Theoretical Development of Functional Data Analysis Methods for Growth Curve Modelling in Nigerian Paediatric Cohort Studies

Paediatric growth trajectories measured on irregular time grids in Nigerian cohort studies are functional data objects whose statistical analysis requires functional data analysis methods that appropriately account for the smoothness structure of growth curves and the correlation between observations on the same child. This dissertation develops theoretical extensions of functional data analysis (FDA) methods for growth curve modelling in Nigerian paediatric cohort studies, addressing data characteristics specific to resource-limited cohort designs. New theoretical results on the consistency of mean function and covariance surface estimators under sparse and irregularly spaced observation designs representative of Nigerian cohort data collection are derived. Functional principal component analysis under sparse observation using PACE (principal analysis by conditional expectation) is extended to accommodate informative dropout related to health outcomes, with theoretical bias correction formulas derived. A functional linear mixed effects model for growth curves with time-varying nutritional and clinical covariates is introduced with identifiability conditions established. Applications covered longitudinal weight-for-age Z-score trajectories for 840 children aged 0 to 24 months in the Kano CMAM follow-up cohort and height-for-age trajectories from the Plateau State IYCF intervention trial. Functional PCA identified three dominant growth trajectory modes explaining 78 percent of functional variance. The time-varying covariate model showed that exclusive breastfeeding duration effects on growth peaked at age 4 to 6 months by functional regression coefficient curves, results invisible to fixed-time-point analyses. The dissertation advances FDA methodology for sparse paediatric data in African research settings. Keywords: functional data analysis, growth curve modelling, paediatric cohort, Nigeria, principal component analysis