Piecewise Constant Model Research Articles

Nonproportional Hazards in Network Meta-Analysis: Efficient Strategies for Model Building and Analysis.

To develop efficient approaches for fitting network meta-analysis (NMA) models with time-varying hazard ratios (such as fractional polynomials and piecewise constant models) to allow practitioners to investigate a broad range of models rapidly and to achieve a more robust and comprehensive model selection strategy. We reformulated the fractional polynomial and piecewise constant NMA models using analysis of variance-like parameterization. With this approach, both models are expressed as generalized linear models (GLMs) with time-varying covariates. Such models can be fitted efficiently with standard frequentist techniques. We applied our approach to the example data from the study by Jansen etal, in which fractional polynomial NMA models were introduced. Fitting frequentist fixed-effect NMAs for a large initial set of candidate models took less than 1 second with standard GLM routines. This allowed for model selection from a large range of hazard ratio structures by comparing a set of criteria including Akaike information criterion/Bayesian information criterion, visual inspection of goodness-of-fit, and long-term extrapolations. The "best" models were then refitted in a Bayesian framework. Estimates agreed very closely. NMA models with time-varying hazard ratios can be explored efficiently with a stepwise approach. A frequentist fixed-effect framework enables rapid exploration of different models. The best model can then be assessed further in a Bayesian framework to capture and propagate uncertainty for decision-making.

Does the Firm Make the Difference? The Influence of Organizational Family-Friendly Arrangements on the Duration of Employment Interruptions after Childbirth

AbstractDespite the increase in dual-earner couples in Germany over recent decades, starting a family still often leads to a (re-)traditionalization of the division of labour in partnerships, with considerable gender differences in working hours and family obligations remaining. Consequently, after a child is born especially women face the challenge of reconciling career and family. Against this backdrop, a growing proportion of firms has started to create family-friendly working conditions to relieve the burden on their (female) employees. In the course of doing so, firms have also increasingly invested in organizational family-friendly arrangements in recent years. In this article, we analyse the effects of these arrangements on employees’ behaviour by using German-linked employer–employee data. We ask how specific organizational family-friendly measures affect a crucial point in women’s careers: the employment interruption after childbirth. Based on time-specific piecewise constant models, our results reveal that organizational family-friendly measures positively influence women’s return to the labour market after childbirth and thus result in benefits for both firms and employees. Furthermore, we find that the effects of the measures are determined by the structural context and are not time constant but vary according to the age of the child.

Design and Characterization of a Modular Hybrid Continuum Robotic Manipulator

We present a new design of a multi-DOF modular soft/rigid hybrid robotic manipulator that includes integrated electronics and is composed of several modules which each provide 1–2 degrees of freedom of motion. To control the robot, we present a new variant of the piece-wise constant curvature model made possible due to the geometry of the robot. Embedded inertial measurement units and pressure sensors are the sole sensors used in conjunction with the robot model to determine its kinematics. With the model, the soft robot can be controlled using traditional forward and inverse kinematics. Thus, its sensing and control are relatively simple compared to other soft robots. Additionally, it has a higher payload than other soft robot arms. We present models for each of the robotic joint modules created, as well as a new model for a bellows actuator based on its mechanics. With these models, we perform calculations about the stiffness of each module, and we compare these to experimental data on the modules and entire robot. The modeling introduced in this article had errors of less than 5%, and the robot arm achieved positioning accuracy of less than 1 cm.

A morphological approach to piecewise constant active contour model incorporated with the geodesic edge term

Traditional level set-based image segmentation method has to solve the level set evolution equation which is the Euler–Lagrange equation of the energy functional defined on the image domain. Solving level set evolution equation is very time-consuming, and reinitialization is usually needed. The level set evolution equation can also be solved by mathematical morphology. The morphological implementation is very simple, fast and stable. The piecewise constant active contour model incorporated with the geodesic edge term is a hybrid active contour model which combines two active contour models which are active contour model without edges and geodesic active contour model. In this paper, the mathematical morphology-based level set evolution method is applied to the piecewise constant active contour model incorporated with the geodesic edge term. The curvature morphological operator is also improved. Experimental results show that, compared with the original piecewise constant active contour model incorporated the geodesic edge term, the new mathematical morphology-based model can segment images more accurately and there are significant gains in simplicity, speed and stability. The new mathematical morphology-based model is also compared to morphological piecewise constant active contour model, morphological geodesic active contour model, traditional piecewise constant active contour model and two other active contour models. Results show that the proposed method gets the segmentation result with faster speed and higher accuracy.

