The traditional goals of quantitative analytics cherish simple, transparent models to generate explainable insights. Large-scale data acquisition, enabled for instance by brain scanning and genomic profiling with microarray-type techniques, has prompted a wave of statistical inventions and innovative applications. Modern analysis approaches 1) tame large variable arrays capitalizing on regularization and dimensionality-reduction strategies, 2) are increasingly backed up by empirical model validations rather than justified by mathematical proofs, 3) will compare against and build on open data and consortium repositories, as well as 4) often embrace more elaborate, less interpretable models in order to maximize prediction accuracy. Here we review these trends in learning from "big data" and illustrate examples from imaging neuroscience.

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Towards Algorithmic Analytics for Large-scale Datasets.

Improved estimation of subject-level functional connectivity using full and partial correlation with empirical Bayes shrinkage.

In recent years, longitudinal neuroimaging study has become increasingly popular in neuroscience research to investigate disease-related changes in brain functions. In current neuroscience literature, one of the most commonly used tools to extract and characterize brain functional networks is independent component analysis (ICA). However, existing ICA methods are not suited for modelling repeatedly measured imaging data. In this paper, we propose a novel longitudinal independent component model (L-ICA) which provides a formal modeling framework for extending ICA to longitudinal studies. By incorporating subject-specific random effects and visit-specific covariate effects, L-ICA is able to provide more accurate estimates of changes in brain functional networks on both the population- and individual-level, borrow information across repeated scans within the same subject to increase statistical power in detecting covariate effects on the networks, and allow for model-based prediction for brain networks changes caused by disease progression, treatment or neurodevelopment. We develop a fully traceable exact EM algorithm to obtain maximum likelihood estimates of L-ICA. We further develop a subspace-based approximate EM algorithm which greatly reduce the computation time while still retaining high accuracy. Moreover, we present a statistical testing procedure for examining covariate effects on brain network changes. Simulation results demonstrate the advantages of our proposed methods. We apply L-ICA to ADNI2 study to investigate changes in brain functional networks in Alzheimer disease. Results from the L-ICA provide biologically insightful findings which are not revealed using existing methods.

A hierarchical independent component analysis model for longitudinal Neuroimaging studies

A hierarchical independent component analysis model for longitudinal neuroimaging studies.

Previous research has shown that individuals with greater cognitive abilities display a greater speed of higher-order cognitive processing. These results suggest that speeded neural information processing may facilitate evidence accumulation during decision making and memory updating and thus yield advantages in general cognitive abilities. We used a hierarchical Bayesian cognitive modeling approach to test the hypothesis that individual differences in the velocity of evidence accumulation mediate the relationship between neural processing speed and cognitive abilities. We found that a higher neural speed predicted both the velocity of evidence accumulation across behavioral tasks and cognitive ability test scores. However, only a negligible part of the association between neural processing speed and cognitive abilities was mediated by individual differences in the velocity of evidence accumulation. The model demonstrated impressive forecasting abilities by predicting 36% of individual variation in cognitive ability test scores in an entirely new sample solely based on their electrophysiological and behavioral data. Our results suggest that individual differences in neural processing speed might affect a plethora of higher-order cognitive processes, that only in concert explain the large association between neural processing speed and cognitive abilities, instead of the effect being entirely explained by differences in evidence accumulation speeds.

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Individual Differences in Cortical Processing Speed Predict Cognitive Abilities: a Model-Based Cognitive Neuroscience Account

Predicting individual brain functional connectivity using a Bayesian hierarchical model.

A New Functional Representation of Broad Sense Agreement.

Summary
Assessing agreement is often of interest in biomedical and clinical research when measurements are obtained on the same subjects by different raters or methods. Most classical agreement methods have been focused on global summary statistics, which cannot be used to describe various local agreement patterns. The objective of this work is to study the local agreement pattern between two continuous measurements subject to censoring. In this article, we propose a new agreement measure based on bivariate hazard functions to characterize the local agreement pattern between two correlated survival outcomes. The proposed measure naturally accommodates censored observations, fully captures the dependence structure between bivariate survival times and provides detailed information on how the strength of agreement evolves over time. We develop a nonparametric estimation method for the proposed local agreement pattern measure and study theoretical properties including strong consistency and asymptotical normality. We then evaluate the performance of the estimator through simulation studies and illustrate the method using a prostate cancer data example.

A local agreement pattern measure based on hazard functions for survival outcomes.

The concept of broad sense agreement (BSA) has recently been proposed for studying the relationship between a continuous measurement and an ordinal measurement. They developed a nonparametric procedure for estimating the BSA index, which is only applicable to completely observed data. In this work, we consider the problem of evaluating BSA index when the continuous measurement is subject to censoring. We propose a nonparametric estimation method built upon a derivation of a new functional representation of the BSA index, which allows for accommodating censoring by plugging in the nonparametric survival function estimators. We establish the consistency and asymptotic normality for the proposed BSA estimator. We also investigate an alternative approach based on the strategy of multiple imputation, which is shown to have better empirical performance with small sample sizes than the plug-in method. Extensive simulation studies are conducted to evaluate our proposals. We illustrate our methods via an application to a Surgical Intensive Care Unit study.

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Tian Dai

Papers

Predicting individual brain functional connectivity using a Bayesian hierarchical model.

A New Functional Representation of Broad Sense Agreement.

A local agreement pattern measure based on hazard functions for survival outcomes.

Nonparametric estimation of broad sense agreement between ordinal and censored continuous outcomes.