establishes a comprehensive framework to tackle challenges associated with the selection and estimation of fixed and random effects in the context of QMMs. To evaluate the performance of the novel method, simulation experiments are conducted. Furthermore, the proposed approach is applied to the analysis of LCGD in Scotland, thus providing practical insights into its real-world applicability. Overall, the novel model demonstrates strong performance in variable selection with simulated data. When applied to LCGD in Scotland, the selected risk factors were consistent across both lower and upper quantiles of physical growth measurements in school-age children and young people in primary or secondary education. The selection of both random intercepts and random slopes suggests variability in individual linear trends.