TENSOR REGRESSION FOR INCOMPLETE OBSERVATIONS WITH APPLICATION TO LONGITUDINAL STUDIES.

Multivariate longitudinal data are frequently encountered in practice such as in our motivating longitudinal microbiome study. It is of general interest to associate such high-dimensional, longitudinal measures with some univariate continuous outcome. However, incomplete observations are common in a regular study design, as not all samples are measured at every time point, giving rise to the so-called blockwise missing values. Such missing structure imposes significant challenges for association analysis and defies many existing methods that require complete samples. In this paper we propose to represent multivariate longitudinal data as a three-way tensor array (i.e., sample-by-feature-by-time) and exploit a parsimonious scalar-on-tensor regression model for association analysis. We develop a regularized covariance-based estimation procedure that effectively leverages all available observations without imputation. The method achieves variable selection and smooth estimation of time-varying effects. The application to the motivating microbiome study reveals interesting links between the preterm infant's gut microbiome dynamics and their neurodevelopment. Additional numerical studies on synthetic data and a longitudinal aging study further demonstrate the efficacy of the proposed method.

Application of microbubble air flotation to harvest Microcystis sp. from agriculture wastewater: The regulation and mechanisms.

The harvesting of microalgae is the main bottleneck of its large-scale biomass production, and seeking an efficient, green, and low-cost microalgae harvesting technology is one of the urgent problems to be solved. Microbubble air flotation has been proven to be an effective measure, but the mechanisms of microbubbles-algal cell attachment are still unclear. In this study, microbubble air flotation was used as a harvesting method for Microcystis cultured in agricultural wastewater. The process mechanism of microbubble air flotation harvesting microalgae in wastewater was fully revealed from three aspects (the design of bubble formation, the adhesion law, and the recovery rate of microalgae under different working conditions). The results show that the length of the release pipe is the main factor affecting the proportion of microbubbles with a particle size of less than 50 µm. In the process of adhesion, when the particle size of microbubbles is 0.6-1.7 times the size of Microcystis, the adhesion efficiency of microbubbles to Microcystis is the highest. Under the conditions of pressure 0.45 MPa, gas-liquid ratio 5%, and release pipe length 100 cm, the harvesting performance of Microcystis was the best. Microbubble air flotation has better harvesting performance (63.5%, collection rate) of Microcystis with higher density. By understanding the mechanism of microbubble flotation, the technical parameters of microbubble flotation for harvesting energy microalgae are optimized to provide support for the development of efficient and low-cost devices and equipment for collecting microalgae.

Efficient Binocular Rendering of Volumetric Density Fields With Coupled Adaptive Cube-Map Ray Marching for Virtual Reality.

Creating visualizations of multiple volumetric density fields is demanding in virtual reality (VR) applications, which often include divergent volumetric density distributions mixed with geometric models and physics-based simulations. Real-time rendering of such complex environments poses significant challenges for rendering quality and performance. This paper presents a novel scheme for efficient real-time rendering of varying translucent volumetric density fields with global illumination (GI) effects on high-resolution binocular VR displays. Our scheme proposes creative solutions to address three challenges involved in the target problem. Firstly, to tackle the doubled heavy workloads of binocular ray marching, we explore the anti-aliasing principles and more advanced potentials of ray marching on interior cube-map faces, and propose a coupled ray-marching technique that converges to multi-resolution cube maps with interleaved adaptive sampling. Secondly, we devise a fully dynamic ambient GI approximation method that leverages spherical-harmonics (SH) transform information of the phase function to reduce the huge amount of ray sampling required for GI while ensuring fidelity. The method catalyzes spatial ray-marching reuse and adaptive temporal accumulation. Thirdly, we deploy a two-phase ray-tracing algorithm with a tiled k-buffer to achieve fast processing of order-independent transparency (OIT) for multiple volume instances. Consequently, high-quality and high-performance real-time dynamic volume rendering can be achieved under constrained budgets controlled by developers. As our solution supports mixed mesh-volume rendering, the test results prove the practical usefulness of our approach for high-resolution binocular VR rendering on hybrid multi-volumetric and geometric environments.

Mixed-Response State-Space Model for Analyzing Multi-Dimensional Digital Phenotypes.

Digital technologies (e.g., mobile phones) can be used to obtain objective, frequent, and real-world digital phenotypes from individuals. However, modeling these data poses substantial challenges since observational data are subject to confounding and various sources of variabilities. For example, signals on patients' underlying health status and treatment effects are mixed with variation due to the living environment and measurement noises. The digital phenotype data thus shows extensive variabilities between- and within-patient as well as across different health domains (e.g., motor, cognitive, and speaking). Motivated by a mobile health study of Parkinson's disease (PD), we develop a mixed-response state-space (MRSS) model to jointly capture multi-dimensional, multi-modal digital phenotypes and their measurement processes by a finite number of latent state time series. These latent states reflect the dynamic health status and personalized time-varying treatment effects and can be used to adjust for informative measurements. For computation, we use the Kalman filter for Gaussian phenotypes and importance sampling with Laplace approximation for non-Gaussian phenotypes. We conduct comprehensive simulation studies and demonstrate the advantage of MRSS in modeling a mobile health study that remotely collects real-time digital phenotypes from PD patients.

