Semiparametric regression splines in matched case-control studies

We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: 1) an approximate cross-validation scheme to estimate the smoothing parameter inherent in regression splines, as well as 2) Monte Carlo expectation maximization (MCEM) and 3) Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM, and Bayesian approaches using simulation, showing that they appear approximately equally efficient; the approximate cross-validation method is computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches.     

Smoothness selection for penalized quantile regression splines

Modern data-rich analyses may call for fitting a large number of nonparametric quantile regressions. For example, growth charts may be constructed for each of a collection of variables, to identify those for which individuals with a disorder tend to fall in the tails of their age-specific distribution; such variables might serve as developmental biomarkers. When such a large set of analyses are carried out by penalized spline smoothing, reliable automatic selection of the smoothing parameter is particularly important. We show that two popular methods for smoothness selection may tend to overfit when estimating extreme quantiles as a smooth function of a predictor such as age; and that improved results can be obtained by multifold cross-validation or by a novel likelihood approach. A simulation study, and an application to a functional magnetic resonance imaging data set, demonstrate the favorable performance of our methods.     

Critical note on the application of the “two-third” spline

The “two-third spline” (2/3S) is a frequently applied method to detrend tree-ring series. It fits a spline with a 50% frequency cutoff at a frequency equal to two-thirds of each sample length in a dataset. It was introduced to ensure a minimum loss of low-frequency variance, which is resolvable during the detrending of ring-width series.In this paper I show potential problems that arise when rusing this method. The 2/3S runs counter the strengths of using a digital filter to detrend – i.e. one is giving up full control over the frequency-removing characteristics of the growth curve and each individual time series retains a different amount of low frequency. Thus, the 2/3S is less suitable for reconstructing climate or to compare environmental impacts on tree growth between groups – both of which comprise the majority of dendrochronological analyses – as it will likely introduce a temporal frequency bias. Within a long chronology it will result in decreasing power to resolve low frequencies towards present in a living-only trees setting, especially when the youngest segment lengths are 100 years and shorter, and more generally during the period where the chronology is constructed from samples with shorter segment lengths compared to the period with longer segment lengths. The frequency bias will also significantly impact regression slopes and correlation coefficients, possibly distorting analyses investigating multiple groups with different mean segment lengths. Highlighting these potential biases, I recommend the community to not use this method on an individual basis but rather to use a fixed spline stiffness for all samples based on the n% criterion (n = 67) of e.g. the mean segment length of the entire dataset.     

Clustering Time-Series Gene Expression Data Using Smoothing Spline Derivatives

Microarray data acquired during time-course experiments allow the temporal variations in gene expression to be monitored. An original postprandial fasting experiment was conducted in the mouse and the expression of 200 genes was monitored with a dedicated macroarray at 11 time points between 0 and 72 hours of fasting. The aim of this study was to provide a relevant clustering of gene expression temporal profiles. This was achieved by focusing on the shapes of the curves rather than on the absolute level of expression. Actually, we combined spline smoothing and first derivative computation with hierarchical and partitioning clustering. A heuristic approach was proposed to tune the spline smoothing parameter using both statistical and biological considerations. Clusters are illustrated a posteriori through principal component analysis and heatmap visualization. Most results were found to be in agreement with the literature on the effects of fasting on the mouse liver and provide promising directions for future biological investigations.     

A new look at state-space models for neural data

State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the state-space setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatially-varying firing rates.     

A partial likelihood approach to smooth estimation of dynamic covariate effects using penalised splines

Survival data are often modelled by the Cox proportional hazards model, which assumes that covariate effects are constant over time. In recent years however, several new approaches have been suggested which allow covariate effects to vary with time. Non-proportional hazard functions, with covariate effects changing dynamically, can be fitted using penalised spline (P-spline) smoothing. By utilising the link between P-spline smoothing and generalised linear mixed models, the smoothing parameters steering the amount of smoothing can be selected. A hybrid routine, combining the mixed model approach with a classical Akaike criterion, is suggested. This approach is evaluated with simulations and applied to data from the West of Scotland Coronary Prevention Study.     

