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generalized additive models to analyze nonlinear trends in biomedical longitudinal data using R: Beyond repeated measures ANOVA and linear mixed models

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STATISTICS IN MEDICINE 2022年第21期41卷 4266-4283页

作者： Mundo, Ariel, I Muldoon, Timothy J. Tipton, John R. Univ Arkansas Dept Biomed Engn Fayetteville AR 72701 USA Univ Arkansas Dept Math Sci Fayetteville AR 72701 USA

In biomedical research, the outcome of longitudinal studies has been traditionally analyzed using the repeated measures analysis of variance (rm-ANOVA) or more recently, linear mixed models (LMEMs). Although LMEMs are less restrictive than rm-ANOVA as they can work with unbalanced data and non-constant correlation between observations, both methodologies assume a linear trend in the measured response. It is common in biomedical research that the true trend response is nonlinear and in these cases the linearity assumption of rm-ANOVA and LMEMs can lead to biased estimates and unreliable inference. In contrast, GAMs relax the linearity assumption of rm-ANOVA and LMEMs and allow the data to determine the fit of the model while also permitting incomplete observations and different correlation structures. Therefore, GAMs present an excellent choice to analyze longitudinal data with non-linear trends in the context of biomedical research. This paper summarizes the limitations of rm-ANOVA and LMEMs and uses simulated data to visually show how both methods produce biased estimates when used on data with non-linear trends. We present the basic theory of GAMs and using reported trends of oxygen saturation in tumors, we simulate example longitudinal data (2 treatment groups, 10 subjects per group, 5 repeated measures for each group) to demonstrate their implementation in R. We also show that GAMs are able to produce estimates with non-linear trends even when incomplete observations exist (with 40% of the simulated observations missing). To make this work reproducible, the code and data used in this paper are available at: .

关键词： longitudinal data biomedical data generalized additive models simulation R

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Time-varying reproduction number estimation: fusing compartmental models with generalized additive models

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JOURNAL OF THE ROYAL SOCIETY INTERFACE 2025年第222期22卷 20240518页

作者： Pang, Xiaoxi Han, Yang Tressier, Elise Aziz, Nurin Abdul Pellis, Lorenzo House, Thomas Hall, Ian Univ Manchester Dept Math Manchester England Univ Nottingham Sch Math Sci Nottingham England UK Hlth Secur Agcy COVID 19 Vaccines & Epidemiol London England

The reproduction number, the mean number of secondary cases infected by each primary case, gives an indication of the effort required to control the disease. Beyond the well-known basic reproduction number, there are two natural extensions, namely the control and effective reproduction numbers. As behaviour, population immunity and viral characteristics can change with time, these reproduction numbers can vary over time. Real-world data can be complex, so in this work we consider a generalized additive model to smooth surveillance data through the explicit incorporation of day-of-the-week effects, to provide a simple measure of the time-varying growth rate associated with the data. Converting the resulting spline into an estimator for both the control and effective reproduction numbers requires assumptions on a model structure, which we here assume to be a compartmental model. The reproduction numbers calculated are based on both simulated and real-world data, and are compared with estimates from an already existing tool. The derived method for estimating the time-varying reproduction number is effective, efficient and comparable with other methods. It provides a useful alternative approach, which can be included as part of a toolbox of models, that is particularly apt at smoothing out day-of-the-week effects in surveillance.

关键词： reproduction number time-varying transmission compartmental models generalized additive models

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Evaluating the robustness of generalized additive models as a tool for threshold detection in variable environments

