We consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can improve the estimation and prediction accuracy. Using information in both functional predictors and multivariate response, we identify the optimal decomposition of the coefficient functions for prediction in population level. Then we propose methods to estimate this decomposition and fit the regression model for the situations of a small and a large number p of functional predictors separately. For a large p, we propose a simultaneous smooth-sparse penalty which can both make curve selection and improve estimation and prediction accuracy. We provide the asymptotic results when both the sample size and the number of functional predictors go to infinity. Our method can be applied to models with thousands of functional predictors and has been implemented in the R package FRegSigCom.

Accurate and reliable forecasting models are critical for guiding public health responses and policy decisions during pandemics such as COVID-19. Retrospective evaluation of forecasting performance provides an essential framework for assessing and improving epidemic prediction methods. In this study, we used COVID-19 wastewater data from CDC's National Wastewater Surveillance System to generate sequential weekly retrospective out-of-sample forecasts for the United States from March 2022 through September 2024, both at the national level and for four major regions (Northeast, Midwest, South, and West). We produced 133 weekly forecasts using 11 models, including ARIMA, generalized additive models (GAM), simple linear regression (SLR), Prophet, and the n-sub-epidemic framework (top-ranked, weighted-ensemble, and unweighted-ensemble variants). Forecast performance was assessed using mean absolute error (MAE), mean squared error (MSE), weighted interval score (WIS), and 95% prediction interval coverage. The n-sub-epidemic unweighted ensembles outperformed all other models at 3-4-week horizons, particularly at the national level and in the Midwest and West. ARIMA and GAM performed best at 1-2-week horizons in most regions, whereas Prophet and SLR consistently underperformed across regions and horizons. These findings highlight the value of region-specific modeling strategies and demonstrate the utility of the n-sub-epidemic framework for real-time outbreak forecasting using wastewater surveillance data.

Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares (NLS) optimization versus Bayesian inference assuming a normal likelihood and using MCMC sampling in Stan. Rather than evaluating all methodological variants, we assess forecasting performance under a shared modeling structure and error assumption. The findings apply to specific implementations of both approaches. Performance is evaluated using simulated datasets (with R0=2 and 1.5) and historical outbreaks, including the 1918 influenza pandemic, the 1896-1897 Bombay plague epidemic, and the COVID-19 pandemic. Metrics include mean absolute error (MAE), root mean squared error (RMSE), weighted interval score (WIS), and 95% prediction interval coverage. Forecasting performance varies by epidemic phase and dataset; no method consistently dominates. The Frequentist method performs well at the peak in simulations and in the post-peak phases of real outbreaks but is less accurate pre-peak. Bayesian methods, especially those with uniform priors, offer higher predictive accuracy early in epidemics and stronger uncertainty quantification when data are sparse or noisy. Frequentist methods often yield more accurate point forecasts with lower MAE, RMSE, and WIS, though their interval estimates are less robust. We also discuss the influence of prior choice and the effects of longer forecasting horizons on convergence and computational efficiency. These findings provide practical guidance for selecting estimation strategies suited to epidemic phase and data quality, aiding forecast-based decision-making.

Background While low body mass index (BMI) is associated with poor tuberculosis (TB) treatment outcomes, the impact of weight gain during TB treatment is unclear. To address this knowledge gap, we assessed whether a lack of weight gain is associated with all-cause mortality during and after TB treatment. Methods We conducted a retrospective cohort study among adults with newly diagnosed multidrug or extensively drug-resistant (MDR/XDR) pulmonary TB in Georgia between 2009-2020. The exposure was a change in BMI during the first 3-6 months of TB treatment. All-cause mortality during and after TB treatment was assessed using the National Death Registry. We used competing-risk Cox proportional hazard models to estimate adjusted hazard ratios (aHRs) between BMI change and all-cause mortality. Results Among 720 adult participants, 21% had low BMI (<18.5 kg m-2) at treatment initiation and 9% died either during (n=16) or after treatment (n=50). During the first 3-6 months of TB treatment, 17% lost weight and 14% had no weight change. Among 479 adults with normal baseline BMI (>= 18.5-<25 kg m-2), weight loss was associated with an increased risk of death during TB treatment (aHR 5.25, 95% CI 1.31-21.10). Among 149 adults with a low baseline BMI, no change in BMI was associated with increased post-TB treatment mortality (aHR 4.99, 95% CI 1.25-19.94). Conclusions Weight loss during TB treatment (among those with normal baseline BMI) or no weight gain (among those with low baseline BMI) was associated with increased rates of all-cause mortality. Our findings suggest that scaling up weight management interventions among those with M/XDR TB may be beneficial.

