Bayesian Semiparametric Longitudinal Inverse-Probit Mixed Models for Category Learning

Understanding how the adult human brain learns novel categories is an important problem in neuroscience. Drift-diffusion models are popular in such contexts for their ability to mimic the underlying neural mechanisms. One such model for gradual longitudinal learning was recently developed in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). In practice, category response accuracies are often the only reliable measure recorded by behavioral scientists to describe human learning. Category response accuracies are, however, often the only reliable measure recorded by behavioral scientists to describe human learning. To our knowledge, however, drift-diffusion models for such scenarios have never been considered in the literature before. To address this gap, in this article, we build carefully on Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021), but now with latent response times integrated out, to derive a novel biologically interpretable class of 'inverse-probit' categorical probability models for observed categories alone. However, this new marginal model presents significant identifiability and inferential challenges not encountered originally for the joint model in Paulon et al. (J Am Stat Assoc 116:1114-1127, 2021). We address these new challenges using a novel projection-based approach with a symmetry-preserving identifiability constraint that allows us to work with conjugate priors in an unconstrained space. We adapt the model for group and individual-level inference in longitudinal settings. Building again on the model's latent variable representation, we design an efficient Markov chain Monte Carlo algorithm for posterior computation. We evaluate the empirical performance of the method through simulation experiments. The practical efficacy of the method is illustrated in applications to longitudinal tone learning studies.

Using Deep Learning and B-Splines to Model Blood Vessel Lumen from 3D Images

Accurate geometric modeling of blood vessel lumen from 3D images is crucial for vessel quantification as part of the diagnosis, treatment, and monitoring of vascular diseases. Our method, unlike other approaches which assume a circular or elliptical vessel cross-section, employs parametric B-splines combined with image formation system equations to accurately localize the highly curved lumen boundaries. This approach avoids the need for image segmentation, which may reduce the localization accuracy due to spatial discretization. We demonstrate that the model parameters can be reliably identified by a feedforward neural network which, driven by the cross-section images, predicts the parameter values many times faster than a reference least-squares (LS) model fitting algorithm. We present and discuss two example applications, modeling the lower extremities of artery-vein complexes visualized in steady-state contrast-enhanced magnetic resonance images (MRI) and the coronary arteries pictured in computed tomography angiograms (CTA). Beyond applications in medical diagnosis, blood-flow simulation and vessel-phantom design, the method can serve as a tool for automated annotation of image datasets to train machine-learning algorithms.

Bayesian kernel machine regression for count data: modelling the association between social vulnerability and COVID-19 deaths in South Carolina

The COVID-19 pandemic created an unprecedented global health crisis. Recent studies suggest that socially vulnerable communities were disproportionately impacted, although findings are mixed. To quantify social vulnerability in the US, many studies rely on the Social Vulnerability Index (SVI), a county-level measure comprising 15 census variables. Typically, the SVI is modelled in an additive manner, which may obscure non-linear or interactive associations, further contributing to inconsistent findings. As a more robust alternative, we propose a negative binomial Bayesian kernel machine regression (BKMR) model to investigate dynamic associations between social vulnerability and COVID-19 death rates, thus extending BKMR to the count data setting. The model produces a 'vulnerability effect' that quantifies the impact of vulnerability on COVID-19 death rates in each county. The method can also identify the relative importance of various SVI variables and make future predictions as county vulnerability profiles evolve. To capture spatio-temporal heterogeneity, the model incorporates spatial effects, county-level covariates, and smooth temporal functions. For Bayesian computation, we propose a tractable data-augmented Gibbs sampler. We conduct a simulation study to highlight the approach and apply the method to a study of COVID-19 deaths in the US state of South Carolina during the 2021 calendar year.

M-quantile regression shrinkage and selection via the Lasso and Elastic Net to assess the effect of meteorology and traffic on air quality

In this work, we intersect data on size-selected particulate matter (PM) with vehicular traffic counts and a comprehensive set of meteorological covariates to study the effect of traffic on air quality. To this end, we develop an M-quantile regression model with Lasso and Elastic Net penalizations. This allows (i) to identify the best proxy for vehicular traffic via model selection, (ii) to investigate the relationship between fine PM concentration and the covariates at different M-quantiles of the conditional response distribution, and (iii) to be robust to the presence of outliers. Heterogeneity in the data is accounted by fitting a B-spline on the effect of the day of the year. Analytic and bootstrap-based variance estimates of the regression coefficients are provided, together with a numerical evaluation of the proposed estimation procedure. Empirical results show that atmospheric stability is responsible for the most significant effect on fine PM concentration: this effect changes at different levels of the conditional response distribution and is relatively weaker on the tails. On the other hand, model selection allows to identify the best proxy for vehicular traffic whose effect remains essentially the same at different levels of the conditional response distribution.

