Inverse Regression Model Research Articles

Leveraging real-world Data from administrative claims and medical records to inform safety and effectiveness of piperacillin-tazobactam in the Management of Pediatric Hospital Acquired Pneumonia.

Pediatric-specific safety data are required during development of pharmaceutical agents. Retrospective studies can leverage real-world data to assess safety and effectiveness in children where prospective, controlled studies are not feasible. A retrospective cohort study combined data from Pediatric Health Information Systems (PHIS) and medical records to evaluate the safety and effectiveness of piperacillin/tazobactam (P/T) in pediatric patients with hospital-acquired pneumonia (HAP). After identifying 407 patients diagnosed with HAP receiving P/T (n=140) or Comparator (n=267) HAP-appropriate antibiotics between 2003-2016 across seven pediatric institutions, we evaluated comparative risk of a serious adverse event (SAE). Clinical improvement 14 days after therapy initiation was studied as a secondary outcome. Incidence rate ratios (IRRs) were calculated to compare between exposure groups using inverse probability-weighted Poisson regression models. The unadjusted and adjusted IRRs with 95% CIs for SAEs were 1.26(0.66-2.39) and 1.24(0.65-2.35). The unadjusted and adjusted ORs with 95% CIs for clinical improvement were 1.14(0.56-2.34) and 1.50(0.67-3.38). Point estimates from this retrospective analysis suggest similar safety and clinical effectiveness of P/T and comparator antibiotics for treating HAP. However, due to wide CIs, actual between-group differences cannot be excluded. Existing real-world data can be utilized to inform pediatric-specific safety and effectiveness of medications used in off-label settings.

A Study of Stock Price Prediction Models Based on Kernel Clustering Localized Sliced Inverse Regression and Bayesian Model Averaging

A Study of Stock Price Prediction Models Based on Kernel Clustering Localized Sliced Inverse Regression and Bayesian Model Averaging

Investigation of goose breeding in Turkiye by linear and nonlinear regression models

In this study, the change in the number of geese breeding in Turkiye over the years was examined by linear and non-linear regression models. Among linear and non-linear regression models, linear, quadratic, cubic, logarithmic, and inverse regression models were used. R2 and MSE values were taken as criteria for comparing the models. As a result of the study, the cubic regression model with the highest R2 value and the lowest MSE value was found to be the best fitting model for the number of geese. According to the cubic regression model, the number of geese in Turkiye in 2023 and 2024 was estimated to be 1849304 and 2107588, respectively.

Likelihood-based surrogate dimension reduction

We consider the problem of surrogate sufficient dimension reduction, that is, estimating the central subspace of a regression model, when the covariates are contaminated by measurement error. When no measurement error is present, a likelihood-based dimension reduction method that relies on maximizing the likelihood of a Gaussian inverse regression model on the Grassmann manifold is well-known to have superior performance to traditional inverse moment methods. We propose two likelihood-based estimators for the central subspace in measurement error settings, which make different adjustments to the observed surrogates. Both estimators are computed based on maximizing objective functions on the Grassmann manifold and are shown to consistently recover the true central subspace. When the central subspace is assumed to depend on only a few covariates, we further propose to augment the likelihood function with a penalty term that induces sparsity on the Grassmann manifold to obtain sparse estimators. The resulting objective function has a closed-form Riemann gradient which facilitates efficient computation of the penalized estimator. We leverage the state-of-the-art trust region algorithm on the Grassmann manifold to compute the proposed estimators efficiently. Simulation studies and a data application demonstrate the proposed likelihood-based estimators perform better than inverse moment-based estimators in terms of both estimation and variable selection accuracy.

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Variable selection in Inverse Gaussian regression model using modified crow search algorithm

Resonator-Loaded Waveguide Notch Filters with Broad Tuning Range and Additive-Manufacturing-Based Operating Frequency Adjustment Procedure

This article presents a new class of ring-resonator-loaded waveguide notch filters with a broad tuning range, low cost, and improved performance. The proposed approach employs a complementary asymmetric split-ring resonator coupled to a microstrip transmission line and excited in a rectangular waveguide. An equivalent circuit model is proposed to explain the working principle of the proposed notch filter. The adjustment of the operating frequency is based on the additive manufacturing of a metallic copper patch allocated on the microstrip transmission line, which enables extensive tuning capabilities and consistent performance with minimum variations across the tuning window. For demonstration purposes, a filter employing a WR-28 waveguide and photolithography-manufactured resonator is prototyped and experimentally validated. The measured results indicate a broad 8 GHz tuning range with a consistent insertion loss, ranging from 23.4 to 31.4 GHz. An inverse regression model is constructed using measurement data obtained for tuning patches of various sizes, which allows for determining the relationships between the operating frequency and the copper patch size. The resulting calibration curve enables rapid filter tuning to the required frequency by inserting metallic patches of the model-predicted size.

