clusterMLD: An Efficient Hierarchical Clustering Method for Multivariate Longitudinal Data

Longitudinal data clustering is challenging because the grouping has to account for the similarity of individual trajectories in the presence of sparse and irregular times of observation. This paper puts forward a hierarchical agglomerative clustering method based on a dissimilarity metric that quantifies the cost of merging two distinct groups of curves, which are depicted by B-splines for the repeatedly measured data. Extensive simulations show that the proposed method has superior performance in determining the number of clusters, classifying individuals into the correct clusters, and in computational efficiency. Importantly, the method is not only suitable for clustering multivariate longitudinal data with sparse and irregular measurements but also for intensely measured functional data. Towards this end, we provide an R package for the implementation of such analyses. To illustrate the use of the proposed clustering method, two large clinical data sets from real-world clinical studies are analyzed.

Multivariate functional partial least squares for classification using longitudinal data

The use of statistical methods to predict outcomes using high dimensional datasets in medicine is becoming increasingly popular for forecasting and monitoring patient health. Our work is motivated by a longitudinal dataset containing 1H NMR spectra of metabolites of 18 patients undergoing a kidney transplant alongside their graft outcomes that fall into one of three categories: acute rejection, delayed graft function and primary function. We proposed a functional partial least squares (FPLS) model that extends existing PLS methods for the analysis of longitudinally measured scalar omics datasets to the case of longitudinally measured functional datasets. We designed an iterative algorithm to link multiple time points, and then applied our proposed method to analyse the data from kidney transplant patients. Finally, we compared the AUC of our method to the AUC of the univariate methods which only use the information of one time-point information. It appeared that our method outperforms the existing methods. A simulation study was performed to mimic the kidney transplant dataset but with a larger sample size and different scenarios performed to evaluate the performance of the new method in larger datasets. We consider scenarios which vary in the difficulty to distinguish the two groups. It appeared that the three time-points model performs better than any of the individual models with average AUCs of 0.909 and 0.811 respectively.

Region of Interest Selection for Functional Features

Feature selection is a critical component in supervised learning to improve model performance. Searching for the optimal feature candidates can be NP-hard. With limited data, cross-validation is widely used to alleviate overfitting, which unfortunately suffers from high computational cost. We propose a highly innovative strategy in feature selection to reduce the overfitting risk but without cross-validation. Our method selects the optimal sub-interval, i.e., region of interest (ROI), of a functional feature for functional linear regression where the response is a scalar and the predictor is a function. For each candidate sub-interval, we evaluate the overfitting risk by calculating a necessary sample size to achieve a pre-specified statistical power. Combining with a model accuracy measure, we rank these sub-intervals and select the ROI. The proposed method has been compared with other state-of-the-art feature selection methods on several reference datasets. The results show that our proposed method achieves an excellent performance in prediction accuracy and reduces computational cost substantially.

Modeling motor learning using heteroskedastic functional principal components analysis

We propose a novel method for estimating population-level and subject-specific effects of covariates on the variability of functional data. We extend the functional principal components analysis framework by modeling the variance of principal component scores as a function of covariates and subject-specific random effects. In a setting where principal components are largely invariant across subjects and covariate values, modeling the variance of these scores provides a flexible and interpretable way to explore factors that affect the variability of functional data. Our work is motivated by a novel dataset from an experiment assessing upper extremity motor control, and quantifies the reduction in motion variance associated with skill learning.

Modeling Criminal Careers as Departures from a Unimodal Population Age-Crime Curve: The Case of Marijuana Use

A major aim of longitudinal analyses of life course data is to describe the within- and between-individual variability in a behavioral outcome, such as crime. Statistical analyses of such data typically draw on mixture and mixed-effects growth models. In this work, we present a functional analytic point of view and develop an alternative method that models individual crime trajectories as departures from a population age-crime curve. Drawing on empirical and theoretical claims in criminology, we assume a unimodal population age-crime curve and allow individual expected crime trajectories to differ by their levels of offending and patterns of temporal misalignment. We extend Bayesian hierarchical curve registration methods to accommodate count data and to incorporate influence of baseline covariates on individual behavioral trajectories. Analyzing self-reported counts of yearly marijuana use from the Denver Youth Survey, we examine the influence of race and gender categories on differences in levels and timing of marijuana smoking. We find that our approach offers a flexible model for longitudinal crime trajectories and allows for a rich array of inferences of interest to criminologists and drug abuse researchers.