Real-Time Correction of Chromatic Aberration in Optical Fluorescence Microscopy

Multi-color fluorescence imaging is a powerful tool for studying the spatial relationships and interactions among sub-cellular structures in biological specimens. However, if improperly corrected, geometrical distortions caused by mechanical drift, refractive index mismatch, or chromatic aberration can lead to lower image resolution. In this paper, we present an extension of the image processing framework of Scipion by integrating a protocol called OFM Corrector, which corrects geometrical distortions in real-time using a B-spline-based elastic continuous registration technique. Our proposal provides a simple strategy to overcome chromatic aberration by digitally re-aligning color channels in multi-color fluorescence microscopy images, even in 3D or time. Our method relies on a geometrical calibration, which we do with fluorescent beads excited by different wavelengths of light and subsequently registered to get the elastic warp as a reference to correct chromatic shift. Our software is freely available with a user-friendly GUI and can be broadly used for various biological imaging problems. The paper presents a valuable tool for researchers working in light microscopy facilities.

Simultaneous Confidence Band Approach for Comparison of COVID-19 Case Counts

The outbreak of the novel coronavirus (COVID-19) was declared to be a global emergency in January of 2020, and everyday life throughout the world was disrupted. Among many questions about COVID-19 that remain unanswered, it is of interest for society to identify whether there is any significant difference in daily case counts between males and females. The daily case count sequences are correlated due to the nature of a contagious disease, and contain a nonlinear trend owing to several unexpected events, such as vaccinations and the appearance of the delta variant. It is possible that these unexpected events have changed the dynamical system that generates data. The classic t-test is not appropriate to analyze such correlated data with a nonconstant trend. This study applies a simultaneous confidence band approach in an attempt to overcome these difficulties; that is, a simultaneous confidence band for the trend of an autoregressive moving-average time series is constructed using B-spline estimation. The proposed method is applied to the daily case count data of seniors of both genders (at least 60 years old) in the State of Ohio from April 1, 2020 to March 31, 2022, and the result shows that there is a significant difference at the 95% confidence level between the two gender case counts adjusted for the population sizes.

clusterMLD: An Efficient Hierarchical Clustering Method for Multivariate Longitudinal Data

Longitudinal data clustering is challenging because the grouping has to account for the similarity of individual trajectories in the presence of sparse and irregular times of observation. This paper puts forward a hierarchical agglomerative clustering method based on a dissimilarity metric that quantifies the cost of merging two distinct groups of curves, which are depicted by B-splines for the repeatedly measured data. Extensive simulations show that the proposed method has superior performance in determining the number of clusters, classifying individuals into the correct clusters, and in computational efficiency. Importantly, the method is not only suitable for clustering multivariate longitudinal data with sparse and irregular measurements but also for intensely measured functional data. Towards this end, we provide an R package for the implementation of such analyses. To illustrate the use of the proposed clustering method, two large clinical data sets from real-world clinical studies are analyzed.

A machine learning method for improving liver cancer staging

Liver cancer is a common malignant tumor, and its clinical stage is closely related to the clinical treatment and prognosis of patients. Currently, the BCLC staging system revised by the BCLC group of University of Barcelona is the globally recognized staging system for liver cancer. However, with the deepening of related research, the current staging system can no longer fully meet the clinical needs. In this work, we propose a novel machine learning method for constructing an automatic hepatocellular carcinoma staging model that incorporates far more clinical variables than any existing staging system. Our model is based on random survival forests, which generates a unique hazard function for each patient. B-splines are used to embed hazard functions into vectors in low-dimensional space and hierarchical clustering method groups similar patients to form staging cohorts. The resulting staging system significantly outperforms the BCLC system in terms of distinctiveness between patients in different stages.

Efficient Approach for Extracting High-Level B-Spline Features from LIDAR Data for Light-Weight Mapping

Light-weight and accurate mapping is made possible by high-level feature extraction from sensor readings. In this paper, the high-level B-spline features from a 2D LIDAR are extracted with a faster method as a solution to the mapping problem, making it possible for the robot to interact with its environment while navigating. The computation time of feature extraction is very crucial when mobile robots perform real-time tasks. In addition to the existing assessment measures of B-spline feature extraction methods, the paper also includes a new benchmark time metric for evaluating how well the extracted features perform. For point-to-point association, the most reliable vertex control points of the spline features generated from the hints of low-level point feature FALKO were chosen. The standard three indoor and one outdoor data sets were used for the experiment. The experimental results based on benchmark performance metrics, specifically computation time, show that the presented approach achieves better results than the state-of-the-art methods for extracting B-spline features. The classification of the methods implemented in the B-spline features detection and the algorithms are also presented in the paper.

