Bayesian Inference Using the Proximal Mapping: Uncertainty Quantification Under Varying Dimensionality.

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of obtaining a point estimate via optimization, it is much more challenging to quantify their uncertainty. In the Bayesian framework, a major difficulty is that if assigning the prior associated with a p -dimensional measure, then there is zero posterior probability on any lower-dimensional subset with dimension d < p . To avoid this caveat, one needs to choose another dimension-selection prior on d , which often involves a highly combinatorial problem. To significantly reduce the modeling burden, we propose a new generative process for the prior: starting from a continuous random variable such as multivariate Gaussian, we transform it into a varying-dimensional space using the proximal mapping. This leads to a large class of new Bayesian models that can directly exploit the popular frequentist regularizations and their algorithms, such as the nuclear norm penalty and the alternating direction method of multipliers, while providing a principled and probabilistic uncertainty estimation. We show that this framework is well justified in the geometric measure theory, and enjoys a convenient posterior computation via the standard Hamiltonian Monte Carlo. We demonstrate its use in the analysis of the dynamic flow network data.

Returners and explorers dichotomy in the face of natural hazards.

Understanding human mobility patterns amid natural hazards is crucial for enhancing urban emergency responses and rescue operations. Existing research on human mobility has delineated two primary types of individuals: returners, who exhibit a tendency to frequent a limited number of locations, and explorers, characterized by a more diverse range of movement across various places. Yet, whether this mobility dichotomy endures in the context of natural hazards remains underexplored. This study addresses this gap by examining anonymized high-resolution mobile phone location data from Lee County, Florida residents, aiming to unravel the dynamics of these distinct mobility groups throughout different phases of Hurricane Ian. The results indicate that returners and explorers maintained their distinct mobility characteristics even during the hurricane, showing increased separability. Before the hurricane, returners favored shorter trips, while explorers embarked on longer journeys, a trend that continued during the hurricane. However, the hurricane heightened people's inclination to explore, leading to a notable increase in longer-distance travel for both groups, likely influenced by evacuation considerations. Spatially, both groups exhibited an uptick in trips towards the southern regions, away from the hurricane's path, particularly converging on major destinations such as Miami, Fort Lauderdale, Naples, and West Palm Beach during the hurricane.

Bayesian Distance Clustering.

Model-based clustering is widely used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a class of Bayesian distance clustering methods, which rely on modeling the likelihood of the pairwise distances in place of the original data. Although some information in the data is discarded, we gain substantial robustness to modeling assumptions. The proposed approach represents an appealing middle ground between distance- and model-based clustering, drawing advantages from each of these canonical approaches. We illustrate dramatic gains in the ability to infer clusters that are not well represented by the usual choices of kernel. A simulation study is included to assess performance relative to competitors, and we apply the approach to clustering of brain genome expression data.

Data driven decision making to characterize clinical personas of parents of children with cystic fibrosis: a mixed methods study.

BACKGROUND: Beginning at a young age, children with cystic fibrosis (CF) embark on demanding care regimens that pose challenges to parents. We examined the extent to which clinical, demographic and psychosocial features inform patterns of adherence to pulmonary therapies and how these patterns can be used to develop clinical personas, defined as aspects of adherence barriers that are presented by parents and/or perceived by clinicians, in order to enhance personalized CF care delivery. METHODS: We undertook an explanatory sequential mixed-methods study consisting of i) multivariate clustering to create clusters corresponding to parental adherence patterns (quantitative phase); ii) parental participant interviews to create clinical personas interpreted from clustering (qualitative phase). Clinical, demographic and psychosocial features were used in supervised clustering against clinical endpoints, which included adherence to airway clearance and aerosolized medications and self-efficacy score, which was used as a feature for modeling adherence. Clinical implications were developed for each persona by combing quantitative and qualitative data (integration phase). RESULTS: The quantitative phase showed that the 87 parent participants were segmented into three distinct patterns of adherence based on use of aerosolized medication and practice of airway clearance. Patterns were primarily influenced by self-efficacy, distance to CF care center and child BMI percentile. The two key patterns that emerged for the self-efficacy model were most heavily influenced by distance to CF care center and child BMI percentile. Eight clinical personas were developed in the qualitative phase from parent and clinician participant feedback of latent components from these models. Findings from the integration phase include recommendations to overcome specific challenges with maintaining treatment regimens and increasing support from social networks. CONCLUSIONS: Adherence patterns from multivariate models and resulting parent personas with their corresponding clinical implications have utility as clinical decision support tools and capabilities for tailoring intervention study designs that promote adherence.

Bayesian constraint relaxation.

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.

Joint hierarchical Gaussian process model with application to personalized prediction in medical monitoring.

A two-level Gaussian process (GP) joint model is proposed to improve personalized prediction of medical monitoring data. The proposed model is applied to jointly analyze multiple longitudinal biomedical outcomes, including continuous measurements and binary outcomes, to achieve better prediction in disease progression. At the population level of the hierarchy, two independent GPs are used to capture the nonlinear trends in both the continuous biomedical marker and the binary outcome, respectively; at the individual level, a third GP, which is shared by the longitudinal measurement model and the longitudinal binary model, induces the correlation between these two model components and strengthens information borrowing across individuals. The proposed model is particularly advantageous in personalized prediction. It is applied to the motivating clinical data on cystic fibrosis disease progression, for which lung function measurements and onset of acute respiratory events are monitored jointly throughout each patient's clinical course. The results from both the simulation studies and the cystic fibrosis data application suggest that the inclusion of the shared individual-level GPs under the joint model framework leads to important improvements in personalized disease progression prediction.

The Effects of Medication Alerts on Prescriber Response in a Pediatric Hospital.