BACKGROUND:Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, epidemic modeling, and healthcare informatics, where they are used to simulate complex dynamic systems and inform decision-making. However, implementing Bayesian calibration and forecasting typically requires substantial coding in Stan or similar tools. To support Bayesian parameter estimation and forecasting for such systems, we introduce BayesianFitForecast, a user-friendly R toolbox specifically developed to streamline Bayesian parameter estimation and forecasting in ODE models, making it particularly relevant to health informatics and public health decision-making ( https://github.com/gchowell/BayesianFitForecast/ ). RESULTS:This toolbox enables automatic generation of Stan files, allowing users to configure models, define priors, and analyze results with minimal programming expertise. By eliminating manual coding, BayesianFitForecast significantly lowers the technical barrier to Bayesian inference with dynamical systems. We demonstrate its flexibility and usability through applications to historical epidemic datasets (e.g., the 1918 influenza pandemic in San Francisco and the 1896-1897 Bombay plague) and simulated data, showing robust parameter estimation and forecasting performance under Poisson and negative binomial observation error structures. The toolbox also provides robust tools for evaluating model performance, including convergence diagnostics, posterior distributions, credible intervals, and performance metrics. CONCLUSION:By improving the accessibility of advanced Bayesian methods, BayesianFitForecast broadens the application of Bayesian inference in time-series modeling, healthcare forecasting, and epidemiological applications. In addition to the R scripting interface, a built-in Shiny web application is included, enabling interactive model configuration, visualization, and forecasting. A tutorial video demonstrating the toolbox's functionality is also available ( https://youtu.be/jnxMjz3V3n8 ).

BACKGROUND:Many disciplines, such as public health, rely on statistical time series models for real-time and retrospective forecasting efforts; however, effectively implementing related methods often requires extensive programming knowledge. Therefore, such tools remain largely inaccessible to those with limited programming experience, including students training in modeling, as well as professionals and policymakers seeking to forecast an epidemic's trajectory. To address the need for accessible and intuitive forecasting applications, we present StatModPredict, an R-Shiny dashboard for conducting robust forecasting analysis utilizing auto-regressive integrated moving average (ARIMA), generalized linear models (GLM), generalized additive models (GAM), and Meta's Prophet model. METHODS:StatModPredict supports robust real-time forecasting and retrospective model analysis, including fitting, forecasting, evaluation, visualization, and comparison of results from four popular models. After loading an incident time series data set into the interface, users can easily customize model parameters and forecasting options to obtain the desired output. Additionally, StatModPredict offers multiple editable figures for, but not limited to, the time series data, the forecasts, and model fit and forecast metrics. Users can also upload external forecasts produced elsewhere and evaluate their performance alongside the dashboard's built-in models, thereby enabling direct comparisons. We provide a detailed demonstration of the dashboard's features using publicly available annual HIV case data in the US. A video tutorial is available at https://www.youtube.com/watch?v=zgZOvqhvqw8. CONCLUSIONS:By eliminating programming barriers, StatModPredict facilitates exploration and use by students training in forecasting, as well as professionals and policymakers aiming to forecast epidemic trajectories. Additionally, the flexibility in the required input data structure and parameter specification process extends the application of StatModPredict to any discipline that employs time series data. By offering this open-source interface, we aim to broaden access to forecasting tools, promote hands-on learning, and foster contributions from users across disciplines.