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ECOSPHERE 2025年第3期16卷

作者： Detmer, A. Raine Ward, Eric J. Hunsicker, Mary E. Andrews, Kelly S. Conrad, Michele Ferriss, Bridget E. Hazen, Elliott L. Holsman, Kirstin K. Indivero, Julia Large, Scott I. Malick, Michael Marshall, Kristin N. Munsch, Stuart H. Oken, Kiva L. Satterthwaite, William H. Shotwell, S. Kalei Thompson, Andrew R. Samhouri, Jameal F. Univ Calif Santa Barbara Dept Ecol Evolut & Marine Biol Santa Barbara CA 93106 USA NOAA Conservat Biol Div Northwest Fisheries Sci Ctr Natl Marine Fisheries Serv Seattle WA USA NOAA Northwest Fisheries Sci Ctr Natl Marine Fisheries Serv Newport OR USA Oceanbeat Consulting LLC Olympia WA USA NOAA Resource Ecol & Fisheries Management Div Alaska Fisheries Sci Ctr Natl Marine Fisheries Serv Seattle WA USA NOAA Ecosyst Sci Div Southwest Fisheries Sci Ctr Monterey CA USA NOAA Natl Marine Fisheries Serv Alaska Fisheries Sci Ctr Seattle WA USA Univ Washington Sch Aquat & Fishery Sci Seattle WA USA NOAA Natl Marine Fisheries Serv Northeast Fisheries Sci Ctr Woods Hole MA USA NOAA Northwest Fisheries Sci Ctr Natl Marine Fisheries Serv Port Orchard WA USA NOAA Fishery Resource Anal & Monitoring Div Northwest Fisheries Sci Ctr Natl Marine Fisheries Serv Seattle WA USA NOAA Northwest Fisheries Sci Ctr Natl Marine Fisheries Serv Pasco WA USA NOAA Fisheries Ecol Div Southwest Fisheries Sci Ctr Natl Marine Fisheries Serv Santa Cruz CA USA NOAA Ecosyst Sci Div Southwest Fisheries Sci Ctr Natl Marine Fisheries Serv La Jolla CA USA

As global climate change and anthropogenic activities amplify widespread environmental variability, there is a strong need for management strategies that incorporate relationships between ecosystem components. This need is especially apparent when changes in environmental drivers cause threshold responses (abrupt, nonlinear changes) in ecosystems. Such ecological thresholds can provide useful reference points for management decisions. However, methods for detecting thresholds in empirical datasets may fail to find an existing threshold, find one that does not exist, or be biased in their estimates of threshold locations. These types of threshold misspecifications can result in high conservation and socioeconomic costs. Simulation studies can mitigate these risks by providing information about method performance across different scenarios. Here, we constructed a series of simulations to evaluate the robustness of threshold detection with generalized additive models (GAMs) when exposed to a variety of common, real-world data characteristics. GAMs generally performed best when time series were long, observation error was low, thresholds were crossed fairly frequently, and covariates were accounted for. Over realistic ranges of values, observation error and frequency of threshold crossing had stronger effects on threshold detectability than time series length. Importantly, detectability was found to depend on both the shape of the threshold relationship and the statistical definition of the threshold location. As a case study, we applied this threshold detection method to an empirical dataset relating ocean temperature and the spatial distribution of Pacific hake (Merluccius productus), the largest volume fishery on the US West Coast. While the data suggest no statistical evidence for a threshold relationship, our simulations indicated approximately equal chances of true and false threshold detection given currently available data. Our results provide general guidelines

关键词： ecosystem thresholds ecosystem-based management generalized additive models Pacific hake reference points simulation studies

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Nonlinear Patterns of Surface Elevation Change in Coastal Wetlands: the Value of generalized additive models for Quantifying Rates of Change

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ESTUARIES AND COASTS 2024年第7期47卷 1893-1902页

作者： Feher, Laura C. Osland, Michael J. Johnson, Darren J. Grace, James B. Guntenspergen, Glenn R. Stewart, David R. Coronado-Molina, Carlos Sklar, Fred H. US Geol Survey Lafayette LA 70506 USA US Geol Survey Laurel MD 20708 USA US Fish & Wildlife Serv Albuquerque NM 87101 USA South Florida Water Management Dist W Palm Beach FL 33406 USA

In the face of accelerating climate change and rising sea levels, quantifying surface elevation change dynamics in coastal wetlands can help to develop a more complete understanding of the implications of sea-level rise on coastal wetland stability. The surface elevation table-marker horizon (SET-MH) approach has been widely used to quantify and characterize surface elevation change dynamics in coastal marshes and mangrove forests. Whereas past studies that utilized the SET-MH approach have most often quantified rates of surface elevation change using simple linear regression analyses, several recent studies have shown that elevation patterns can include a diverse combination of linear and non-linear patterns. generalized additive models (GAMs) are an extension of generalized linear models (GLMs) that have previously been used to analyze a variety of complex ecological processes such as cyclical changes in water quality, species distributions, long-term patterns in wetland area change, and palaeoecological time series. Here, we use long-term SET data to demonstrate the value of generalized additive models for analyzing non-linear patterns of surface elevation change in coastal wetlands. Additionally, we illustrate how the GAM approach can be used to effectively quantify rates of elevation change at both landscape- and local site-level scales.