The more data, the better? Demystifying deletion-based methods in linear regression with missing data.

We compare two deletion-based methods for dealing with the problem of missing observations in linear regression analysis. One is the complete-case analysis (CC, or listwise deletion) that discards all incomplete observations and only uses common samples for ordinary least-squares estimation. The other is the available-case analysis (AC, or pairwise deletion) that utilizes all available data to estimate the covariance matrices and applies these matrices to construct the normal equation. We show that the estimates from both methods are asymptotically unbiased under missing completely at random (MCAR) and further compare their asymptotic variances in some typical situations. Surprisingly, using more data (i.e., AC) does not necessarily lead to better asymptotic efficiency in many scenarios. Missing patterns, covariance structure and true regression coefficient values all play a role in determining which is better. We further conduct simulation studies to corroborate the findings and demystify what has been missed or misinterpreted in the literature. Some detailed proofs and simulation results are available in the online supplemental materials.

Self-matched learning to construct treatment decision rules from electronic health records.

Electronic health records (EHRs) collected from large-scale health systems provide rich subject-specific information on a broad patient population at a lower cost compared to randomized controlled trials. Thus, EHRs may serve as a complementary resource to provide real-world data to construct individualized treatment rules (ITRs) and achieve precision medicine. However, in the absence of randomization, inferring treatment rules from EHR data may suffer from unmeasured confounding. In this article, we propose a self-matched learning method inspired by the self-controlled case series (SCCS) design to mitigate this challenge. We alleviate unmeasured time-invariant confounding between patients by matching different periods of treatments within the same patient (self-controlled matching) to infer the optimal ITRs. The proposed method constructs a within-subject matched value function for optimizing ITRs and bears similarity to the SCCS design. We examine assumptions that ensure Fisher consistency, and show that our method requires weaker assumptions on unmeasured confounding than alternative methods. Through extensive simulation studies, we demonstrate that self-matched learning has comparable performance to other existing methods when there are no unmeasured confounders, but performs markedly better when unobserved time-invariant confounders are present, which is often the case for EHRs. Sensitivity analyses show that the proposed method is robust under different scenarios. Finally, we apply self-matched learning to estimate the optimal ITRs from type 2 diabetes patient EHRs, which shows our estimated decision rules lead to greater advantages in reducing patients' diabetes-related complications.

Effects of different amino acids and their configurations on methane yield and biotransformation of intermediate metabolites during anaerobic digestion.

Anaerobic digestion (AD) comprises a series of biochemical reactions, with methane as one of the target products. Amino acids (AAs) are important molecular and primary intermediate products when protein is the main component of organic waste/wastewater. The L (levorotatory, left-handed)-configuration is natural for AAs, while D (dextrorotatory, right-handed) -AAs also widely exist in the natural environment and can be generated by racemization. However, the effects and underlying mechanisms of natural AAs and their enantiomers on the methane yield and the underlying mechanisms remain unclear. In this study, the effects of certain widespread L-AAs and their enantiomers on two-stage AD and the mechanisms therein were investigated. The AAs enantiomers showed variable or even opposite effects on different processes. The methane yield from a model monosaccharide (glucose) decreased by 57% with D-leucine addition. The butyrate generation and the methane yield from propionate were sensitive to the AA configuration and were inhibited by D-leucine by 80% and 61.8%, respectively, with D-leucine addition, while the volatile fatty acids concentration was slightly increased with the addition of L-leucine. The related mechanisms were further investigated in terms of key enzymes and microbial communities. The addition of D-Leucine decreased acetic acid production from homoacetogens by 30.2% due to the inhibition of key enzymes involved in hydrogen generation and consumption. The transform of butyryl CoA to butyryl phosphate was the rate-limiting step, with the related enzyme (phosphotransbutylase) was inhibited by D-leucine. Furthermore, the bacteria related to butyric acid generation and organic matter degradation were inhibited by D-leucine, while the methanogenic archaea remained stable irrespective of leucine addition. The effect of D-AAs on microorganisms is related to the type of sludge. In this study, the methanogenetic seed sludge was granular and did not dissociate after treatment; however, the D-AAs could trigger biofilm disassembly and reduce the stability of the sludge floc. The study provides a novel method for regulating AD by adding specific AAs with L or D configuration.

Time Course of Relapse Following Acute Treatment for Anorexia Nervosa.