Assessment of return value estimates from stationary and non-stationary extreme value models

This article compares the accuracy of return value estimates from stationary and non-stationary extreme value models when the data exhibits covariate dependence. The non-stationary covariate representation used is a penalised piecewise-constant (PPC) model, in which the data are partitioned into bins defined by covariates and the extreme value distribution is assumed to be homogeneous within each bin. A generalised Pareto model is assumed, where the scale parameter can vary between bins but is penalised for the variance across bins, and the shape parameter is assumed constant over all covariate bins. The number and sizes of covariate bins must be defined by the user based on physical considerations. Numerical simulations are conducted to compare the performance of stationary and non-stationary models for various case studies, in terms of quality of estimation of the T-year return value over the full covariate domain. It is shown that a non-stationary model can give improved estimates of return values, provided that model assumptions are consistent with the data. When the data exhibits non-stationarity in the generalised Pareto tail shape, the use of non-stationary model assuming a constant shape parameter can produce biases in return values. In such cases, a stationary model can give a more accurate estimate of return value over the full covariate domain as only the most extreme observations (regardless of covariate) are used to estimate tail shape. In other cases, the assumption of a stationary model will ignore key features of the data and be less reliable than a non-stationary model. For example, if a relatively benign covariate interval exhibits a long (or heavy) tail, extreme values from this interval may influence the T-year return value for very large T. However the sample of peaks over threshold, with high threshold, used to estimate a stationary model in this case may not include sufficient observations from this interval to estimate the return value adequately.

On an Improved State Parametrization for Soft Robots With Piecewise Constant Curvature and Its Use in Model Based Control

Piecewise constant curvature models have proven to be an useful tool for describing kinematics and dynamics of soft robots. However, in their three dimensional formulation they suffer from many issues limiting their range of applicability - as discontinuities and singularities - mainly concerning the straight configuration of the robot. In this work we analyze these flaws, and we show that they are not due to the piecewise constant curvature assumption itself, but that instead they are a byproduct of the commonly employed direction/angle of bending parametrization of the state. We therefore consider an alternative state representation which solves all the discussed issues, and we derive a model based controller based on it. Examples in simulation are provided to support and describe the theoretical results. When using the novel parametrization, the system is able to perform more complex tasks, with a strongly reduced computational burden, and without incurring in spikes and discontinuous behaviors.

Outlier robust modeling of survival curves in the presence of potentially time-varying coefficients.

In time to event studies, censoring often occurs and models that take this into account are wide-spread. In the presence of outliers, standard estimators of model parameters may be affected such that results and conclusions are not reliable anymore. This in turn also hampers the detection of these outliers due to masking effects. To cope with outliers when using proportional hazard models, we propose to use the Brier score as a loss function. Since the coefficients often vary over time, we focus on the piecewise constant hazard model, which can flexibly model time-varying coefficients if a large number of cut-points is used. To prevent overfitting, we add a penalty term that potentially shrinks time-varying effects to constant effects. By fitting the coefficients of the piecewise constant hazard model using a penalized Brier score loss, we obtain a robust model that can handle time-varying coefficients. Its good performance is illustrated in a simulation study and using two datasets from practice.

Bayesian Estimation in Piecewise Constant Model with Gamma Noise by Using Reversible Jump MCMC

A piecewise constant model is often applied to model data in many fields. Several noises can be added in the piecewise constant model. This paper proposes the piecewise constant model with a gamma multiplicative noise and a method to estimate a parameter of the model. The estimation is done in a Bayesian framework. A prior distribution for the model parameter is chosen. The prior distribution for the parameter model is multiplied with a likelihood function for the data to build a posterior distribution for the parameter. Because a number of models are also parameters, a form of the posterior distribution for the parameter is too complex. A Bayes estimator cannot be calculated easily. A reversible jump Monte Carlo Markov Chain (MCMC) is used to find the Bayes estimator of the model parameter. A result of this paper is the development of the piecewise constant model and the method to estimate the model parameter. An advantage of this method can simultaneously estimate the constant piecewise model parameter.

Predicting the duration of sickness absence spells due to back pain: a population-based study from Sweden

ObjectivesWe aimed to develop and validate a prediction model for the duration of sickness absence (SA) spells due to back pain (International Statistical Classification of Diseases and Related Health Problems...