关键词： Surface elevation change Vertical accretion Sea-level rise Coastal wetlands SET-MH Surface elevation table Marker horizon generalized additive models

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Modeling Complex Concentration-Discharge Relationships with generalized additive models

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ENVIRONMENTAL MODELING & ASSESSMENT 2023年第6期28卷 925-937页

作者： von Bromssen, Claudia Folster, Jens Kyllmar, Katarina Bieroza, Magdalena Swedish Univ Agr Sci Dept Energy & Technol Div Appl Stat & Math POB 7032 S-75007 Uppsala Sweden Swedish Univ Agr Sci Dept Aquat Sci & Assessment Sect Geochem & Hydrol POB 7050 S-75007 Uppsala Sweden Swedish Univ Agr Sci Dept Soil & Environm Agr Water Management POB 7014 S-75007 Uppsala Sweden

Concentration-discharge relationships in water chemical time series can provide important insights into sources, mobilization, and delivery of solutes and particulates into stream networks. The observed relationships are often complex, including nonlinear and hysteretic patterns reflecting seasonal, climatic, and land management changes in biogeochemical release and hydrological transport of solutes and particulates to streams. Using standard single concentration-discharge (c-q) slopes can obscure this wealth of information. In this study, we suggest a new approach using generalized additive models for evaluation of complex c-q patterns in low-frequency water quality data (only monthly or biweekly observations). We used these models to estimate c-q slopes together with their uncertainty, to provide evidence of changes in c-q behaviors and their controls. We estimated c-q slopes for a selection of Swedish streams and evaluated their nonlinear, seasonal, and temporal structure as indicators of changing hydrological or biochemical drivers.

关键词： Concentration-discharge relationship generalized additive models Time-varying relationships Nonlinearity Water quality

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generalized additive models reveal among-stand variation in live tree biomass equations

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CANADIAN JOURNAL OF FOREST RESEARCH 2021年第4期51卷 546-564页

作者： Levine, Jacob de Valpine, Perry Battles, John Univ Calif Berkeley Dept Environm Sci Policy & Management Berkeley CA 94720 USA

Accurate estimation of forest biomass is important for scientists and policymakers interested in carbon accounting, nutrient cycling, and forest resilience. Estimates often rely on the allometry of trees;however, limited datasets, uncertainty in model form, and unaccounted-for sources of variation warrant a reexamination of allometric relationships using modern statistical techniques. We asked the following questions: (i) Is there among-stand variation in allometric relationships? (ii) Is there nonlinearity in allometric relationships? ( iii) Can among-stand variation or nonlinearities in allometric equations be attributed to differences in stand age? (iv) What are the implications for biomass estimation? To answer these questions, we synthesized a dataset of small trees from six different studies in the White Mountains of New Hampshire. We compared the performance of generalized additive models (GAMs) and linear models and found that GAMs consistently outperform linear models. The best-fitting model indicates that allometries vary among both stands and species and contain subtle nonlinearities that are themselves variable by species. Using a planned contrasts analysis, we were able to attribute some of the observed among- stand heterogeneity to differences in stand age. However, variability in these results points to additional sources of stand-level heterogeneity, which if identified could improve the accuracy of live tree biomass estimation.

关键词： biomass estimation tree allometry generalized additive models stand effects

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Statistical modelling of COVID-19 data: Putting generalized additive models to work

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STATISTICAL MODELLING 2024年第4期24卷 344-367页

作者： Fritz, Cornelius De Nicola, Giacomo Rave, Martje Weigert, Maximilian Khazaei, Yeganeh Berger, Ursula Kuechenhoff, Helmut Kauermann, Goeran Ludwig Maximilians Univ Munchen Dept Stat Ludwigstr 33 D-80539 Munich Germany Ludwig Maximilians Univ Munchen Inst Med Informat Proc Biometry & Epidemiol Munich Germany

Over the course of the COVID-19 pandemic, generalized additive models (GAMs) have been successfully employed on numerous occasions to obtain vital data-driven insights. In this article we further substantiate the success story of GAMs, demonstrating their flexibility by focusing on three relevant pandemic-related issues. First, we examine the interdepency among infections in different age groups, concentrating on school children. In this context, we derive the setting under which parameter estimates are independent of the (unknown) case-detection ratio, which plays an important role in COVID-19 surveillance data. Second, we model the incidence of hospitalizations, for which data is only available with a temporal delay. We illustrate how correcting for this reporting delay through a nowcasting procedure can be naturally incorporated into the GAM framework as an offset term. Third, we propose a multinomial model for the weekly occupancy of intensive care units (ICU), where we distinguish between the number of COVID-19 patients, other patients and vacant beds. With these three examples, we aim to showcase the practical and 'off-the-shelf' applicability of GAMs to gain new insights from real-world data.