OBJECTIVE: There is long-standing interest in how best to define stages of illness for anorexia nervosa, including remission and recovery. The authors used data from a previously published study to examine the time course of relapse over the year following full weight restoration. METHODS: Following weight restoration in an acute care setting, 93 women with anorexia nervosa were randomly assigned to receive fluoxetine or placebo and were discharged to outpatient care, where they also received cognitive-behavioral therapy for up to 1 year. Relapse was defined on the basis of a priori clinical criteria. Fluoxetine had no impact on the time to relapse. In the present analysis, for each day after entry into the study, the risk of relapse over the following 60 days and the following 90 days was calculated and a parametric function was fitted to approximate the Kaplan-Meier estimator. RESULTS: The risk of relapse rose immediately after entry into the study, reached a peak after approximately 60 days, and then gradually declined. There was no indication of an inflection point at which the risk of relapse fell precipitously after the initial peak. CONCLUSIONS: This analysis highlights the fact that adult patients with anorexia nervosa are at increased risk of relapse in the first months following discharge from acute care, suggesting a need for frequent follow-up and relapse prevention-focused treatment during this period. After approximately 2 months, the risk of relapse progressively decreases over time.

Zero-inflated Poisson factor model with application to microbiome read counts.

Dimension reduction of high-dimensional microbiome data facilitates subsequent analysis such as regression and clustering. Most existing reduction methods cannot fully accommodate the special features of the data such as count-valued and excessive zero reads. We propose a zero-inflated Poisson factor analysis model in this paper. The model assumes that microbiome read counts follow zero-inflated Poisson distributions with library size as offset and Poisson rates negatively related to the inflated zero occurrences. The latent parameters of the model form a low-rank matrix consisting of interpretable loadings and low-dimensional scores that can be used for further analyses. We develop an efficient and robust expectation-maximization algorithm for parameter estimation. We demonstrate the efficacy of the proposed method using comprehensive simulation studies. The application to the Oral Infections, Glucose Intolerance, and Insulin Resistance Study provides valuable insights into the relation between subgingival microbiome and periodontal disease.

Representation Learning for Integrating Multi-domain Outcomes to Optimize Individualized Treatments.

For mental disorders, patients' underlying mental states are non-observed latent constructs which have to be inferred from observed multi-domain measurements such as diagnostic symptoms and patient functioning scores. Additionally, substantial heterogeneity in the disease diagnosis between patients needs to be addressed for optimizing individualized treatment policy in order to achieve precision medicine. To address these challenges, we propose an integrated learning framework that can simultaneously learn patients' underlying mental states and recommend optimal treatments for each individual. This learning framework is based on the measurement theory in psychiatry for modeling multiple disease diagnostic measures as arising from the underlying causes (true mental states). It allows incorporation of the multivariate pre- and post-treatment outcomes as well as biological measures while preserving the invariant structure for representing patients' latent mental states. A multi-layer neural network is used to allow complex treatment effect heterogeneity. Optimal treatment policy can be inferred for future patients by comparing their potential mental states under different treatments given the observed multi-domain pre-treatment measurements. Experiments on simulated data and a real-world clinical trial data show that the learned treatment polices compare favorably to alternative methods on heterogeneous treatment effects, and have broad utilities which lead to better patient outcomes on multiple domains.

Learning Personalized Treatment Rules from Electronic Health Records Using Topic Modeling Feature Extraction.

To address substantial heterogeneity in patient response to treatment of chronic disorders and achieve the promise of precision medicine, individualized treatment rules (ITRs) are estimated to tailor treatments according to patient-specific characteristics. Randomized controlled trials (RCTs) provide gold standard data for learning ITRs not subject to confounding bias. However, RCTs are often conducted under stringent inclusion/exclusion criteria, and participants in RCTs may not reflect the general patient population. Thus, ITRs learned from RCTs lack generalizability to the broader real world patient population. Real world databases such as electronic health records (EHRs) provide new resources as complements to RCTs to facilitate evidence-based research for personalized medicine. However, to ensure the validity of ITRs learned from EHRs, a number of challenges including confounding bias and selection bias must be addressed. In this work, we propose a matching-based machine learning method to estimate optimal individualized treatment rules from EHRs using interpretable features extracted from EHR documentation of medications and ICD diagnoses codes. We use a latent Dirichlet allocation (LDA) model to extract latent topics and weights as features for learning ITRs. Our method achieves confounding reduction in observational studies through matching treated and untreated individuals and improves treatment optimization by augmenting feature space with clinically meaningful LDA-based features. We apply the method to EHR data collected at New York Presbyterian Hospital clinical data warehouse in studying optimal second-line treatment for type 2 diabetes (T2D) patients. We use cross validation to show that ITRs outperforms uniform treatment strategies (i.e., assigning same treatment to all individuals), and including topic modeling features leads to more reduction of post-treatment complications.