Practical Smoothing

Eilers, Paul H.C.; Marx, Brian D.

doi:10.1017/9781108610247

Cited by 53 publications

(42 citation statements)

References 132 publications

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“…P-splines (penalized B-splines) are B-splines with a difference penalty applied to the coefficients to control the smoothness, and thus overfitting ( Eilers and Marx, 1996 ). The P-spline approach is very powerful to model any profile without a priori knowledge of the data and to provide interpretable coefficients ( Eilers and Marx, 2021 ; Wood, 2006 ). It has been used in many applications and theoretical works ( Eilers et al , 2015 ), such as data smoothing ( Currie and Durban, 2002 ), Bayesian statistics ( Gressani and Lambert, 2021 ) and machine learning with generalized additive models ( Brezger and Lang, 2006 ; Wood, 2006 ).…”

Section: Methodsmentioning

confidence: 99%

ptairMS: real-time processing and analysis of PTR-TOF-MS data for biomarker discovery in exhaled breath

2022

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Motivation Analysis of Volatile Organic Compounds (VOCs) in exhaled breath by Proton Transfer Reaction Time-of-Flight Mass Spectrometry (PTR-TOF-MS) is of increasing interest for real-time, non-invasive diagnosis, phenotyping and therapeutic drug monitoring in the clinics. However, there is currently a lack of methods and software tools for the processing of PTR-TOF-MS data from cohorts and suited for biomarker discovery studies. Results We developed a comprehensive suite of algorithms that process raw data from patient acquisitions and generate the table of feature intensities. Notably, we included an innovative 2D peak deconvolution model based on penalized splines signal regression for accurate estimation of the temporal profile and feature quantification, as well as a method to specifically select the VOCs from exhaled breath. The workflow was implemented as the ptairMS software, which contains a graphical interface to facilitate cohort management and data analysis. The approach was validated on both simulated and experimental data sets, and we showed that the sensitivity and specificity of the VOC detection reached 99% and 98.4%, respectively, and that the error of quantification was below 8.1% for concentrations down to 19 ppb. Availability The ptairMS software is publicly available as an R package on Bioconductor (doi:10.18129/B9.bioc.ptairMS), as well as its companion experiment package ptairData (doi:10.18129/B9.bioc.ptairData). Supplementary information Supplementary data are available at Bioinformatics online.

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Section: Methodsmentioning

confidence: 99%

ptairMS: real-time processing and analysis of PTR-TOF-MS data for biomarker discovery in exhaled breath

2022

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“…The parameter λ > 0 acts as a tuning parameter calibrating the “degree” of smoothness and is a penalty matrix built from r th order difference matrices D r of dimension ( K − r ) × K perturbed by an ε -multiple (here ε = 10 −6 ) of the K -dimensional identity matrix I K to ensure full rankedness. The reader is redirected to Eilers and Marx (2021) for a complete textbook treatment of P-splines. Following Lang and Brezger (2004), we impose a Gaussian prior on the spline vector , with precision matrix Q λ = λP .…”

Section: Methodology Behind Epilpsmentioning

confidence: 99%

EpiLPS: a fast and flexible Bayesian tool for near real-time estimation of the time-varying reproduction number

Gressani

Wallinga

Althaus

et al. 2021

Preprint

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In infectious disease epidemiology, the instantaneous reproduction number R(t) is a timevarying metric defined as the average number of secondary infections generated by individuals who are infectious at time t. It is therefore a crucial epidemiological parameter that assists public health decision makers in the management of an epidemic. We present a new Bayesian tool for robust estimation of the time-varying reproduction number. The proposed methodology smooths the epidemic curve and allows to obtain (approximate) point estimates and credible envelopes of R(t) by employing the renewal equation, using Bayesian P-splines coupled with Laplace approximations of the conditional posterior of the spline vector. Two alternative approaches for inference are presented: (1) an approach based on a maximum a posteriori argument for the model hyperparameters, delivering estimates of R(t) in only a few seconds; and (2) an approach based on a MCMC scheme with underlying Langevin dynamics for efficient sampling of the posterior target distribution. Case counts per unit of time are assumed to follow a Negative Binomial distribution to account for potential excess variability in the data that would not be captured by a classic Poisson model. Furthermore, after smoothing the epidemic curve, a “plug-in” estimate of the reproduction number can be obtained from the renewal equation yielding a closed form expression of R(t) as a function of the spline parameters. The approach is extremely fast and free of arbitrary smoothing assumptions. EpiLPS is applied on data of SARS-CoV-1 in Hong-Kong (2003), influenza A H1N1 (2009) in the USA and current SARS-CoV-2 pandemic (2020-2021) for Belgium, Portugal, Denmark and France.Author summaryThe instantaneous reproduction number R(t) is a key metric that provides important insights into an epidemic outbreak. We present a flexible Bayesian approach called EpiLPS (Epidemiological modeling with Laplacian-P-splines) for smooth estimation of the epidemic curve and R(t). Computational speed and absence of arbitrary assumptions on smoothing makes EpiLPS an interesting tool for near real-time estimation of the reproduction number. An R software package is available (https://github.com/oswaldogressani).