Data-Driven Reachability and Support Estimation With Christoffel Functions

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an empirical inverse Christoffel function: empirical inverse Christoffel functions are known to provide good approximations to the support of probability distributions. In addition to reachability analysis, the same approach can be applied to general problems of estimating the support of a random variable, which has applications in data science towards detection of novelties and outliers in data sets. In applications where safety is a concern, having a guarantee of accuracy that holds on finite data sets is critical. In this paper, we prove such bounds for our algorithms under the Probably Approximately Correct (PAC) framework. In addition to applying classical Vapnik- Chervonenkis (VC) dimension bound arguments, we apply the PAC-Bayes theorem by leveraging a formal connection between kernelized empirical inverse Christoffel functions and Gaussian process regression models.

Association of Very Early Treatment Initiation With the Risk of Long-term Disability in Patients With a First Demyelinating Event.

Early treatment is associated with better long-term outcomes in patients with a first demyelinating event and early multiple sclerosis (MS). However, magnetic resonance (MR) findings are not usually integrated to construct propensity scores (PSs) when evaluating outcomes. We assessed the association of receiving very early treatment with the risk of long-term disability including an MR score (MRS) in patients with a first demyelinating event. We included 580 patients with a first demyelinating event prospectively collected between 1994 and 2021, who received at least 1 disease-modifying drug (DMD). Patients were classified into tertiles according to the cohort's distribution of the time from the first demyelinating event to the first DMD: first tertile (FT) or very early treatment (6 months; n = 194), second tertile (6.1-16 months, n = 192), and third tertile (TT) (16.1 months, n = 194). A 5-point MRS was built according to the sum of the following indicators: ≥9 brain lesions (1 point); ≥1 infratentorial lesion (1 point); ≥1 spinal cord (SC) lesion (1 point); ≥1 contrast-enhancing (CE) brain lesion (1 point); and ≥1 CE SC lesion (1 point). PS based on covariates and the MRS was computed for each of the outcomes. Inverse PS-weighted Cox and linear regression models assessed the risk of different outcomes between tertile groups. Finally, to confirm the role of MR in treatment decision, we studied the time elapsed from the first demyelinating event to treatment initiation according to the MRS in all patients with radiologic available information, renamed as raw-MRS. Very early treatment decreased the risk of reaching Expanded Disability Status Scale 3.0 (hazard ratio [HR] 0.55, 95% CI 0.32-0.97), secondary progressive MS (HR 0.40, 95% CI 0.19-0.85), and sustained disease progression at 12 months after treatment initiation (HR 0.50, 95% CI 0.29-0.84), when compared with patients from the TT group. Patients from the FT group had a lower disability progression rate (β estimate -0.009, 95% CI -0.016 to -0.002) and a lower severe disability measured by the Patient-Determined Disease Step (β estimate -0.52, 95% CI -0.91 to -0.13) than the TT group. Finally, there was a 62.4% reduction in the median time between the first demyelinating event and the first-ever treatment initiation from patients displaying a raw-MRS 1 to patients with a raw-MRS 5. Using PS models with and without MRS, we showed that treatment initiation at very early stages is associated with a reduction in the risk of long-term disability accrual in patients with a first demyelinating event. This study provides Class III evidence that earlier treatment of patients with MS presenting with a first demyelinating event is associated with improved clinical outcomes.

Comprehensive Evaluation and Stepwise Regression Model of Light Pollution in Topsis Based on Entropy Weight Method

Light pollution is a phenomenon that affects our environment. It is of great significance to make a quantitative analysis of light pollution and establish an evaluation system for energy saving, environment improvement and social and economic benefits. In order to establish a reasonable evaluation system, based on a comprehensive evaluation model of light pollution risk level based on the entropy weight method of Topsis analysis, combined a multiple linear regression model to test the significance of the indicator data and performed the White's test and the VIF test for multiple covariance on the model.Then this paper used the standard inverse stepwise regression model to solve the linear regression model, constructed a comprehensive evaluation model of light pollution.

