Factor-assisted learning of ultrahigh-dimensional covariates with distributed functional and scalar mixtures with applications to the Avon Longitudinal Study of Parents and Children

Atherosclerosis is a chronic, multifaceted disease that affects multiple arterial systems. Its progression is primarily driven by low-density lipoprotein (LDL) cholesterol accumulation, which promotes localized arterial lesion formation. These lesions can lead to severe complications, including ischemic heart disease (IHD) and stroke. Both genetic factors, particularly single nucleotide polymorphisms (SNPs), and age-related changes in body composition significantly influence LDL levels, generating extensive ultrahigh-dimensional covariates from functional and scalar mixtures (UDFSM), which may be stored at different sites due to the massive amount of data and the different data representations. To analyze the impact of genetic and physiological variables on LDL levels, we first separately extract features from ultrahigh-dimensional functional and scalar covariates in an unsupervised manner. Then we propose a novel regression model that incorporates these features, which may be correlated due to the underlying correlations in the ultrahigh-dimensional covariates comprising both functional and scalar mixtures. Our methodology employs a factor regression model with an additive multiple-index component to sufficiently and effectively capture latent feature-response variable relationships. We enhance model interpretability and account for covariate correlations by imposing column sparsity and low-rank structures on the regression coefficients matrix, thereby incorporating structural information to improve efficiency and robustness. This distribution-agnostic approach to the response variable ensures greater flexibility and versatility. For model fitting we develop a sieve likelihood-based framework that leverages the problem’s inherent structure to provide efficient and robust estimates. We apply our method to the Avon Longitudinal Study of Parents and Children (ALSPAC) dataset, achieving high prediction accuracy for LDL levels and identifying significant SNPs and anthropometric measures affecting LDL. We specifically examine how various anthropometric measures influence LDL levels over ages. We further extend our analysis to identify key parental and individual characteristics that influence adult body mass index (BMI).