Background: Alzheimer's Disease (AD) is a progressive neurodegenerative disorder characterized by gray matter (GM) changes, such as amyloid-beta (Aβ) plaques and neurofibrillary tangles. While GM alterations are well-established, the fine-grained, spatially distinct patterns of homogeneous Aβ uptake and their changes remain poorly understood. Additionally, white matter (WM) pathology is less explored. This study addresses these gaps by leveraging high-model-order independent component analysis (ICA) to identify spatially granular amyloid networks in both GM and WM. Methods: We analyzed [18F]Florbetapir (FBP) PET images from 716 participants in the Alzheimer's Disease Neuroimaging Initiative (ADNI), classified as cognitively normal (CN), mild cognitive impairment (MCI), or AD dementia. High-model-order ICA was applied to identify 80 GM and 13 WM FBP-related networks, which were labeled using terms from the Neuromark 2.2 Atlas. Statistical analyses assessed diagnostic effects and relationships between these networks and cognitive and neuropsychiatric variables. Results: Significant diagnostic differences were observed across GM and WM networks, revealing a continuous pattern of change from CN to MCI to AD. The analysis showed that the extended hippocampal, extended thalamic, basal ganglia, and frontal subdomains displayed an MCI profile closer to AD than to CN. In contrast, other subdomains exhibited a more mixed pattern, with MCI sometimes aligning more closely with CN and other times with AD. Notably, the hippocampal-entorhinal complex (HEC) within the extended hippocampal subdomain and the precuneus within the default mode subdomain were consistently associated with cognitive decline, highlighting their roles in disease progression. Additionally, WM networks, particularly the retrolenticular internal capsule (RICap), also demonstrated significant relationships with cognitive measures, suggesting that AD pathology extends beyond GM and disrupts broader network connectivity. These findings were validated in an independent replication dataset. Conclusion: High-model-order ICA effectively captures distinct fine-grained amyloid distributions, offering a network- level perspective that enhances our understanding of AD neurobiology. By decomposing complex PET signal patterns into distinct networks, this approach underscores the critical role of both GM and WM integrity in AD pathology. The consistent associations of the HEC, precuneus, and WM networks with cognitive decline highlight the widespread impact of AD-related pathology, emphasizing the value of this methodology in advancing AD research. ### Competing Interest Statement The authors have declared no competing interest.

OBJECTIVES:Pneumonia continues to be a major health issue worldwide, especially impacting those at risk across various age categories. This study aims to forecast pneumonia mortality trends by age group through 2030 using diverse modeling techniques to inform targeted public health interventions. STUDY DESIGN:A predictive modeling study utilizing publicly available secondary data. METHODS:We employed five forecasting models-Auto-Regressive Integrated Moving Average (ARIMA), Generalized Additive Model (GAM), Simple Linear Regression (SLR), Facebook's Prophet model, and the n-sub-epidemic framework- to global, age-specific pneumonia mortality data from 2020 to 2030, based on data from 1990 to 2019. The percentage change in pneumonia deaths from 2020 to 2030 and forecasting uncertainty were assessed for all models. RESULTS:Our model-based projections suggest a sustained increase in global pneumonia mortality among individuals aged ≥70 years (6.0 %-35.4 %), a gradual increase in ages 50-69 (0.4 %-19.9 %), while children under 5 years of age (-33.2 % to -97.3 %) and 5-14 years (-22.7 % to -45.9 %) showed a decline by 2030. The n-sub-epidemic models predicted a decrease in mortality for ages 15-49 (-9.1 % to -11.6 %), contrasting with statistical models that showed increasing trends among ages 15-49 (0.1 %-11.6 %). CONCLUSIONS:Pneumonia mortality trends are projected to vary considerably by age group, emphasizing the importance of age-specific policies. The use of multiple robust forecasting methods revealed consistent trends across most age groups and provided valuable insights into mortality dynamics. Future efforts should integrate region-specific data and retrospective model validation to improve predictive accuracy.