Bayesian time-varying autoregressive models of COVID-19 epidemics

The COVID-19 pandemic has highlighted the importance of reliable statistical models which, based on the available data, can provide accurate forecasts and impact analysis of alternative policy measures. Here we propose Bayesian time-dependent Poisson autoregressive models that include time-varying coefficients to estimate the effect of policy covariates on disease counts. The model is applied to the observed series of new positive cases in Italy and in the United States. The results suggest that our proposed models are capable of capturing nonlinear growth of disease counts. We also find that policy measures and, in particular, closure policies and the distribution of vaccines, lead to a significant reduction in disease counts in both countries.

Estimate of the rate of unreported COVID-19 cases during the first outbreak in Rio de Janeiro

In this work we fit an epidemiological model SEIAQR (Susceptible - Exposed - Infectious - Asymptomatic - Quarantined - Removed) to the data of the first COVID-19 outbreak in Rio de Janeiro, Brazil. Particular emphasis is given to the unreported rate, that is, the proportion of infected individuals that is not detected by the health system. The evaluation of the parameters of the model is based on a combination of error-weighted least squares method and appropriate B-splines. The structural and practical identifiability is analyzed to support the feasibility and robustness of the parameters’ estimation. We use the Bootstrap method to quantify the uncertainty of the estimates. For the outbreak of March–July 2020 in Rio de Janeiro, we estimate about 90% of unreported cases, with a 95% confidence interval (85%, 93%).

Noise Reduction in Human Motion-Captured Signals for Computer Animation based on B-Spline Filtering

Motion capturing is used to record the natural movements of humans for a particular task. The motions recorded are extensively used to produce animation characters with natural movements and for virtual reality (VR) devices. The raw captured motion signals, however, contain noises introduced during the capturing process. Therefore, the signals should be effectively processed before they can be applied to animation characters. In this study, we analyzed several common methods used for smoothing signals. The smoothed signals were then compared based on the smoothness metrics defined. It was concluded that the filtering based on the B-spline-based least square method could achieve high-quality outputs with predetermined continuity and minimal parameter adjustments for a variety of motion signals.

Joint Estimation of Monotone Curves via Functional Principal Component Analysis

A functional data approach is developed to jointly estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. In this approach, the unconstrained relative curvature curves instead of the monotone-constrained functions are directly modeled. Functional principal components are used to describe the major modes of variations of curves and allow borrowing strength across curves for improved estimation. A two-step approach and an integrated approach are considered for model fitting. The simulation study shows that the integrated approach is more efficient than separate curve estimation and the two-step approach. The integrated approach also provides more interpretable principle component functions in an application of estimating weekly wind power curves of a wind turbine.

BCurve: Bayesian Curve Credible Bands Approach for the Detection of Differentially Methylated Regions

High-throughput assays have been developed to measure DNA methylation, among which bisulfite-based sequencing (BS-seq) and microarray technologies are the most popular for genome-wide profiling. A major goal in DNA methylation analysis is the detection of differentially methylated genomic regions under two different conditions. To accomplish this, many state-of-the-art methods have been proposed in the past few years; only a handful of these methods are capable of analyzing both types of data (BS-seq and microarray), though. On the other hand, covariates, such as sex and age, are known to be potentially influential on DNA methylation; and thus, it would be important to adjust for their effects on differential methylation analysis. In this chapter, we describe a Bayesian curve credible bands approach and the accompanying software, BCurve, for detecting differentially methylated regions for data generated from either microarray or BS-Seq. The unified theme underlying the analysis of these two different types of data is the model that accounts for correlation between DNA methylation in nearby sites, covariates, and between-sample variability. The BCurve R software package also provides tools for simulating both microarray and BS-seq data, which can be useful for facilitating comparisons of methods given the known "gold standard" in the simulated data. We provide detailed description of the main functions in BCurve and demonstrate the utility of the package for analyzing data from both platforms using simulated data from the functions provided in the package. Analyses of two real datasets, one from BS-seq and one from microarray, are also furnished to further illustrate the capability of BCurve.