A least squares algorithm to determine the mechanical time constant distribution of the lung during forced expiration

A method to determine the mechanical time-constant distribution of the lung during a forced expiration manoeuvre is proposed. The method is based on a least squares algorithm constrained to give reasonably smooth non-negative solutions. The smoothing constraint was imposed by minimizing the second derivative of the distribution function in accordance with the physiological meaning of the time-constant distribution. Nevertheless, the obtained solution depends greatly on the relative weights of the two terms in the objective function to be minimized i.e., the error on the fit of the volume signal and the smoothness of the distribution function. To select the optimum smoothing weight, a criterion based on the stability of the reconstructed distribution shape was defined. The performance of the algorithm and that of the defined criterion were evaluated by using simulated signals of forced expired volume. The error of reconstructed distributions was quantified by means of the area enclosed between this distribution and the original one used to generate the simulated volume signal. The results obtained showed that for all the analyzed signals: (1) There is a value of the weight of the smoothing constraint which gives rise to a solution that is optimum in a least squares sense. (2) The proposed stabilization criterion enables us to approach this optimum solution from experimental signals.     

Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.     

Defining window-boundaries for genomic analyses using smoothing spline techniques

Background

High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the data and then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome.

Results

Simulations applying this method were performed to identify selection signatures from pooled sequencing F_ST data, for which allele frequencies were estimated from a pool of individuals. The relative ratio of true to false positives was twice that generated by existing techniques. A comparison of the approach to a previous study that involved pooled sequencing F_ST data from maize suggested that outlying windows were more clearly separated from their neighbors than when using a standard sliding window approach.

Conclusions

We have developed a novel technique to identify window boundaries for subsequent analysis protocols. When applied to selection studies based on F_ST data, this method provides a high discovery rate and minimizes false positives. The method is implemented in the R package GenWin, which is publicly available from CRAN.     

Smoothing noisy data using dynamic programming and generalized cross-validation

Smoothing and differentiation of noisy data using spline functions requires the selection of an unknown smoothing parameter. The method of generalized cross-validation provides an excellent estimate of the smoothing parameter from the data itself even when the amount of noise associated with the data is unknown. In the present model only a single smoothing parameter must be obtained, but in a more general context the number may be larger. In an earlier work, smoothing of the data was accomplished by solving a minimization problem using the technique of dynamic programming. This paper shows how the computations required by generalized cross-validation can be performed as a simple extension of the dynamic programming formulas. The results of numerical experiments are also included.     

Application of splines to the calculation of bacterial swimming speed distributions.

A new method of extracting information about bacterial speeds from photon correlation spectroscopy is presented. This method has the advantage that an estimation of the translational speed distribution is directly varied so as to achieve a best least-squares fit to the experimental autocorrelation function. The theory of spline approximations to continuous functions is briefly outlined. The importance of the previously disregarded diffusional component of bacterial motion is discussed. Experimental data from Salmonella at a low scattering angle is analyzed by this method of spline approximation and the distribution of translational speeds is obtained.     

Estimation of growth and survival in size-structured cohort data: an application to larval striped bass (Morone saxatilis)

We present a method for estimating growth and mortality rates in size-structured population models. The methods are based on least-square fits to data using approximate models (using spline approximations) for the underlying partial differential equation population model. In a series of numerical tests, we compare our approach to an existing method (due to Hackney and Webb). As an example, we apply our techniques to experimental data from larval striped bass field studies.Research supported in part under grants at Brown University from the National Science Foundation: UINT-8521208, NSFDMS-8818530 (H.T.B., F.K. and CW.); from the Air Force Office of Scientific Research: AFOSR F49620-86-C-0111 (H.T.B., C.W.); and at University of California, Davis from the Alford P. Sloan Foundation (L.W.B.)     

Fast state-space methods for inferring dendritic synaptic connectivity

We present fast methods for filtering voltage measurements and performing optimal inference of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled voltage observations we develop fast l ₁-penalized regression methods for Kalman state-space models of the neuron voltage dynamics. The value of the l ₁-penalty parameter is chosen using cross-validation or, for low signal-to-noise ratio, a Mallows’ C _p -like criterion. Using low-rank approximations, we reduce the inference runtime from cubic to linear in the number of dendritic compartments. We also present an alternative, fully Bayesian approach to the inference problem using a spike-and-slab prior. We illustrate our results with simulations on toy and real neuronal geometries. We consider observation schemes that either scan the dendritic geometry uniformly or measure linear combinations of voltages across several locations with random coefficients. For the latter, we show how to choose the coefficients to offset the correlation between successive measurements imposed by the neuron dynamics. This results in a “compressed sensing” observation scheme, with an important reduction in the number of measurements required to infer the synaptic weights.     

