An additive Gaussian process regression model for interpretable non-parametric analysis of longitudinal data

Biomedical research typically involves longitudinal study designs where samples from individuals are measured repeatedly over time and the goal is to identify risk factors (covariates) that are associated with an outcome value. General linear mixed effect models are the standard workhorse for statistical analysis of longitudinal data. However, analysis of longitudinal data can be complicated for reasons such as difficulties in modelling correlated outcome values, functional (time-varying) covariates, nonlinear and non-stationary effects, and model inference. We present LonGP, an additive Gaussian process regression model that is specifically designed for statistical analysis of longitudinal data, which solves these commonly faced challenges. LonGP can model time-varying random effects and non-stationary signals, incorporate multiple kernel learning, and provide interpretable results for the effects of individual covariates and their interactions. We demonstrate LonGP’s performance and accuracy by analysing various simulated and real longitudinal -omics datasets

Advanced Methods for Discovering Genetic Markers Associated with High Dimensional Imaging Data

Imaging genetic studies have been widely applied to discover genetic factors of inherited neuropsychiatric diseases. Despite the notable contribution of genome-wide association studies (GWAS) in neuroimaging research, it has always been difficult to efficiently perform association analysis on imaging phenotypes. There are several challenges arising from this topic, such as the large dimensionality of imaging data and genetic data, the potential spatial dependency of imaging phenotypes and the computational burden of the GWAS problem. All the aforementioned issues motivate us to investigate new statistical methods in neuroimaging genetic analysis. In the first project, we develop a hierarchical functional principal regression model (HFPRM) to simultaneously study diffusion tensor bundle statistics on multiple fiber tracts. Theoretically, the asymptotic distribution of the global test statistic on the common factors has been studied. Simulations are conducted to evaluate the finite sample performance of HFPRM. Finally, we apply our method to a GWAS of a neonate population to explore important genetic architecture in early human brain development. In the second project, we consider an association test between functional data acquired on a single curve and scalar variables in a varying coefficient model. We propose a functional projection regression model and an associated global test statistic to aggregate weak signals across the domain of functional data. Theoretically, we examine the asymptotic distribution of the global test statistic and provide a strategy to adaptively select the tuning parameter. Simulation experiments show that the proposed test outperforms existing state-of-the-art methods in functional statistical inference. We also apply the proposed method to a GWAS in the UK Biobank dataset. In the third project, we introduce an adaptive projection regression model (APRM) to perform statistical inference on high dimensional imaging responses in the presence of high correlations. Dimension reduction of the phenotypes is achieved through a linear projection regression model. We also implement an adaptive inference procedure to detect signals at multiple levels. Numerical simulations demonstrate that APRM outperforms many state-of-the-art methods in high dimensional inference. Finally, we apply APRM to a GWAS of volumetric data on 93 regions of interest in the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset.Doctor of Philosoph