Informative and adaptive distances and summary statistics in sequential approximate Bayesian computation.

Calibrating model parameters on heterogeneous data can be challenging and inefficient. This holds especially for likelihood-free methods such as approximate Bayesian computation (ABC), which rely on the comparison of relevant features in simulated and observed data and are popular for otherwise intractable problems. To address this problem, methods have been developed to scale-normalize data, and to derive informative low-dimensional summary statistics using inverse regression models of parameters on data. However, while approaches only correcting for scale can be inefficient on partly uninformative data, the use of summary statistics can lead to information loss and relies on the accuracy of employed methods. In this work, we first show that the combination of adaptive scale normalization with regression-based summary statistics is advantageous on heterogeneous parameter scales. Second, we present an approach employing regression models not to transform data, but to inform sensitivity weights quantifying data informativeness. Third, we discuss problems for regression models under non-identifiability, and present a solution using target augmentation. We demonstrate improved accuracy and efficiency of the presented approach on various problems, in particular robustness and wide applicability of the sensitivity weights. Our findings demonstrate the potential of the adaptive approach. The developed algorithms have been made available in the open-source Python toolbox pyABC.

Effectiveness of an inactivated SARS-CoV-2 vaccine in children and adolescents: a large-scale observational study

Policymakers urgently need evidence to adequately balance the costs and benefits of mass vaccination against COVID-19 across all age groups, including children and adolescents. In this study, we aim to assess the effectiveness of CoronaVac's primary series among children and adolescents in Chile. We used a large prospective national cohort of about two million children and adolescents 6-16 years to estimate the effectiveness of an inactivated SARS-CoV-2 vaccine (CoronaVac) in preventing laboratory-confirmed symptomatic SARS-CoV-2 infection (COVID-19), hospitalisation, and admission to an intensive care unit (ICU) associated with COVID-19. We compared the risk of individuals treated with a complete primary immunization schedule (two doses, 28 days apart) with the risk of unvaccinated individuals during the follow-up period. The study was conducted in Chile from June 27, 2021, to January 12, 2022, when the SARS-CoV-2 Delta variant was predominant but other variants of concern were co-circulating, including Omicron. We used inverse probability-weighted survival regression models to estimate hazard ratios of complete immunization over the unvaccinated status, accounting for time-varying vaccination exposure and adjusting for relevant demographic, socioeconomic, and clinical confounders. The estimated adjusted vaccine effectiveness for the inactivated SARS-CoV-2 vaccine in children aged 6-16 years was 74.5% (95% CI, 73.8-75.2), 91.0% (95% CI, 87.8-93.4), 93.8% (95% CI, 87.8-93.4) for the prevention of COVID-19, hospitalisation, and ICU admission, respectively. For the subgroup of children 6-11 years, the vaccine effectiveness was 75.8% (95% CI, 74.7-76.8) for the prevention of COVID-19 and 77.9% (95% CI, 61.5-87.3) for the prevention of hospitalisation. Our results suggest that a complete primary immunization schedule with the inactivated SARS-CoV-2 vaccine provides effective protection against severe COVID-19 disease for children 6-16 years. Agencia Nacional de Investigación y Desarrollo (ANID) Millennium Science Initiative Program and Fondo de Financiamiento de Centros de Investigación en Áreas Prioritarias (FONDAP).

Structured time-dependent inverse regression (STIR).

We propose and study structured time-dependent inverse regression (STIR), a novel sufficient dimension reduction model, to analyze longitudinally measured, correlated biomarkers in relation to an outcome. The time structure is accommodated in an inverse regression model for the markers that can be applied both to equally and unequally spaced time points for each sample. The inverse regression structure also naturally accommodates retrospectively sampled markers, that is, markers measured in case-control studies. We estimate the corresponding linear combinations of the markers, the reduction, using least squares. We show that under additional distributional assumptions the reduction contains sufficient information about the outcome. In extensive simulations the STIR linear combinations perform well in predictive models based on samples of realistic size. A Wald-type test for association of a particular marker with outcome at any time point based on the STIR reduction has better power overall than assessing associations based on logistic or linear regression models that include all longitudinally measured markers as independent predictors. As illustrations we estimate the STIR reductions for a cohort study of diabetes and hyperlipidemia and a case-control study of brain cancer with multiple longitudinally measured biomarkers. We assess the STIR reductions' predictive performance and identify outcome-associated biomarkers.