Objectives The type of electronic nicotine delivery system (ENDS) used by different age groups may be associated with ENDS and cigarette use behaviours. This study sought to identify differences in the use of ENDS device type based on age and cigarette use status to inform policy about regulating ENDS. Design This was a cross-sectional study. Setting Data was derived from a national survey conducted in 2021 in the USA. Participants Participants include 2369 US youth and adults (13 years or older) who reported past 30-day ENDS use. Outcome measures Past 30-day fairly regular use (i.e., several times a week or more) of ENDS device types, namely cigalikes, disposables, refillable tank/box mods, closed pods, refillable pods and drippers. Cigarette smoking status was also measured. Results We used weighted regression models to determine the association between ENDS device type current regular use and age group and the association between each ENDS type current regular use and smoking status separately for each age group. Youth ENDS users 13–17 years old were more likely to regularly use cigalikes (OR=2.71), disposables (OR=3.44), closed pods (OR=2.57) and drippers (OR=2.86) and 18–29 years old were more likely to regularly use disposables (OR=3.67), closed pods (OR=1.58) and drippers (OR=1.94), compared with 30+ years old ENDS users (all p<0.05). Among 13–17 years old, current (vs never) smokers had greater odds of current regular use for cigalikes (OR=2.79), disposables (OR=2.33), refillable tanks (OR=2.27), closed pods (OR=2.62) and drippers (OR=6.32; all p<0.05). Similarly, 18–29 years old current (vs never) smokers had higher odds of reporting current regular use of refillable tanks (OR=1.80), refillable pods (OR=2.63), closed pods (OR=2.20) and drippers (OR=4.89; p<0.05). Conclusions Both age and smoking status were associated with current regular use of ENDS, especially for youth and young adults. These findings inform regulatory agencies as they monitor and enforce policy on ENDS allowed on the US market.

The use of Electronic Nicotine Delivery Systems (ENDS), or vaping devices, has raised concerns about their potential impact on oral health, particularly periodontal disease. While traditional smoking is a well-established risk factor for periodontal disease, the biological and microbial effects of ENDS use are less well understood. Our study examined how vaping and vaping behaviors influence the subgingival plaque microbiome and the associated metabolic pathways that may contribute to oral disease. We enrolled 70 healthy adults aged 18-35, including 48 regular ENDS users and 22 non-vaping controls. ENDS users were categorized by puffing behavior into low, medium, and high flow groups using a validated topography device. All participants underwent periodontal screening and provided saliva and subgingival plaque samples. To evaluate exposure profiles, ENDS users also submitted their personal devices for emissions testing, and volatile organic compounds (VOCs) were collected and analyzed using gas chromatography-mass spectrometry and high-performance liquid chromatography. Compared to non-vapers, ENDS users demonstrated distinct shifts in their oral microbiome, with reductions in beneficial taxa and increased bacteria associated with inflammation and periodontal disease. These changes were more pronounced in high-puff volume users, who also exhibited lower microbial diversity. Functional profiling revealed vaping-associated enrichment of pathways related to lipid metabolism, inflammation, and xenobiotic degradation. Untargeted salivary metabolomics identified metabolic disruptions consistent with these functional shifts. Integrative network analyses incorporating VOC measurements demonstrated correlations between microbial composition, puff volume, and metabolic disruptions, particularly in lipid-regulated and inflammatory pathways. To our knowledge, this is one of the first studies to integrate vaping behavior, oral microbiome profiling, salivary metabolomics, and VOC emissions analysis in a human cohort. These findings suggest ENDS use, especially at higher intensities, may disrupt oral microbial and metabolic homeostasis through both biological and chemical pathways potentially enhancing periodontal disease risk. These patterns point to potential biological and chemical pathways of concern, warranting further investigation and informing public health priorities.