Using Markov assumption with covariates to assess the Plasmodium falciparum malaria serological markers evolution

In this study, we develop Three Markov models which are continuous time-homogeneous Model, time piecewise constant intensities Markov model and semi-Markov model with Weibull distribution as the waiting time distribution to evaluate malaria serology evolution. We consider two-state model describing antibody reactivity defined by immunologists. We discuss in detail the application of these models to identify relationships between malaria control program and serological measurements of malaria transmission

Using Markov assumption with covariates to assess the Plasmodium falciparum malaria serological markers evolution

In this study, we develop Three Markov models which are continuous time-homogeneous Model, time piecewise constant intensities Markov model and semi-Markov model with Weibull distribution as the waiting time distribution to evaluate malaria serology evolution. We consider two-state model describing antibody reactivity defined by immunologists. We discuss in detail the application of these models to identify relationships between malaria control program and serological measurements of malaria transmission

Research and analysis of stiffness-enhanced soft gripper

In view of the problems of low stiffness, small driving force and large balloon effect existing in the current soft actuator, this paper proposes an optimization method to enhance the overall stiffness of the soft gripper by using rigid components based on the multi-cavity soft pneumatic actuator. This paper introduces the main components of the actuator: the soft part poured by liquid silica gel, and the open rectangular rigid structures by 3D printed. The kinematics model of the finger is established based on the Piecewise Constant Curvature model(PCC). The bending performance of the enhanced stiffness gripper is verified by finite element analysis(FEA): the tip force of actuator increased with the increase of the number of rigid structures when the bending angle is constant. According to the and experimental data, the overall stiffness of soft gripper is increased by the rigid structure without affecting the flexibility of operation. And the maximum weight which can grasp is 3.4 times that of the traditional soft gripper, improved the grasping range of the soft gripper effectively.

Changepoint Detection by the Quantile LASSO Method

A simultaneous changepoint detection and estimation in a piece-wise constant model is a common task in modern statistics. If, in addition, the whole estimation can be performed fully automatically in a single step without requiring any statistical tests or a posteriori methods, it also becomes a very interesting but challenging idea. In this paper, we introduce the estimation method based on the quantile LASSO approach. Unlike standard LASSO approaches, our method does not rely on classical assumptions common for the model errors, sub-Gaussian or Normal distributions in particular. The quantile LASSO method can handle, for instance, outlying observations or heavy-tailed error distributions, and it provides, in general, a more complex insight into the data: any conditional quantile can be obtained rather than providing just the conditional mean. Under some reasonable assumptions, the number of changepoints is not underestimated with probability tenting to one. Moreover, if the number of changepoints is estimated correctly, the quantile LASSO changepoint estimators are consistent. Numerical simulations demonstrate the theoretical results, and they illustrate the empirical performance and the robust favor of the proposed quantile LASSO method. The real example is used to show a practical applicability of the proposed method.

Automated Framework for Time-Domain Piecewise-Linear Fitting Method Based on Digital Wave Processing of $S$ -Parameters

An innovative full time-domain macromodeling technique for general, linear multiport systems is described. The methodology is defined in a digital wave framework and time-domain simulations are performed via an efficient method called Segment Fast Convolution (SFC). It is based on a piecewise-constant (PWC) model of the impulse response of scattering parameters, computed starting from a piecewise-linear fitting of their step response (PWLFIT). Such step response is directly available from time-domain reflectometer measurements (TDR/TDT) or equivalent simulations. The model-building phase is performed in a fast automated framework and an analytic formulation of computational efficiency of the SFC with respect to the standard time-domain convolution is given. Two application examples are used to verify the PWLFIT performance and to perform a comparison with macromodeling methods defined in the frequency-domain, such as Vector Fitting (VF).

Optimal data-based binning for histograms and histogram-based probability density models

Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a straightforward data-based method of determining the optimal number of bins in a uniform bin-width histogram. By assigning a multinomial likelihood and a non-informative prior, we derive the posterior probability for the number of bins in a piecewise-constant density model given the data. In addition, we estimate the mean and standard deviations of the resulting bin heights, examine the effects of small sample sizes and digitized data, and demonstrate the application to multi-dimensional histograms.

Unsupervised SAR image segmentation based on kernel TMFs with belief propagation

The triplet Markov field (TMF) model has achieved promising results in synthetic aperture radar (SAR) image segmentation. Focusing on the simple likelihood modelling of an SAR image and the effective optimisation of the TMF model, an unsupervised SAR image segmentation algorithm based on kernel TMF with belief propagation is proposed in this study. Instead of complex speckle noise statistical models in a spatial domain, a piecewise constant likelihood model in the kernel mapped space is used in the TMF model by mapping the SAR image data into a higher dimension space via a kernel function. The max-product belief propagation algorithm is used to realise effective optimisation of the proposed kernel TMF model. Experiments on both simulated and real SAR images demonstrate the effectiveness of the proposed algorithm.