Rapid Design Optimization and Calibration of Microwave Sensors Based on Equivalent Complementary Resonators for High Sensitivity and Low Fabrication Tolerance

This paper presents the design, optimization, and calibration of multivariable resonators for microwave dielectric sensors. An optimization technique for the circular complementary split ring resonator (CC-SRR) and square complementary split ring resonator (SC-SRR) is presented to achieve the required transmission response in a precise manner. The optimized resonators are manufactured using a standard photolithographic technique and measured for fabrication tolerance. The fabricated sensor is presented for the high-resolution characterization of dielectric substrates and oil samples. A three-dimensional dielectric container is attached to the sensor and acts as a pool for the sample under test (SUT). In the presented technique, the dielectric substrates and oil samples can interact directly with the electromagnetic (EM) field emitted from the resonator. For the sake of sensor calibration, a relation between the relative permittivity of the dielectric samples and the resonant frequency of the sensor is established in the form of an inverse regression model. Comparisons with state-of-the-art sensors indicate the superiority of the presented design in terms of oil characterization reliability. The significant technical contributions of this work include the employment of the rigorous optimization of geometry parameters of the sensor, leading to its superior performance, and the development and application of the inverse-model-based calibration procedure.

A Bayesian-Weighted Inverse Gaussian Regression Model with Application to Seismological Data

Developing an efficient model for analyzing right-skewed positive observations has a long history, and many authors have attempt in this direction. This is because the common analytic modeling procedures such as linear regression are often inappropriate for such data and leads to inadequate results. In this article, we proposed a new model for regression analysis of the right-skewed data by assuming the weighted inverse Gaussian, as a great flexible distribution, for response observations. In the proposed model, the complementary reciprocal of the location parameter of response variable is considered to be a linear function of the explanatory variables. We developed a fully Bayesian framework to infer about the model parameters based on a general noninformative prior structure and employed a Gibbs sampler to derive the posterior inferences by using the Markov chain Monte Carlo methods. A comparative simulation study is worked out to assess and compare the proposed model with other usual competitor models, and it is observed that efficiency is quite satisfactory. A real seismological data set is also analyzed to explain the applicability of the proposed Bayesian model and to access its performance. The results indicate to the more accuracy of proposed regression model in estimation of model parameters and prediction of future observations in comparison to its usual competitors in literature. Particularly, the relative prediction efficiency of the proposed regression model to the inverse Gaussian and log-normal regression models has been obtained to be 1.16 and 64, respectively, for the real-world example discussed in this paper.

Circular split‐ring resonator‐based sensor for dielectric constant measurement

AbstractThis paper presents the development of a metamaterial‐based microwave sensor for dielectric constant measurements. The sensor is constructed with a circular split‐ring resonator on one side and a coplanar waveguide transmission line on the other side. The proposed sensor has a size of 35 mm × 35 mm × 1.27 mm and resonates at 3.31 GHz. The sensor is fabricated on a RO3210 substrate with a dielectric constant of 10.2 and a loss tangent of 0.003. Both the simulation and experimental measurements show a linear relationship between the shift of the resonance frequency and the dielectric constants of the test samples, with a coefficient of determination R2 above 0.99. The dielectric constant of an unknown material can therefore be easily estimated using the inverse linear regression model. To validate the performance of the sensor, three known substrate materials, namely, Rogers RT6002, FR4, and Rogers TMM10, were used as test samples. The measured dielectric constants for these three materials were 2.8045, 4.3775, and 8.8719, respectively. The results agree closely with those indicated in the data sheets, with discrepancies of less than 5%.

