Gamma Regression Model Research Articles

The Maxwell-Boltzmann-Exponential distribution with regression model

Abstract This paper proposes a new probability model called as Maxwell-Boltzmann-Exponential (MBE) distribution. The MBE distribution arises as a mixture distribution of the Maxwell-Boltzmann and exponential distributions. The statistical properties of the distributions are studied and obtained in closed-form expressions. Three methodologies are assessed and compared for the estimation of parameters in the MBE distribution. The MBE regression model is defined, with the proposed regression model being an alternative to the gamma regression model for response variables that are extremely right-skewed and bimodal. Two real data sets are used to demonstrate the applicability of the proposed models against the existing models.

On the attribution of changes in streamflow conditions to climate variability in North Carolina Piedmont, United States

ABSTRACT Changes in streamflow magnitudes have ecological, hydrological, and geomorphological implications. Improved knowledge and understanding of the drivers of changes in streamflow conditions remain critical in water resource management. Spatiotemporal patterns of changes in streamflow conditions for five flow percentiles between two comparative periods: historical period (1944–1980) and recent period (1984‒2022) were determined in 18 watersheds of North Carolina Piedmont. The observed percentage changes in streamflow magnitudes for the five flow percentiles were attributed to change magnitudes in monthly mean precipitation and monthly mean temperature using a statistical modeling framework (i.e. gamma regression model). The results showed reduced streamflow magnitudes for the 10th, 25th, 50th, and 75th percentile flows, respectively, while an increased streamflow magnitude was found for the 90th percentile flow at many of the sites in recent period. The regression models captured the relationships between change magnitudes in streamflow conditions and changes in climate variables across all the sites.

Accounting for informative observation process in transition models of binary longitudinal outcome: Application to medical record data.

When extracting medical record data to form a retrospective cohort, investigators typically focus on a pre-specified study window, and select subjects who had hospital visits during that study window. However, such data extraction may suffer from an informative observation process, since sicker patients may have hospital visits more frequently. For example, Consecutive Pregnancy Study is a retrospective cohort study of women with multiple pregnancies in 23 Utah hospitals from 2003 to 2010, where the interest is to understand the risk factors of recurrent pregnancy outcomes, such as preterm birth. The observation process is informative in the sense that, women with adverse pregnancy outcomes may be less likely/willing/able to endure subsequent pregnancies. We proposed a three-part joint model with shared random effects structure to address this analytic complication. Particularly, a first-order transition model is used to model the longitudinal binary outcome; a gamma regression model is assumed for the inter-pregnancy intervals; a continuation ratio model specifies the probability of continuing with more births in the future. We note that the latter two parts give rise to a parametric cure-rate survival model. The performance of the proposed method was examined in extensive simulation studies, with both correctly and mis-specified models. The analyses of Consecutive Pregnancy Study data further demonstrate the inadequacies of fitting the transition model alone ignoring the informative observation process.

Could an increased risk of obstructive sleep apnoea be one of the determinants associated with disability in individuals with cardiovascular and cerebrovascular diseases?

To investigate a possible association between the risk of obstructive sleep apnoea (OSA) and disability in individuals with cardiovascular or cerebrovascular diseases. Cross-sectional study was conducted with 373 individuals (313 with cardiovascular or cerebrovascular diseases and 60 healthy). Disability was assessed by the 12-item World Health Organization Disability Assessment Schedule (WHODAS), and the risk of OSA was assessed by STOP-BANG. Anxiety and depression symptoms, daytime sleepiness, and cognition were assessed by the Hospital Anxiety and Depression Scale (HADS), Epworth Sleepiness Scale (ESS), and Mini Mental State Examination (MMSE). Greater disability was found in individuals with intermediate or high risk of OSA, considering healthy individuals (p=0.03), or individuals diagnosed with arrhythmia (p<0.01) or coronary artery disease (p=0.04). A high risk of OSA and higher WHODAS scores was significant among women as well as between OSA risk categories (p<0.01). Cognitive deficit and level of education also showed differences between OSA risk categories. Age, depression, and sleepiness were also associated with the subjects' disability (p<0.01). Gamma regression model showed higher WHODAS scores in female, in those with intermediate and high risk of OSA, and in those with depressive symptoms and cognitive deficit. Age also showed a correlation with higher WHODAS scores. The presence of all investigated cardio and cerebrovascular diseases showed an increase in the WHODAS score, implying a greater disability compared to healthy individuals. Moderate and high risk of OSA is associated with disability, as well as gender, age, depressive symptoms, cognitive deficit, and cardiovascular diseases.