Smoothing for signals with discontinuities using higher order Mumford–Shah models

Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is that linear trends -- and in general polynomial trends -- in the data are not well preserved. This can be improved by building on splines of higher order which leads to higher order Mumford-Shah models. In this work, we study these models in the univariate situation: we discuss important differences to the first order Mumford-Shah model, and we obtain uniqueness results for their solutions. As a main contribution, we derive fast minimization algorithms for Mumford-Shah models of arbitrary orders. We show that the worst case complexity of all proposed schemes is quadratic in the length of the signal. Remarkably, they thus achieve the worst case complexity of the fastest solver for the piecewise constant Mumford-Shah model (which is the simplest model of the class). Further, we obtain stability results for the proposed algorithms. We complement these results with a numerical study. Our reference implementation processes signals with more than 10,000 elements in less than one second.

3D non-smooth inversion of gravity data by zero order minimum entropy stabilizing functional

The inversion of gravity data can generate subsurface density models by minimizing a Tikhonov parametric functional. The Tikhonov parametric functional has a misfit functional and a stabilizing functional which the latter functional governs the solution to be smooth or piecewise-constant. Piecewise-constant models can discern sharp geological interfaces. Therefore the models are highly demanded especially for mineral exploration. Some stabilizing functionals such as minimum support (MS) and minimum gradient support (MGS) stabilizing functionals produce piecewise-constant and compact models so that they are governed by a focusing parameter that must be selected properly. Choosing a suitable focusing parameter complicates the inversion process. In this paper, the zero order minimum entropy stabilizing functional is proposed for focusing inversion of gravity data based on a reweighted regularized conjugate gradient algorithm. The new algorithm avoids the selection of an optimal focusing parameter and generates piecewise-constant models. The effectiveness of the algorithm is validated by inversion of synthetic gravity data and field gravity data from the San Nicolas deposit in Mexico.

Narrowest-Over-Threshold Detection of Multiple Change Points and Change-Point-Like Features

SummaryWe propose a new, generic and flexible methodology for non-parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.

Impact of rates of referral and systemic therapy on 1-year outcomes in metastatic NSCLC: A real-world population based study.

e18238 Background: EGFR/ALK inhibitors and immunotherapy represent promising treatments for metastatic NSCLC, but patients must be referred to a cancer center (CC) to be considered for these treatments. Local referral rates to a CC for advanced pancreatic cancer are only 51%. We hypothesized that rates of referral for stage IV NSCLC are also low, thereby affecting survival. Methods: Using linked data from the provincial cancer registry, oncology specific EMR, administrative claims and vital statistics, we identified all patients diagnosed with stage IV NSCLC from 2009 to 2016 in Alberta, Canada. Demographics, Charlson Comorbidity Index (CCI), method of diagnosis, year of diagnosis and site of metastasis were compared between patients referred vs not referred (NR) to a CC and between those who received systemic therapy (ST) vs those who did not. A multivariable piecewise constant hazard model was constructed to estimate the hazard ratio (HR) of death in the 1st year. Results: We identified 9717 stage IV NSCLC patients among whom 65.8% and 34.2% were diagnosed pre and post 2012. In this cohort, 6907 (71%) were seen at a CC. Factors which predict referral to a cancer center are: dx by cytology (OR 6.81, 95% CI: 5.99-7.75; p < 0.001) or histology (OR 6.29, 95% CI: 5.40-7.34; p < 0.001) vs radiologic dx; Age < 70 (OR 1.87, 95% CI: 1.69-2.07; p < 0.001); dx after 2012 (OR 1.52, 95% Cl 1.36-1.70; p < 0.001) and CCI≤1 (OR 1.50, 95% Cl 1.34-1.68; p < 0.001). ST was administered to 2057(21.2%). Factors that predict ST are: dx by cytology (OR 6.48, 95% CI: 5.18-8.11; p < 0.001) or histology (OR 6.35.18 , 95% CI: 5.02-8.04; p < 0.001); Age < 70 (OR 2.55, 95% Cl 2.33-2.82; p < 0.001); CCI≤1 (OR 1.56, 95% Cl 1.39-1.76; p < 0.001); dx after 2012 (OR 1.28, 95% CI: 1.16-1.41 and female gender (OR 1.18 , 95% CI: 1.07-1.29; p < 0.001; p < 0.001). Within the 1st year post dx, HR for mortality was lower both in patients referred to a CC vs NR (HR 0.3, 95%CI .28-0.31, p < 0.0001) and patients receiving ST vs no ST (HR 0.3, 95% CI .28-0.32, p < 0.0001). Conclusions: Close to 1 in 3 patients with stage IV NSCLC were not referred to a CC even though referral and receipt of ST were associated with a significantly lower risk of death in the 1st year following diagnosis. Clear delineation and wide dissemination of appropriate referral pathways are needed to improve outcomes, especially among older patients.