Inverse Modeling and Optimization of CSRR-Based Microwave Sensors for Industrial Applications

Design optimization of multivariable resonators is a challenging topic in the area of microwave sensors for industrial applications. This article proposes a novel methodology for rapid redesign and parameter tuning of complementary split-ring resonators (CSRRs). Our approach involves inverse surrogate models established using preoptimized resonator data as well as analytical correction techniques to enable rapid adjustment of geometry parameters and CSRR optimization over broad ranges of operating frequencies. The tuning process is arranged to precisely allocate the operating frequency while maximizing the quality factor of the circuit. The procedure is generic and characterized by an extremely low computational cost of up to two electromagnetic (EM) analyses of the circuit at hand (not counting the inverse model setup). The presented technique is demonstrated using a circular CSRR coupled to a microstrip transmission line (MTL) and optimized to operate between 5 and 20 GHz. The design optimized for 15 GHz is fabricated and experimentally validated using a vector network analyzer. The sensor works in the transmission mode and senses the shift in resonance frequency determined by the properties of the material under test (MUT). Furthermore, an inverse regression model is developed that allows for directly finding the unknown permittivity of the MUT based on the measured resonant frequencies of the sensor. The obtained results corroborate the design utility of the proposed optimization method, as well as the practical usefulness of the specific CSRR structure developed with the aid thereof.

Modelling and forecasting new cases of Covid-19 in Nigeria: Comparison of regression, ARIMA and machine learning models

Covid-19 remains a global pandemic threatening hundreds of countries in the world. The impact of Covid-19 has been felt in almost every aspect of life and it has introduced globally, a new normal of livelihood. This global pandemic has triggered unparalleled global health and economic crisis. Therefore, modelling and forecasting the dynamics of this pandemic is very crucial as it will help in decision making and strategic planning. Nigeria as the most populous country in Africa and most populous black nation in the world has been adversely affected by Covid-19 pandemic. This study models and compares forecasting performance of regression, ARIMA and Machine Learning models in predicting new cases of Covid-19 in Nigeria. The study obtained data on daily new cases of Covid-19 in Nigeria between 27th February, 2020 and 30th November, 2021. Graphical analysis showed that Nigeria had witnessed three waves of Covid-19 with the first wave between 27th February, 2020 and 23rd October, 2020, the second wave between 24th October, 2020 and 20th June, 2021 and the third wave between 21st June, 2021 and 30th November, 2021.The second wave recorded the highest spikes in new cases compared to the first wave and third wave. Result reveals that in terms of forecasting performance, inverse regression model outperformed other regression models considered as it shows lowest RMSE of 0.4130 compared with other regression models. Also, the ARIMA (4, 1, 4) outperformed other ARIMA models as it reveals the highest R2 of 0.856 (85.6%), least RMSE (0.6364), AIC (-8.6024) and BIC (-8.5299). Result reveals that Fine tree which is one of the Machine Learning models is more reliable in forecasting new cases of Covid-19 in Nigeria compared to other models as Fine tree gave the highest R2 of 0.90 (90.0%) and least RMSE of 0.22165. Result of 15 days forecasting indicates that Covid-19 pandemic is not over yet in Nigeria as new cases of Covid-19 is projected to increase on 15/12/2021 with predicted new cases of 988 compared with that of 14/12/2021, where only 729 new cases was predicted. This therefore emphasizes the need to strengthen and maintain the existing Covid-19 preventive measures in Nigeria.

The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters

AbstractWe introduce a multivariate Poisson‐Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson‐Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson‐Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation‐Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance.

Women’s modern pentathlon scoring systems and predictive modelling for decision support

The purpose of the current investigation was to develop and evaluate an analytics approach to identifying the disciplines that female modern pentathletes should focus on to most improve their total points score. The study comprises of three analyses as well as the description and evaluation of an analytics approach to identify the event that a modern pentathlete should focus on to most improve their overall points. Analysis I revealed that the proportion of total points score derived from the laser run was significantly greater under the currently used scoring system than under the scoring system used prior to 2014 (p < 0.001). Analysis II considered year to year change in points scored for a set of 243 athletes who had completed performances in successive calendar years. The variability of year to year change in points was significantly influenced by discipline (p < 0.001) with the highest variability being in the laser run followed by fencing, riding and swimming. Linear and inverse regression models of year to year change were created during Analysis III and used in a simulation package that allowed year to year change to be predicted synthesising increased emphasis being made on different disciplines. The simulation approach suggests that female athletes can expect to make the greatest gains by emphasising the laser run and fencing within training. An evaluation study using six cases largely agreed with this but there was one of the athletes whose highest actual points improvement was in riding.