Right-Censored Time Series Modeling by Modified Semi-Parametric A-Spline Estimator

This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan-Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data's structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.

Varying Coefficient Mediation Model and Application to Analysis of Behavioral Economics Data

This article is concerned with causal mediation analysis with varying indirect and direct effects. We propose a varying coefficient mediation model, which can also be viewed as an extension of moderation analysis on a causal diagram. We develop a new estimation procedure for the direct and indirect effects based on B-splines. Under mild conditions, rates of convergence and asymptotic distributions of the resulting estimates are established. We further propose a F-type test for the direct effect. We conduct simulation study to examine the finite sample performance of the proposed methodology, and apply the new procedures for empirical analysis of behavioral economics data.

Magnification-driven B-spline interpolation for cone-beam projection and backprojection

PURPOSE

Discretizing tomographic forward and backward operations is a crucial step in the design of model-based reconstruction algorithms. Standard projectors rely on linear interpolation, whose adjoint introduces discretization errors during backprojection. More advanced techniques are obtained through geometric footprint models that may present a high computational cost and an inner logic that is not suitable for implementation on massively parallel computing architectures. In this work, we take a fresh look at the discretization of resampling transforms and focus on the issue of magnification-induced local sampling variations by introducing a new magnification-driven interpolation approach for tomography.

METHODS

Starting from the existing literature on spline interpolation for magnification purposes, we provide a mathematical formulation for discretizing a one-dimensional homography. We then extend our approach to two-dimensional representations in order to account for the geometry of cone-beam computed tomography with a flat panel detector. Our new method relies on the decomposition of signals onto a space generated by nonuniform B-splines so as to capture the spatially varying magnification that locally affects sampling. We propose various degrees of approximations for a rapid implementation of the proposed approach. Our framework allows us to define a novel family of projector/backprojector pairs parameterized by the order of the employed B-splines. The state-of-the-art distance-driven interpolation appears to fit into this family thus providing new insight and computational layout for this scheme. The question of data resampling at the detector level is handled and integrated with reconstruction in a single framework.

RESULTS

Results on both synthetic data and real data using a quality assurance phantom, were performed to validate our approach. We show experimentally that our approximate implementations are associated with reduced complexity while achieving a near-optimal performance. In contrast with linear interpolation, B-splines guarantee full usage of all data samples, and thus the X-ray dose, leading to more uniform noise properties. In addition, higher-order B-splines allow analytical and iterative reconstruction to reach higher resolution. These benefits appear more significant when downsampling frames acquired by X-ray flat-panel detectors with small pixels.

CONCLUSIONS

Magnification-driven B-spline interpolation is shown to provide high-accuracy projection operators with good-quality adjoints for iterative reconstruction. It equally applies to backprojection for analytical reconstruction and detector data downsampling.

Spline-Based Dense Medial Descriptors for Lossy Image Compression

Medial descriptors are of significant interest for image simplification, representation, manipulation, and compression. On the other hand, B-splines are well-known tools for specifying smooth curves in computer graphics and geometric design. In this paper, we integrate the two by modeling medial descriptors with stable and accurate B-splines for image compression. Representing medial descriptors with B-splines can not only greatly improve compression but is also an effective vector representation of raster images. A comprehensive evaluation shows that our Spline-based Dense Medial Descriptors (SDMD) method achieves much higher compression ratios at similar or even better quality to the well-known JPEG technique. We illustrate our approach with applications in generating super-resolution images and salient feature preserving image compression.

Comparison of functional and discrete data analysis regimes for Raman spectra

Raman spectral data are best described by mathematical functions; however, due to the spectroscopic measurement setup, only discrete points of these functions are measured. Therefore, we investigated the Raman spectral data for the first time in the functional framework. First, we approximated the Raman spectra by using B-spline basis functions. Afterwards, we applied the functional principal component analysis followed by the linear discriminant analysis (FPCA-LDA) and compared the results with those of the classical principal component analysis followed by the linear discriminant analysis (PCA-LDA). In this context, simulation and experimental Raman spectra were used. In the simulated Raman spectra, normal and abnormal spectra were used for a classification model, where the abnormal spectra were built by shifting one peak position. We showed that the mean sensitivities of the FPCA-LDA method were higher than the mean sensitivities of the PCA-LDA method, especially when the signal-to-noise ratio is low and the shift of the peak position is small. However, for a higher signal-to-noise ratio, both methods performed equally. Additionally, a slight improvement of the mean sensitivity could be shown if the FPCA-LDA method was applied to experimental Raman data.