Modeling spectral tuning in monomeric teal fluorescent protein mTFP1

We present results of theoretical studies of the variants of the monomeric teal fluorescent protein from Clavularia coral (mTFP1) which present promising members from the GFP family. Predictions of quantum chemical approaches including density functional theory and semiempirical approximations are presented for the model systems which mimic the chromophores in different environments. We describe the excitation energy spectrum of the cyan mTFP1 fluorescent protein with the original chromophore and with chromophore mutants Tyr67His and Tyr67Trp.     

Estimating a predator-prey dynamical model with the parameter cascades method

Summary .   Ordinary differential equations (ODEs) are widely used in ecology to describe the dynamical behavior of systems of interacting populations. However, systems of ODEs rarely provide quantitative solutions that are close to real field observations or experimental data because natural systems are subject to environmental and demographic noise and ecologists are often uncertain about the correct parameterization. In this article we introduce "parameter cascades" as an improved method to estimate ODE parameters such that the corresponding ODE solutions fit the real data well. This method is based on the modified penalized smoothing with the penalty defined by ODEs and a generalization of profiled estimation, which leads to fast estimation and good precision for ODE parameters from noisy data. This method is applied to a set of ODEs originally developed to describe an experimental predator–prey system that undergoes oscillatory dynamics. The new parameterization considerably improves the fit of the ODE model to the experimental data sets. At the same time, our method reveals that important structural assumptions that underlie the original ODE model are essentially correct. The mathematical formulations of the two nonlinear interaction terms (functional responses) that link the ODEs in the predator–prey model are validated by estimating the functional responses nonparametrically from the real data. We suggest two major applications of "parameter cascades" to ecological modeling: It can be used to estimate parameters when original data are noisy, missing, or when no reliable priori estimates are available; it can help to validate the structural soundness of the mathematical modeling approach.     

Comparison of endpoint data treatment methods for estimation of kinematics and kinetics near impact during the tennis serve

Tennis stroke mechanics have attracted considerable biomechanical analysis, yet current filtering practice may lead to erroneous reporting of data near the impact of racket and ball. This research had three aims: (1) to identify the best method of estimating the displacement and velocity of the racket at impact during the tennis serve, (2) to demonstrate the effect of different methods on upper limb kinematics and kinetics and (3) to report the effect of increased noise on the most appropriate treatment method. The tennis serves of one tennis player, fit with upper limb and racket retro-reflective markers, were captured with a Vicon motion analysis system recording at 500 Hz. The raw racket tip marker displacement and velocity were used as criterion data to compare three different endpoint treatments and two different filters. The 2nd-order polynomial proved to be the least erroneous extrapolation technique and the quintic spline filter was the most appropriate filter. The previously performed "smoothing through impact" method, using a quintic spline filter, underestimated the racket velocity (9.1%) at the time of impact. The polynomial extrapolation method remained effective when noise was added to the marker trajectories.     

Towards automatic wild animal monitoring: Identification of animal species in camera-trap images using very deep convolutional neural networks

Non-intrusive monitoring of animals in the wild is possible using camera trapping networks. The cameras are triggered by sensors in order to disturb the animals as little as possible. This approach produces a high volume of data (in the order of thousands or millions of images) that demands laborious work to analyze both useless (incorrect detections, which are the most) and useful (images with presence of animals). In this work, we show that as soon as some obstacles are overcome, deep neural networks can cope with the problem of the automated species classification appropriately. As case of study, the most common 26 of 48 species from the Snapshot Serengeti (SSe) dataset were selected and the potential of the Very Deep Convolutional neural networks framework for the species identification task was analyzed. In the worst-case scenario (unbalanced training dataset containing empty images) the method reached 35.4% Top-1 and 60.4% Top-5 accuracy. For the best scenario (balanced dataset, images containing foreground animals only, and manually segmented) the accuracy reached a 88.9% Top-1 and 98.1% Top-5, respectively. To the best of our knowledge, this is the first published attempt on solving the automatic species recognition on the SSe dataset. In addition, a comparison with other approaches on a different dataset was carried out, showing that the architectures used in this work outperformed previous approaches. The limitations of the method, drawbacks, as well as new challenges in automatic camera-trap species classification are widely discussed.     