This study evaluated the prevalence of various electronic nicotine delivery systems (ENDS) modifications among U.S. ENDS users and reasons for these modifications. We conducted a national survey of U.S. youth (13–17 years old, n = 553), young adults (18–29 years old, n = 634), and older adults (30 + , n = 760) who reported past 30-day ENDS use in 2021. The result showed that, in each age group, a large majority had engaged in at least one ENDS modification (youth, young adults, and older adults respectively: 84.3%, 84.1%, 76.9%), with modifications to e-liquid (68.1%, 61.2%, 48.7%) and coils (63.7%, 61.4%, 57.2%) being the most common. For some modifications, prevalence varied by age group and race/ethnicity. Participants endorsed various reasons for modifications, many related to accessing or enhancing the flavor of the aerosol. For youth, having heard about the modification was an important reason for trying a modification. Conversely, young adults and older adults frequently mentioned making the device last longer and saving money. ENDS modifications are widespread, but the reasons for modification differ between age groups. Some of these common modifications can lead to potential harm; they need to be regulated through product standards and marketing decisions, and ENDS users should be educated about potentially dangerous modifications.

Electronic nicotine delivery systems (ENDSs), commonly termed e-cigarettes, have been advertised as a safer alternative to traditional tobacco cigarettes and promoted for smoking cessation. However, emerging evidence suggests a connection between e-cigarette use or vaping and an increased risk of oral disease, particularly among minoritized populations such as Black and African Americans (AAs). AA communities have historically experienced disproportionate harm from tobacco use, which could extend to vaping. In this study, we recruited 20 AAs and 28 individuals of other races, oversampled for vapers, with no statistical differences in age, sex, sugar intake, income, or education across groups. Whole saliva samples collected at the time of the visit were processed for untargeted UHPLC-ESI-MS/MS proteomics and HPLC-MS/MS metabolomics. Our results revealed vaping preferentially impaired redox pathways and amino acid metabolism among AAs, with elevated malondialdehyde levels and an oxidized glutathione to glutathione ratio and lowered levels of glucose-6-phosphate dehydrogenase and ascorbate. Salivary proteomics demonstrated salivary secretion was upregulated in AAs while Fc gamma R-mediated phagocytosis, bacterial invasion defense, natural killer cell function, leukocyte migration, and phagosome function were downregulated, suggesting dysregulated innate immune function in AA vapers. Additionally, focal adhesion, cell-substrate junction, and actin cytoskeleton regulation were downregulated in AA vapers, indicating that mucous epithelium barrier integrity may be disrupted. Lastly, the Community Periodontal Index of Treatment Need (CPITN), a dental assessment tool developed by the World Health Organization (WHO) to evaluate periodontal health and determine the need for treatment, revealed that a significantly higher proportion of AA vapers had CPITN scores of 3 or higher, suggesting the need for further clinical assessment of periodontal disease. Collectively, our results suggest that AAs may be more susceptible to oral health effects of vaping than individuals of other racial groups, with elevated levels of oxidative stress, dysregulated innate immune function, mucous epithelium barrier integrity disruption, and varying nicotine metabolism.

During the 2022-2023 unprecedented mpox epidemic, near real-time short-term forecasts of the epidemic's trajectory were essential in intervention implementation and guiding policy. However, as case levels have significantly decreased, evaluating model performance is vital to advancing the field of epidemic forecasting. Using laboratory-confirmed mpox case data from the Centers for Disease Control and Prevention and Our World in Data teams, we generated retrospective sequential weekly forecasts for Brazil, Canada, France, Germany, Spain, the United Kingdom, the United States and at the global scale using an auto-regressive integrated moving average (ARIMA) model, generalized additive model, simple linear regression, Facebook's Prophet model, as well as the sub-epidemic wave and n-sub-epidemic modelling frameworks. We assessed forecast performance using average mean squared error, mean absolute error, weighted interval scores, 95% prediction interval coverage, skill scores and Winkler scores. Overall, the n-sub-epidemic modelling framework outcompeted other models across most locations and forecasting horizons, with the unweighted ensemble model performing best most frequently. The n-sub-epidemic and spatial-wave frameworks considerably improved in average forecasting performance relative to the ARIMA model (greater than 10%) for all performance metrics. Findings further support sub-epidemic frameworks for short-term forecasting epidemics of emerging and re-emerging infectious diseases.