Improving deformable image registration with point metric and masking technique for postoperative breast cancer radiotherapy

Background

Deformable image registration (DIR) is increasingly used for target volume definition in radiotherapy. However, this method is challenging for postoperative breast cancer patients due to the large deformations and non-correspondence caused by tumor resection and clip insertion. In this study, an improved B-splines based DIR method was developed to address this issue for higher registration accuracy.

Methods

The conventional B-splines based DIR method was improved with the introduction of point metric and masking technique. The point metric minimizes the distance between 2 point sets with known correspondence for regularization of intensity-based B-splines registration. The masking technique reduces the influence of non-corresponding regions in breast computed tomography (CT) images. Two sets of CT images before and after breast surgery were used for image registration. One set was the diagnostic CT image acquired before surgery, and another set was the planning CT image acquired after surgery for breast cancer radiotherapy. A total of 26 sets of CT images from 13 patients were collected retrospectively for the test. The improved DIR method's registration accuracy was evaluated by target registration error (TRE), the Jacobian determinant, and visual assessment.

Results

For soft tissue, the difference in the median TRE between the improved DIR method and the conventional DIR method was statistically significant (2.27 vs. 5.88, P<0.05). The Jacobian determinant of the deformation field was positive for all patients. For visual assessment, the improved DIR method with point metric achieved better matching for soft tissue.

Conclusions

The improved DIR method's registration accuracy was higher than the conventional DIR method based on the preliminary results. With point metric and masking technique, the influence of large deformations and non-correspondence on registration between pre- and post-operative CT images can be effectively reduced. Therefore, this method provides a feasible way for target volume definition in postoperative breast cancer radiotherapy treatment planning.

Fast 4D elastic group-wise image registration. Convolutional interpolation revisited

BACKGROUND AND OBJECTIVE

This paper proposes a new and highly efficient implementation of 3D+t groupwise registration based on the free-form deformation paradigm.

METHODS

Deformation is posed as a cascade of 1D convolutions, achieving great reduction in execution time for evaluation of transformations and gradients.

RESULTS

The proposed method has been applied to 4D cardiac MRI and 4D thoracic CT monomodal datasets. Results show an average runtime reduction above 90%, both in CPU and GPU executions, compared with the classical tensor product formulation.

CONCLUSIONS

Our implementation, although fully developed for the metric sum of squared differences, can be extended to other metrics and its adaptation to multiresolution strategies is straightforward. Therefore, it can be extremely useful to speed up image registration procedures in different applications where high dimensional data are involved.

Fitting a shared frailty illness-death model to left-truncated semi-competing risks data to examine the impact of education level on incident dementia

BACKGROUND

Semi-competing risks arise when interest lies in the time-to-event for some non-terminal event, the observation of which is subject to some terminal event. One approach to assessing the impact of covariates on semi-competing risks data is through the illness-death model with shared frailty, where hazard regression models are used to model the effect of covariates on the endpoints. The shared frailty term, which can be viewed as an individual-specific random effect, acknowledges dependence between the events that is not accounted for by covariates. Although methods exist for fitting such a model to right-censored semi-competing risks data, there is currently a gap in the literature for fitting such models when a flexible baseline hazard specification is desired and the data are left-truncated, for example when time is on the age scale. We provide a modeling framework and openly available code for implementation.

METHODS

We specified the model and the likelihood function that accounts for left-truncated data, and provided an approach to estimation and inference via maximum likelihood. Our model was fully parametric, specifying baseline hazards via Weibull or B-splines. Using simulated data we examined the operating characteristics of the implementation in terms of bias and coverage. We applied our methods to a dataset of 33,117 Kaiser Permanente Northern California members aged 65 or older examining the relationship between educational level (categorized as: high school or less; trade school, some college or college graduate; post-graduate) and incident dementia and death.

RESULTS

A simulation study showed that our implementation provided regression parameter estimates with negligible bias and good coverage. In our data application, we found higher levels of education are associated with a lower risk of incident dementia, after adjusting for sex and race/ethnicity.

CONCLUSIONS

As illustrated by our analysis of Kaiser data, our proposed modeling framework allows the analyst to assess the impact of covariates on semi-competing risks data, such as incident dementia and death, while accounting for dependence between the outcomes when data are left-truncated, as is common in studies of aging and dementia.