Short-term supplementation with flavanol-rich cocoa improves lipid profile,antioxidant status and positively influences the AA/EPA ratio in healthy subjects

We evaluated the short-term effects of a flavanol-rich cocoa (FRC) on lipid profile and selected oxidative stress biomarkers such as oxidized low-density lipoprotein (oxLDL), glutathione (GSH), and F₂-isoprostane. We also assessed whether FRC modulates plasma levels of polyunsaturated fatty acids (PUFA) in healthy individuals. The subjects (n=48) were randomly assigned to a low-cocoa group (1 g/d; ~55 mg flavanols) (n=16), middle-cocoa group (2 g/d; ~110 mg flavanols) (n=16), or a high-cocoa group (4 g/d; ~220 mg flavanols) (n=16). The samples were collected at baseline, at 1, 2, and 4 h post initial consumption of FRC, and after 4 weeks of FRC supplementation. The peak plasma concentration of (−)-epicatechin metabolites reached a maximum level (578±61 nM; P<.05) at 2 h after ingestion of FRC. After 4 weeks, total cholesterol (−12.37±6.63; P<.0001), triglycerides (−3.81±2.45; P<.0001), plasma LDL (−14.98±6.77; P<.0001), and oxLDL (−95.61±41.69; P<.0001) decreased in the high-cocoa group, compared with baseline. We also found that plasma high-density lipoprotein (HDL) (+3.37±2.06; P<.0001) concentrations increased significantly in the same group. Total GSH significantly increased in all FRC-treated groups (+209.73±146.8; P<.0001), while urinary F₂-isoprostane levels decreased in the middle- (−0.73±0.16; P<.0001) and high-cocoa (−1.62±0.61; P<.0001) groups. At the end of the four-week study, a significant reduction of arachidonic acid (AA)/eicosapentaenoic acid (EPA) ratio was observed in the low-(−2.62±2.93; P=.003), middle- (−5.24±2.75; P<.0001) and high-cocoa (−7.76±4.96; P<.0001) groups, compared with baseline. Despite the small sample size used in this study, these data extend previous clinical and experimental studies, providing new insights into the health benefits of cocoa flavanols.     

The influence of framework design on the load-bearing capacity of laboratory-made inlay-retained fibre-reinforced composite fixed dental prostheses

Delamination of the veneering composite is frequently encountered with fibre-reinforced composite (FRC) fixed dental prosthesis (FDPs). The aim of this study is to evaluate the influence of framework design on the load-bearing capacity of laboratory-made three-unit inlay-retained FRC-FDPs. Inlay-retained FRC-FDPs replacing a lower first molar were constructed. Seven framework designs were evaluated: PFC, made of particulate filler composite (PFC) without fibre-reinforcement; FRC1, one bundle of unidirectional FRC; FRC2, two bundles of unidirectional FRC; FRC3, two bundles of unidirectional FRC covered by two pieces of short unidirectional FRC placed perpendicular to the main framework; SFRC1, two bundles of unidirectional FRC covered by new experimental short random-orientated FRC (S-FRC) and veneered with 1.5 mm of PFC; SFRC2, completely made of S-FRC; SFRC3, two bundles of unidirectional FRC covered by S-FRC. Load-bearing capacity was determined for two loading conditions (n=6): central fossa loading and buccal cusp loading. FRC-FDPs with a modified framework design made of unidirectional FRC and S-FRC exhibited a significant higher load-bearing capacity (p<0.05) (927±74 N) than FRC-FDPs with a conventional framework design (609±119 N) and PFC-FDPs (702±86 N). Central fossa loading allowed significant higher load-bearing capacities than buccal cusp loading. This study revealed that all S-FRC frameworks exhibited comparable or higher load-bearing capacity in comparison to an already established improved framework design. So S-FRC seems to be a viable material for improving the framework of FRC-FDPs. Highest load-bearing capacity was observed with FRC frameworks made of a combination of unidirectional FRC and S-FRC.