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“…The TCATA data were fitted by generalized linear models (GLM) (Fahrmeir & Gerhard, 2001), using a Poisson link function to accommodate for the binary data and an additional roughness penalty to suppress differences between adjacent counts (Eilers, 2007, 2017). For background information on Poisson regression for count data, the reader is referred to (Eilers & Marx, 2021; Hilbe, 2014).…”

Section: Theorymentioning

confidence: 99%

“…The fitted curve should be made as smooth as possible but not at the cost of a lack‐of‐fit. Optimal smoothing can be obtained by estimation of

λ

by means of cross‐validation (Eilers & Marx, 2021) or by applying Akaikes's information criterion (Akaike, 1974). For this study, the choice of

λ

did not appear to be critical as the curves were already fairly smooth through data processing (bucketing).…”

Section: Theorymentioning

confidence: 99%

“…Temporal resolution can safely be decreased (up to a factor of 2 or 3) because the panelists sensory response time is much larger compared to the sampling time (commonly 1 s). The improved TCATA data analysis tool was implemented as an R‐package (Eilers & Marx, 2021; CTAN‐repository libraries used: stats, tictoc, reshape, stringr, colorspace, ggplot2, directlabels, and RColorBrewer) and applied to sweetened yogurt and fortified gummy bear candy to assess sensory specificity (targeted attributes) and sensitivity (counts) as evoked by flavor‐enhancing formulations, that is, both for initial and long‐term (aftertaste and lingering) effects. The TCATA data were obtained with professionally trained and experienced panels, using replicates for each sample.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Visualizing dynamic (after)taste effects by means of time‐discrete TCATA data analysis

Derks

Ramnarain²,

Zhang³

et al. 2022

Journal of Sensory Studies

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A time-discrete temporal check-all-that-apply (TCATA) data analysis method was implemented and applied to two different commercial use cases: (I) exploration of the dynamic sensory effects evoked by sweetened yogurt, and (II) a dynamic flavor profile comparison of nutritionally fortified gummy bears. The purpose of the first study was to explore opportunities for calorie reduction while maintaining the original dynamic sensory profile. The purpose of the second study was to benchmark commercially available fortified candy for (after)taste. The resulting time-discrete data were fitted with Poisson regression allowing means for computing confidence intervals for each discrete time bucket. A roughness penalty was added to impose smoothness to the fitted TCATA profiles. Both studies demonstrated improved visualization and revealed underlying dynamic sensory insights which were hidden in conventional TCATA profiles based on the primary data. Practical ApplicationsTemporal sensory effects-determining onset, intensity, and duration (aka lingering) of various attributes-are key for consumer acceptance of new food products. However, cross-modal interactions and the complexity of sensory attributes can limit the discrimination between different products. This study established a generic toolbox to process raw temporal (i.e., TCATA) data and improve visualization and discrimination. These results help to quantify and identify possible methodologies to improve ingredient applications for healthy foods (e.g., sugar reduction, nutrient fortification).The tool is available for analyzing TCATA data acquired with commercially available sensory data acquisition software products like EyeQuestion, FIZZ, and Compusense. | INTRODUCTIONTCATA is a time-resolved extension of the classical CATA (Adams,

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Practical Smoothing

Cited by 53 publications

References 132 publications

ptairMS: real-time processing and analysis of PTR-TOF-MS data for biomarker discovery in exhaled breath

ptairMS: real-time processing and analysis of PTR-TOF-MS data for biomarker discovery in exhaled breath

EpiLPS: a fast and flexible Bayesian tool for near real-time estimation of the time-varying reproduction number

Visualizing dynamic (after)taste effects by means of time‐discrete TCATA data analysis

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