Aliasing mitigation in optical microscopy of dynamic biological samples by use of temporally modulated color illumination and a standard RGB camera

SIGNIFICANCE

Despite recent developments in microscopy, temporal aliasing can arise when imaging dynamic samples. Modern sampling frameworks, such as generalized sampling, mitigate aliasing but require measurement of temporally overlapping and potentially negative-valued inner products. Conventional cameras cannot collect these directly as they operate sequentially and are only sensitive to light intensity.

AIM

We aim to mitigate aliasing in microscopy of dynamic monochrome samples by implementing generalized sampling via the use of a color camera and modulated color illumination.

APPROACH

We solve the overlap problem by spectrally multiplexing the acquisitions and using (positive) B-spline segments as projection kernels. Reconstruction involves spectral unmixing and inverse filtering. We implemented this method using a color LED illuminator. We evaluated its performance by imaging a rotating grid and its applicability by imaging the beating zebrafish embryo heart in transmission and light-sheet microscopes.

RESULTS

Compared to stroboscopic imaging, our method mitigates aliasing with performance improving as the projection order increases. The approach can be implemented in conventional microscopes but is limited by the number of available LED colors and camera channels.

CONCLUSIONS

Generalized sampling can be implemented via color modulation in microscopy to mitigate temporal aliasing. The simple hardware requirements could make it applicable to other optical imaging modalities.

Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

Semiparametric estimation of the attributable fraction when there are interactions under monotonicity constraints

BACKGROUND

The population attributable fraction (PAF) is the fraction of disease cases in a sample that can be attributed to an exposure. Estimating the PAF often involves the estimation of the probability of having the disease given the exposure while adjusting for confounders. In many settings, the exposure can interact with confounders. Additionally, the exposure may have a monotone effect on the probability of having the disease, and this effect is not necessarily linear.

METHODS

We develop a semiparametric approach for estimating the probability of having the disease and, consequently, for estimating the PAF, controlling for the interaction between the exposure and a confounder. We use a tensor product of univariate B-splines to model the interaction under the monotonicity constraint. The model fitting procedure is formulated as a quadratic programming problem, and, thus, can be easily solved using standard optimization packages. We conduct simulations to compare the performance of the developed approach with the conventional B-splines approach without the monotonicity constraint, and with the logistic regression approach. To illustrate our method, we estimate the PAF of hopelessness and depression for suicidal ideation among elderly depressed patients.

RESULTS

The proposed estimator exhibited better performance than the other two approaches in the simulation settings we tried. The estimated PAF attributable to hopelessness is 67.99% with 95% confidence interval: 42.10% to 97.42%, and is 22.36% with 95% confidence interval: 12.77% to 56.49% due to depression.

CONCLUSIONS

The developed approach is easy to implement and supports flexible modeling of possible non-linear relationships between a disease and an exposure of interest.

Accelerating B-spline interpolation on GPUs: Application to medical image registration

BACKGROUND AND OBJECTIVE

B-spline interpolation (BSI) is a popular technique in the context of medical imaging due to its adaptability and robustness in 3D object modeling. A field that utilizes BSI is Image Guided Surgery (IGS). IGS provides navigation using medical images, which can be segmented and reconstructed into 3D models, often through BSI. Image registration tasks also use BSI to transform medical imaging data collected before the surgery and intra-operative data collected during the surgery into a common coordinate space. However, such IGS tasks are computationally demanding, especially when applied to 3D medical images, due to the complexity and amount of data involved. Therefore, optimization of IGS algorithms is greatly desirable, for example, to perform image registration tasks intra-operatively and to enable real-time applications. A traditional CPU does not have sufficient computing power to achieve these goals and, thus, it is preferable to rely on GPUs. In this paper, we introduce a novel GPU implementation of BSI to accelerate the calculation of the deformation field in non-rigid image registration algorithms.

METHODS

Our BSI implementation on GPUs minimizes the data that needs to be moved between memory and processing cores during loading of the input grid, and leverages the large on-chip GPU register file for reuse of input values. Moreover, we re-formulate our method as trilinear interpolations to reduce computational complexity and increase accuracy. To provide pre-clinical validation of our method and demonstrate its benefits in medical applications, we integrate our improved BSI into a registration workflow for compensation of liver deformation (caused by pneumoperitoneum, i.e., inflation of the abdomen) and evaluate its performance.

RESULTS

Our approach improves the performance of BSI by an average of 6.5×  and interpolation accuracy by 2×  compared to three state-of-the-art GPU implementations. Through pre-clinical validation, we demonstrate that our optimized interpolation accelerates a non-rigid image registration algorithm, which is based on the Free Form Deformation (FFD) method, by up to 34%.

