Tree representations of brain structural connectivity via persistent homology

The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the structural connectome varies across individuals in relation to their traits, ranging from age and gender to neuropsychiatric outcomes. After applying tractography to dMRI to get white matter fiber bundles, a key question is how to represent the brain connectome to facilitate statistical analyses relating connectomes to traits. The current standard divides the brain into regions of interest (ROIs), and then relies on an adjacency matrix (AM) representation. Each cell in the AM is a measure of connectivity, e.g., number of fiber curves, between a pair of ROIs. Although the AM representation is intuitive, a disadvantage is the high-dimensionality due to the large number of cells in the matrix. This article proposes a simpler tree representation of the brain connectome, which is motivated by ideas in computational topology and takes topological and biological information on the cortical surface into consideration. We demonstrate that our tree representation preserves useful information and interpretability, while reducing dimensionality to improve statistical and computational efficiency. Applications to data from the Human Connectome Project (HCP) are considered and code is provided for reproducing our analyses.

Initial refinement of data from video-based single-cell tracking

Background

Video recording of cells offers a straightforward way to gain valuable information from their response to treatments. An indispensable step in obtaining such information involves tracking individual cells from the recorded data. A subsequent step is reducing such data to represent essential biological information. This can help to compare various single-cell tracking data yielding a novel source of information. The vast array of potential data sources highlights the significance of methodologies prioritizing simplicity, robustness, transparency, affordability, sensor independence, and freedom from reliance on specific software or online services.

Methods

The provided data presents single-cell tracking of clonal (A549) cells as they grow in two-dimensional (2D) monolayers over 94 hours, spanning several cell cycles. The cells are exposed to three different concentrations of yessotoxin (YTX). The data treatments showcase the parametrization of population growth curves, as well as other statistical descriptions. These include the temporal development of cell speed in family trees with and without cell death, correlations between sister cells, single-cell average displacements, and the study of clustering tendencies.

Results

Various statistics obtained from single-cell tracking reveal patterns suitable for data compression and parametrization. These statistics encompass essential aspects such as cell division, movements, and mutual information between sister cells.

Conclusion

This work presents practical examples that highlight the abundant potential information within large sets of single-cell tracking data. Data reduction is crucial in the process of acquiring such information which can be relevant for phenotypic drug discovery and therapeutics, extending beyond standardized procedures. Conducting meaningful big data analysis typically necessitates a substantial amount of data, which can stem from standalone case studies as an initial foundation.

Does splitting make sentence easier?

In this study, we focus on sentence splitting, a subfield of text simplification, motivated largely by an unproven idea that if you divide a sentence in pieces, it should become easier to understand. Our primary goal in this study is to find out whether this is true. In particular, we ask, does it matter whether we break a sentence into two, three, or more? We report on our findings based on Amazon Mechanical Turk. More specifically, we introduce a Bayesian modeling framework to further investigate to what degree a particular way of splitting the complex sentence affects readability, along with a number of other parameters adopted from diverse perspectives, including clinical linguistics, and cognitive linguistics. The Bayesian modeling experiment provides clear evidence that bisecting the sentence leads to enhanced readability to a degree greater than when we create simplification with more splits.

Utility based approach in individualized optimal dose selection using machine learning methods

The goal in personalized medicine is to individualize treatment using patient characteristics and improve health outcomes. Selection of optimal dose must balance the effect of dose on both treatment efficacy and toxicity outcomes. We consider a setting with one binary efficacy and one binary toxicity outcome. The goal is to find the optimal dose for each patient using clinical features and biomarkers from available dataset. We propose to use flexible machine learning methods such as random forest and Gaussian process models to build models for efficacy and toxicity depending on dose and biomarkers. A copula is used to model the joint distribution of the two outcomes and the estimates are constrained to have non‐decreasing dose‐efficacy and dose‐toxicity relationships. Numerical utilities are elicited from clinicians for each potential bivariate outcome. For each patient, the optimal dose is chosen to maximize the posterior mean of the utility function. We also propose alternative approaches to optimal dose selection by adding additional toxicity based constraints and an approach taking into account the uncertainty in the estimation of the utility function. The proposed methods are evaluated in a simulation study to compare expected utility outcomes under various estimated optimal dose rules. Gaussian process models tended to have better performance than random forest. Enforcing monotonicity during modeling provided small benefits. Whether and how, correlation between efficacy and toxicity, was modeled, had little effect on performance. The proposed methods are illustrated with a study of patients with liver cancer treated with stereotactic body radiation therapy.

Semiparametric analysis of clustered interval-censored survival data using soft Bayesian additive regression trees (SBART)

Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesian ensemble learning, called soft Bayesian additive regression trees or SBART (Linero and Yang, 2018), which combines multiple sparse (soft) decision trees to attain excellent predictive accuracy. We develop a novel semiparametric hazards regression model by modeling the hazard function as a product of a parametric baseline hazard function and a nonparametric component that uses SBART to incorporate clustering, unknown functional forms of the main effects, and interaction effects of various covariates. In addition to being applicable for left-censored, right-censored, and interval-censored survival data, our methodology is implemented using a data augmentation scheme which allows for existing Bayesian backfitting algorithms to be used. We illustrate the practical implementation and advantages of our method via simulation studies and an analysis of a prostate cancer surgery study where dependence on the experience and skill level of the physicians leads to clustering of survival times. We conclude by discussing our method's applicability in studies involving high-dimensional data with complex underlying associations.

Application of Bayesian Additive Regression Trees for Estimating Daily Concentrations of PM2.5 Components

Bayesian additive regression tree (BART) is a recent statistical method that combines ensemble learning and nonparametric regression. BART is constructed under a probabilistic framework that also allows for model-based prediction uncertainty quantification. We evaluated the application of BART in predicting daily concentrations of four fine particulate matter (PM_2.5) components (elemental carbon, organic carbon, nitrate, and sulfate) in California during the period 2005 to 2014. We demonstrate in this paper how BART can be tuned to optimize prediction performance and how to evaluate variable importance. Our BART models included, as predictors, a large suite of land-use variables, meteorological conditions, satellite-derived aerosol optical depth parameters, and simulations from a chemical transport model. In cross-validation experiments, BART demonstrated good out-of-sample prediction performance at monitoring locations (R² from 0.62 to 0.73). More importantly, prediction intervals associated with concentration estimates from BART showed good coverage probability at locations with and without monitoring data. In our case study, major PM_2.5 components could be estimated with good accuracy, especially when collocated PM_2.5 total mass observations were available. In conclusion, BART is an attractive approach for modeling ambient air pollution levels, especially for its ability to provide uncertainty in estimates that may be useful for subsequent health impact and health effect analyses.