关键词： Case-detection ratio COVID-19 generalized additive models modelling icu occupancy nowcasting

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A sparse estimate based on variational approximations for semiparametric generalized additive models

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COMPUTATIONAL STATISTICS 2024年第4期39卷 1971-1992页

作者： Yang, Fan Yang, Yuehan Cent Univ Finance & Econ Sch Stat & Math Beijing Peoples R China

In semiparametric regression, traditional methods such as mixed generalized additive models (GAM), computed via Laplace approximation or variational approximation using penalized marginal likelihood estimation, may not achieve sparsity and unbiasedness simultaneously, and may sometimes suffer from convergence problems. To address these issues, we propose an estimator for semiparametric generalized additive models based on the marginal likelihood. Our approach provides sparsity estimates and allows for statistical inference. To estimate and select variables, we use the smoothly clipped absolute deviation penalty (SCAD) within the framework of variational approximation. We also propose efficient iterative algorithms to obtain estimations. Simulation results support our theoretical characteristics, and we demonstrate that our method is more effective than the original variational approximations framework and many other penalized methods under certain conditions. Moreover, applications with actual data further demonstrate the superior performance of the proposed method.

关键词： Variational approximation generalized additive models Penalized splines Semiparametric regression

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generalized additive models to assess Truck Driver's Perceived LOS of Signalized Intersections

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Transportation Research Procedia 2025年 82卷 2232-2244页

作者： Sujeet Sahoo Changati Sudha Prasanta kumar Bhuyan Ph. D. Scholar Civil Engineering department National Insititute of Technology Rourkela Odisha 769008 India Former M. Tech. Student National Insititute of Technology Rourkela Odisha 769008 India Asisstant professor National Insititute of Technology Rourkela Odisha 769008 India

Modern freight transportation relies on trucks delivering millions of packages daily. There is limited research on urban infrastructure service quality, particularly signalized intersections for truck traffic use. Trucks experiences different service levels due to their low maneuverability, acceleration and deceleration. As India's economy grows rapidly in turn, resulting high truck demand in turn requiring truck service quality examination. This study collects traffic, geometric and conglomerative data from five Indian cities with 30 signalized intersections and 105 approaches. Truck drivers' satisfaction is collected at city outskirts where truck traffic is significant. Truck Level of Service (TLOS) is modelled using variables which have statistically significant correlation with perceived satisfaction score using Spearman correlation analysis. generalized additive models (GAMs) use these variables as inputs. It is a intermediate modelling approach to black box machine learning algorithms and simple statistical models; which has a strong capability of handling the non-linearity in the perceived scores. In this study, six parameters affect TLOS, while some manuals use V/C ratio or control delay only for LOS estimation. Final GAM-TLOS model shows high accuracy with 0.92 R2. GAM-TLOS scores for service classes A-F obtained by linear interpretation of Likert Scale is valuable tool for Planners and designers.

关键词： Truck Traffic Heterogeinous Traffic Level of Service Perception Modelling generalized additive models

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Distill knowledge of additive tree models into generalized linear models: a new learning approach for non-smooth generalized additive models

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ANNALS OF ACTUARIAL SCIENCE 2024年第3期18卷 692-711页

作者： Maillart, Arthur Robert, Christian Detralytics Saint Josse Ten Noode Belgium Univ Lyon 1 Inst Sci Financiere & Assurances Lyon France Ctr Res Econ & Stat Lab Finance & Insurance LFA CREST Paris France

generalized additive models (GAMs) are a leading model class for interpretable machine learning. GAMs were originally defined with smooth shape functions of the predictor variables and trained using smoothing splines. Recently, tree-based GAMs where shape functions are gradient-boosted ensembles of bagged trees were proposed, leaving the door open for the estimation of a broader class of shape functions (e.g. Explainable Boosting Machine (EBM)). In this paper, we introduce a competing three-step GAM learning approach where we combine (i) the knowledge of the way to split the covariates space brought by an additive tree model (ATM), (ii) an ensemble of predictive linear scores derived from generalized linear models (GLMs) using a binning strategy based on the ATM, and (iii) a final GLM to have a prediction model that ensures auto-calibration. Numerical experiments illustrate the competitive performances of our approach on several datasets compared to GAM with splines, EBM, or GLM with binarsity penalization. A case study in trade credit insurance is also provided.

关键词： additive tree ensembles auto-calibration generalized additive models generalized linear models partitioning methods XAI

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