ObjectiveSexual violence is endemic on college campuses. Four-year campuses present high-risk environments for sexual violence and heavy episodic drinking is a robust risk factor for victimization. However, limited literature exists on sexual violence at two-year institutions, with most research focused on four-year campuses. We examined whether campus climates affect sexual violence prevalence rates.ParticipantsSexual misconduct campus climate data from two-year and four-year campus students.MethodsWe used Bayesian logistic regressions to compare sexual victimization odds between two- and four-year campuses.ResultsFour-year students were twice as likely to have experienced sexual victimization and 2.5 times more likely to engage in heavy episodic drinking compared to two-year students. The risk of sexual victimization associated with heavy episodic drinking was reliably similar across campus types.ConclusionsCampus climates reliably impact student's risk of sexual victimization. Based on these findings, two- and four-year campuses may need to implement distinct prevention services.

Simple dynamic modeling tools can help generate real-time short-term forecasts with quantified uncertainty of the trajectory of diverse growth processes unfolding in nature and society, including disease outbreaks. An easy-to-use and flexible toolbox for this purpose is lacking. This tutorial-based primer introduces and illustrates GrowthPredict, a user-friendly MATLAB toolbox for fitting and forecasting time-series trajectories using phenomenological dynamic growth models based on ordinary differential equations. This toolbox is accessible to a broad audience, including students training in mathematical biology, applied statistics, and infectious disease modeling, as well as researchers and policymakers who need to conduct short-term forecasts in real-time. The models included in the toolbox capture exponential and sub-exponential growth patterns that typically follow a rising pattern followed by a decline phase, a common feature of contagion processes. Models include the 1-parameter exponential growth model and the 2-parameter generalized-growth model, which have proven useful in characterizing and forecasting the ascending phase of epidemic outbreaks. It also includes the 2-parameter Gompertz model, the 3-parameter generalized logistic-growth model, and the 3-parameter Richards model, which have demonstrated competitive performance in forecasting single peak outbreaks. We provide detailed guidance on forecasting time-series trajectories and available software ( https://github.com/gchowell/forecasting_growthmodels ), including the full uncertainty distribution derived through parametric bootstrapping, which is needed to construct prediction intervals and evaluate their accuracy. Functions are available to assess forecasting performance across different models, estimation methods, error structures in the data, and forecasting horizons. The toolbox also includes functions to quantify forecasting performance using metrics that evaluate point and distributional forecasts, including the weighted interval score. This tutorial and toolbox can be broadly applied to characterizing and forecasting time-series data using simple phenomenological growth models. As a contagion process takes off, the tools presented in this tutorial can help create forecasts to guide policy regarding implementing control strategies and assess the impact of interventions. The toolbox functionality is demonstrated through various examples, including a tutorial video, and the examples use publicly available data on the monkeypox (mpox) epidemic in the USA.

Mathematical models based on systems of ordinary differential equations (ODEs) are frequently applied in various scientific fields to assess hypotheses, estimate key model parameters, and generate predictions about the system's state. To support their application, we present a comprehensive, easy-to-use, and flexible MATLAB toolbox, QuantDiffForecast, and associated tutorial to estimate parameters and generate short-term forecasts with quantified uncertainty from dynamical models based on systems of ODEs. We provide software (https://github.com/gchowell/paramEstimation_forecasting_ODEmodels/) and detailed guidance on estimating parameters and forecasting time-series trajectories that are characterized using ODEs with quantified uncertainty through a parametric bootstrapping approach. It includes functions that allow the user to infer model parameters and assess forecasting performance for different ODE models specified by the user, using different estimation methods and error structures in the data. The tutorial is intended for a diverse audience, including students training in dynamic systems, and will be broadly applicable to estimate parameters and generate forecasts from models based on ODEs. The functions included in the toolbox are illustrated using epidemic models with varying levels of complexity applied to data from the 1918 influenza pandemic in San Francisco. A tutorial video that demonstrates the functionality of the toolbox is included.