CONCLUSION

Our study shows that we can achieve significant performance and accuracy gains with our novel parallelization scheme that makes effective use of the GPU resources. We show that our method improves the performance of real medical imaging registration applications used in practice today.

A varying-coefficient generalized odds rate model with time-varying exposure: An application to fitness and cardiovascular disease mortality

Varying-coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time-varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying-coefficient generalized odds rate model that allows flexible estimation of age-modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed-effects model, and its associated age-varying coefficient function is represented by cubic B-splines. An expectation-maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian-Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E-step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.

Localized G-splines for quad & T-gon meshes

Enriching tensor-product B-spline control nets by allowing T-gons (where strips of quadrilaterals start or end) and irregular nodes (where n ≠ 4 quadrilaterals meet) reduces the requirements on quad-meshing and increases the flexibility for polyhedral design with associated smooth surfaces. This paper introduces a family of piecewise polynomial, geometrically continuous surface constructions that yield good highlight line distributions also in the presence of irregular nodes next to a T-gon. Such tight juxtaposition can further reduce the quad-meshing requirements and increase the space of polyhedral design control structures. The surfaces can be chosen to cover T-gons with G ¹ caps of degree bi-4 - or with caps of degree bi-3 that are almost G ¹ and preserve the good highlight line distribution of the bi-4 G ¹ surfaces.

Semiparametric regression for measurement error model with heteroscedastic error

Covariate measurement error is a common problem. Improper treatment of measurement errors may affect the quality of estimation and the accuracy of inference. Extensive literature exists on homoscedastic measurement error models, but little research exists on heteroscedastic measurement. In this paper, we consider a general parametric regression model allowing for a covariate measured with heteroscedastic error. We allow both the variance function of the measurement errors and the conditional density function of the error-prone covariate given the error-free covariates to be completely unspecified. We treat the variance function using B-spline approximation and propose a semiparametric estimator based on efficient score functions to deal with the heteroscedasticity of the measurement error. The resulting estimator is consistent and enjoys good inference properties. Its finite-sample performance is demonstrated through simulation studies and a real data example.

Bayesian Semiparametric Multivariate Density Deconvolution

We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls. Supplementary Material presents substantive additional details.

Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles.

A Semiparametric Single-Index Risk Score Across Populations

We consider a problem motivated by issues in nutritional epidemiology, across diseases and populations. In this area, it is becoming increasingly common for diseases to be modeled by a single diet score, such as the Healthy Eating Index, the Mediterranean Diet Score, etc. For each disease and for each population, a partially linear single-index model is fit. The partially linear aspect of the problem is allowed to differ in each population and disease. However, and crucially, the single-index itself, having to do with the diet score, is common to all diseases and populations, and the nonparametrically estimated functions of the single-index are the same up to a scale parameter. Using B-splines with an increasing number of knots, we develop a method to solve the problem, and display its asymptotic theory. An application to the NIH-AARP Study of Diet and Health is described, where we show the advantages of using multiple diseases and populations simultaneously rather than one at a time in understanding the effect of increased Milk consumption. Simulations illustrate the properties of the methods.

FLEXIBLE RISK PREDICTION MODELS FOR LEFT OR INTERVAL-CENSORED DATA FROM ELECTRONIC HEALTH RECORDS

Electronic health records are a large and cost-effective data source for developing risk-prediction models. However, for screen-detected diseases, standard risk models (such as Kaplan-Meier or Cox models) do not account for key issues encountered with electronic health record data: left-censoring of pre-existing (prevalent) disease, interval-censoring of incident disease, and ambiguity of whether disease is prevalent or incident when definitive disease ascertainment is not conducted at baseline. Furthermore, researchers might conduct novel screening tests only on a complex two-phase subsample. We propose a family of weighted mixture models that account for left/interval-censoring and complex sampling via inverse-probability weighting in order to estimate current and future absolute risk: we propose a weakly-parametric model for general use and a semiparametric model for checking goodness of fit of the weakly-parametric model. We demonstrate asymptotic properties analytically and by simulation. We used electronic health records to assemble a cohort of 33,295 human papillomavirus (HPV) positive women undergoing cervical cancer screening at Kaiser Permanente Northern California (KPNC) that underlie current screening guidelines. The next guidelines would focus on HPV typing tests, but reporting 14 HPV types is too complex for clinical use. National Cancer Institute along with KPNC conducted a HPV typing test on a complex subsample of 9258 women in the cohort. We used our model to estimate the risk due to each type and grouped the 14 types (the 3-year risk ranges 21.9-1.5) into 4 risk-bands to simplify reporting to clinicians and guidelines. These risk-bands could be adopted by future HPV typing tests and future screening guidelines.