OBJECTIVE: More than 70% of hospitals in the United States have electronic health records (EHRs). Clinical decision support (CDS) presents clinicians with electronic alerts during the course of patient care; however, alert fatigue can influence a provider's response to any EHR alert. The primary goal was to evaluate the effects of alert burden on user response to the alerts. METHODS: We performed a retrospective study of medication alerts over a 24-month period (1/2013-12/2014) in a large pediatric academic medical center. The institutional review board approved this study. The primary outcome measure was alert salience, a measure of whether or not the prescriber took any corrective action on the order that generated an alert. We estimated the ideal number of alerts to maximize salience. Salience rates were examined for providers at each training level, by day of week, and time of day through logistic regressions. RESULTS: While salience never exceeded 38%, 49 alerts/day were associated with maximal salience in our dataset. The time of day an order was placed was associated with alert salience (maximal salience 2am). The day of the week was also associated with alert salience (maximal salience on Wednesday). Provider role did not have an impact on salience. CONCLUSION: Alert burden plays a role in influencing provider response to medication alerts. An increased number of alerts a provider saw during a one-day period did not directly lead to decreased response to alerts. Given the multiple factors influencing the response to alerts, efforts focused solely on burden are not likely to be effective.

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data.

We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online.

Longitudinal Patterns of Glycemic Control and Blood Pressure in Pregnant Women with Type 1 Diabetes Mellitus: Phenotypes from Functional Data Analysis.

Objective To identify phenotypes of type 1 diabetes control and associations with maternal/neonatal characteristics based on blood pressure (BP), glucose, and insulin curves during gestation, using a novel functional data analysis approach that accounts for sparse longitudinal patterns of medical monitoring during pregnancy. Methods We performed a retrospective longitudinal cohort study of women with type 1 diabetes whose BP, glucose, and insulin requirements were monitored throughout gestation as part of a program-project grant. Scores from sparse functional principal component analysis (fPCA) were used to classify gestational profiles according to the degree of control for each monitored measure. Phenotypes created using fPCA were compared with respect to maternal and neonatal characteristics and outcome. Results Most of the gestational profile variation in the monitored measures was explained by the first principal component (82-94%). Profiles clustered into three subgroups of high, moderate, or low heterogeneity, relative to the overall mean response. Phenotypes were associated with baseline characteristics, longitudinal changes in glycohemoglobin A1 and weight, and to pregnancy-related outcomes. Conclusion Three distinct longitudinal patterns of glucose, insulin, and BP control were found. By identifying these phenotypes, interventions can be targeted for subgroups at highest risk for compromised outcome, to optimize diabetes management during pregnancy.

Concentration of fractional excretion of nitric oxide (FENO): A potential airway biomarker of restored CFTR function.

BACKGROUND: Lower airway biomarkers of restored cystic fibrosis transmembrane conductance regulator (CFTR) function are limited. We hypothesized that fractional excretion of nitric oxide (FENO), typically low in CF patients, would demonstrate reproducibility during CFTR-independent therapies, and increase during CFTR-specific intervention (ivacaftor) in patients with CFTR gating mutations. METHODS: Repeated FENO and spirometry measurements in children with CF (Cohort 1; n=29) were performed during hospital admission for acute pulmonary exacerbations and routine outpatient care. FENO measurements before and after one month of ivacaftor treatment (150 mg every 12h) were completed in CF patients with CFTR gating mutations (Cohort 2; n=5). RESULTS: Cohort 1: Mean forced expiratory volume in 1s (FEV1 % predicted) at enrollment was 72.3% (range 25%-102%). Mean FENO measurements varied minimally over the two inpatient and two outpatient measurements (9.8-10.9 ppb). There were no clear changes related to treatment of pulmonary exacerbations, gender, genotype or microbiology, and weak correlation with inhaled corticosteroid use (P<0.05). Between the two inpatient measurements, FEV1 % predicted increased by 7.3% (P<0.03) and FENO did not change. In Cohort 2, mean FENO increased from 6.6 ppb (SD=2.19) to 11.8 ppb (SD=4.97) during ivacaftor treatment. Mean sweat chloride dropped by 58 mM and mean FEV1 % predicted increased by 10.2%. CONCLUSIONS: Repeated FENO measurements were stable in CF patients, whereas FENO increased in all patients with CFTR gating mutations treated with ivacaftor. Acute changes in FENO may serve as a biomarker of restored CFTR function in the CF lower airway during CFTR modulator treatment.

A semiparametric approach to estimate rapid lung function decline in cystic fibrosis.

PURPOSE: Detecting the onset of rapid lung function decline is important to reduce mortality rates in cystic fibrosis (CF) and other lung diseases. The most common approach is conventional linear mixed modeling-estimating a population-level slope of lung function decline and using random effects to address serial correlation-but this ignores nonlinear features of disease progression and distinct sources of variability. The purpose of this article was to estimate patient-specific timing and degree of rapid decline while appropriately characterizing natural progression and variation in CF. METHODS: We propose longitudinal semiparametric mixed modeling and contrast it with the conventional approach, which restricts lung function (measured as forced expiratory volume in 1 second as a percentage of predicted, FEV1%) to linear decline. Each approach is applied to clinical encounter data from the United States CF Foundation Patient Registry. RESULTS: Timing and degree of rapid FEV1% decline vary across patients and as a function of key covariates. Patients experience maximal FEV1% loss by early adulthood more severe than indicated by conventional slope analysis. CONCLUSIONS: Semiparametric mixed modeling provides a means to estimate patient-specific changes in CF disease progression and may be used to inform prognostic decisions in chronic care settings and clinical studies.