The 2022–2023 mpox outbreak exhibited an uneven global distribution. While countries such as the UK, Brazil, and the USA were most heavily affected in 2022, many Asian countries, specifically China, Japan, South Korea, and Thailand, experienced the outbreak later, in 2023, with significantly fewer reported cases relative to their populations. This variation in timing and scale distinguishes the outbreaks in these Asian countries from those in the first wave. This study evaluates the predictability of mpox outbreaks with smaller case counts in Asian countries using popular epidemic forecasting methods, including the ARIMA, Prophet, GLM, GAM, n-Sub-epidemic, and Sub-epidemic Wave frameworks. Despite the fact that the ARIMA and GAM models performed well for certain countries and prediction windows, their results were generally inconsistent and highly dependent on the country, i.e., the dataset, as well as the prediction interval length. In contrast, n-Sub-epidemic Ensembles demonstrated more reliable and robust performance across different datasets and predictions, indicating the effectiveness of this model on small datasets and its utility in the early stages of future pandemics.

We consider general nonlinear function-on-scalar (FOS) regression models, where the functional response depends on multiple scalar predictors in a general unknown nonlinear form. Existing methods either assume specific model forms (e.g., additive models) or directly estimate the nonlinear function in a space with dimension equal to the number of scalar predictors, which can only be applied to models with a few scalar predictors. To overcome these shortcomings, motivated by the classic universal approximation theorem used in neural networks, we develop a functional universal approximation theorem which can be used to approximate general nonlinear FOS maps and can be easily adopted into the framework of functional data analysis. With this theorem and utilizing smoothness regularity, we develop a novel method to fit the general nonlinear FOS regression model and make predictions. Our new method does not make any specific assumption on the model forms, and it avoids the direct estimation of nonlinear functions in a space with dimension equal to the number of scalar predictors. By estimating a sequence of bivariate functions, our method can be applied to models with a relatively large number of scalar predictors. The good performance of the proposed method is demonstrated by empirical studies on various simulated and real datasets.

Background:While low body mass index (BMI) is associated with poor tuberculosis (TB) treatment outcomes, the impact of weight gain during TB treatment is unclear. To address this knowledge gap, we assessed if lack of weight gain is associated with all-cause mortality during and after TB treatment. Methods:We conducted a retrospective cohort study among adults with newly diagnosed multi- or extensively drug-resistant (M/XDR) pulmonary TB in Georgia between 2009-2020. The exposure was a change in BMI during the first 3-6 months of TB treatment. All-cause mortality during and after TB treatment was assessed using the National Death Registry. We used competing-risk Cox proportional hazard models to estimate adjusted hazard ratios (aHR) between BMI change and all-cause mortality. Results:Among 720 adult participants, 21% had low BMI (<18.5 kg/m2) at treatment initiation and 9% died either during (n=16) or after treatment (n=50). During the first 3-6 months of TB treatment, 17% lost weight and 14% had no weight change. Among 479 adults with normal baseline BMI ( ≥18.5-24.9 kg/m2), weight loss was associated with an increased risk of death during TB treatment (aHR=5.25; 95%CI: 1.31-21.10). Among 149 adults with a low baseline BMI, no change in BMI was associated with increased post-TB treatment mortality (aHR=4.99; 95%CI: 1.25-19.94). Conclusions:Weight loss during TB treatment (among those with normal baseline BMI) or no weight gain (among those with low baseline BMI) was associated with increased rates of all-cause mortality. Our findings suggest that scaling up weight management interventions among those with M/XDR TB may be beneficial.