Estimating varying coefficients for partial differential equation models

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data.

Functional Mixed Effects Model for Small Area Estimation

Functional data analysis has become an important area of research due to its ability of handling high dimensional and complex data structures. However, the development is limited in the context of linear mixed effect models, and in particular, for small area estimation. The linear mixed effect models are the backbone of small area estimation. In this article, we consider area level data, and fit a varying coefficient linear mixed effect model where the varying coefficients are semi-parametrically modeled via B-splines. We propose a method of estimating the fixed effect parameters and consider prediction of random effects that can be implemented using a standard software. For measuring prediction uncertainties, we derive an analytical expression for the mean squared errors, and propose a method of estimating the mean squared errors. The procedure is illustrated via a real data example, and operating characteristics of the method are judged using finite sample simulation studies.

Gradient Matching Methods for Computational Inference in Mechanistic Models for Systems Biology: A Review and Comparative Analysis

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimized, so as to minimize some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data.

Trends in Classroom Observation Scores

Observations and ratings of classroom teaching and interactions collected over time are susceptible to trends in both the quality of instruction and rater behavior. These trends have potential implications for inferences about teaching and for study design. We use scores on the Classroom Assessment Scoring System-Secondary (CLASS-S) protocol from 458 middle school teachers over a 2-year period to study changes over time in (a) the average quality of teaching for the population of teachers, (b) the average severity of the population of raters, and (c) the severity of individual raters. To obtain these estimates and assess them in the context of other factors that contribute to the variability in scores, we develop an augmented G study model that is broadly applicable for modeling sources of variability in classroom observation ratings data collected over time. In our data, we found that trends in teaching quality were small. Rater drift was very large during raters' initial days of observation and persisted throughout nearly 2 years of scoring. Raters did not converge to a common level of severity; using our model we estimate that variability among raters actually increases over the course of the study. Variance decompositions based on the model find that trends are a modest source of variance relative to overall rater effects, rater errors on specific lessons, and residual error. The discussion provides possible explanations for trends and rater divergence as well as implications for designs collecting ratings over time.

Nonparametric inference in hidden Markov models using P-splines

Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness.

Unimodal regression using Bernstein-Schoenberg splines and penalties

Research in the field of nonparametric shape constrained regression has been intensive. However, only few publications explicitly deal with unimodality although there is need for such methods in applications, for example, in dose-response analysis. In this article, we propose unimodal spline regression methods that make use of Bernstein-Schoenberg splines and their shape preservation property. To achieve unimodal and smooth solutions we use penalized splines, and extend the penalized spline approach toward penalizing against general parametric functions, instead of using just difference penalties. For tuning parameter selection under a unimodality constraint a restricted maximum likelihood and an alternative Bayesian approach for unimodal regression are developed. We compare the proposed methodologies to other common approaches in a simulation study and apply it to a dose-response data set. All results suggest that the unimodality constraint or the combination of unimodality and a penalty can substantially improve estimation of the functional relationship.

Multigrid methods for isogeometric discretization

We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness.

Estimating Volumes of Near-Spherical Molded Artifacts

The Food and Drug Administration (FDA) is conducting research on developing reference lung cancer lesions, called phantoms, to test computed tomography (CT) scanners and their software. FDA loaned two semi-spherical phantoms to the National Institute of Standards and Technology (NIST), called Green and Pink, and asked to have the phantoms' volumes estimated. This report describes in detail both the metrology and computational methods used to estimate the phantoms' volumes. Three sets of coordinate measuring machine (CMM) measured data were produced. One set of data involved reference surface data measurements of a known calibrated metal sphere. The other two sets were measurements of the two FDA phantoms at two densities, called the coarse set and the dense set. Two computational approaches were applied to the data. In the first approach spherical models were fit to the calibrated sphere data and to the phantom data. The second approach was to model the data points on the boundaries of the spheres with surface B-splines and then use the Divergence Theorem to estimate the volumes. Fitting a B-spline model to the calibrated sphere data was done as a reference check on the algorithm performance. It gave assurance that the volumes estimated for the phantoms would be meaningful. The results for the coarse and dense data sets tended to predict the volumes as expected and the results did show that the Green phantom was very near spherical. This was confirmed by both computational methods. The spherical model did not fit the Pink phantom as well and the B-spline approach provided a better estimate of the volume in that case.