A two-parameter estimator for correlated regressors in gamma regression model

Gamma Modified Two Parameter (GMTP) is a novel biased two-parameter estimator proposed to address the effects of multicollinearity in Generalized Linear Models (GLMs). An expansion of the linear regression model's Modified Two Parameters (MTP) is the newly suggested estimator. The performance of the GMTP estimator over the maximum likelihood estimator (MLE), gamma ridge estimator (GRE), gamma Liu estimator (GLE), and gamma Liu-type estimator (GLTE) reviewed in this article are theoretically compared, and the estimator's properties is discussed. A simulation study that examine the effects of the dispersion parameter, sample size, explanatory variables, and degree of correlation are used to examine the superiority of the GMTP with four different biasing parameters over the MLE, GRE, GLE, and GLTE with regard to the estimated MSE criterion. The GMTP estimator with biasing parameters and outperforms the MLE, GRE, GLE, and GLTE, according to simulation research. More research can be done to see how well the GMTP estimator performs in comparison to other estimators that were not examined in this study. 2 k 4 k

A New Modified Liu Ridge-Type Estimator for the Gamma Regression Model

The Gamma Regression Model (GRM) is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The most popular technique for estimating GRM coefficients is maximum likelihood (ML) estimation. The ML estimation method performs better if there is no correlation between the explanatory variables. It is known that the variance of the maximum likelihood estimator of the gamma regression coefficients is impacted in situations when the explanatory variables are correlated. Based on Aslam and Ahmad’s Modified Liu-Ridge-Type (MLRT) estimator, which has been demonstrated to lessen the effects of multicollinearity in the linear regression model, the paper presented a New Modified Liu Ridge-Type Estimator for the Gamma Regression Model (GMLRT) to address the problem of multicollinearity. Simulation and real-world application results show the superiority of the GMLRT estimator using the mean square error criterion.

Shewhart ridge profiling for the Gamma response model

ABSTRACT When product quality follows the Gamma distribution and is related to one or more covariate(s), then Gamma regression model (GRM) profiling will be used. The Gamma profiling is generally based on a maximum likelihood estimator (MLE). In GRM profiling, when two or more covariates are linearly related, the MLE-based GRM profiling is unsuitable. In this situation, an alternative to MLE-based profiling is required. So, this study develops the Gamma ridge regression profiling based on Pearson and deviance residuals. The performance of the proposed profiling is evaluated with the help of a simulation study under different conditions, where average run length is considered as the performance evaluation criterion. The simulation findings show that the Pearson residual based profiling with ridge estimator is better than the deviance residuals-based profiling with MLE as well as ridge estimator. Furthermore, we consider an application to evaluate the performance of the proposed methods.

Inequality restricted estimator for gamma regression: Bayesian approach as a solution to the multicollinearity

In this article, we consider the multicollinearity problem in the gamma regression model when model parameters are bounded linearly restricted. The linear restrictions are available from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. To make relevant statistical inference for a model, any available knowledge and prior information on the model parameters should be taken into account. This article proposes therefore an algorithm to acquire Bayesian estimator for the parameters of a gamma regression model subjected to some linear inequality restrictions. We then show that the proposed estimator outperforms the ordinary estimators such as the maximum likelihood and ridge estimators in terms of pertinence and accuracy through Monte Carlo simulations and application to a real dataset.

Influence of deprivation on hospital care pathways and costs for people with ischaemic stroke: A trajectory modelling study

BackgroundSocioeconomic characteristics have a strong impact on the incidence of stroke. The highest levels of morbidity and mortality are associated with the lowest socioeconomic positions. Moreover, the health insurance budget for stroke is significant. ObjectivesTo describe typical Hospital Care Pathways (HCPs) and their costs 1 year after acute stroke and to assess the impact of individuals’ socioeconomic characteristics on HCPs and costs. MethodsThis retrospective observational study used hospital data on people with primary ischaemic stroke in a region of France (Haute-Garonne).HCPs were identified by sequential analysis. Multinomial logistic regression was used to analyse the impact of socioeconomic characteristics on HCPs as measured using an ecological index of deprivation, and a gamma regression model was used to analyse costs. ResultsThe analysis identified 4 typical HCPs. The first HCP consisted exclusively of consultations, the second was composed of consultations and hospitalisations, the third included hospitalisations during the first 2 months after stroke followed by consultations, and the fourth included long-term hospitalisations.After adjustment, deprivation was associated with HCPs and determined its costs: a high level of social disadvantage determined the type of pathway and increased the costs. ConclusionsThis study is one of the first to assess the impact of social inequalities in health on post-stroke HCPs in France and their corresponding costs. Our results confirm the hypothesis that healthcare costs differ according to the level of deprivation.

Baldur: Bayesian Hierarchical Modeling for Label-Free Proteomics with Gamma Regressing Mean-Variance Trends

Label-free proteomics is a fast-growing methodology to infer abundances in mass spectrometry proteomics. Extensive research has focused on spectral quantification and peptide identification. However, research toward modeling and understanding quantitative proteomics data is scarce. Here we propose a Bayesian hierarchical decision model (Baldur) to test for differences in means between conditions for proteins, peptides, and post-translational modifications. We developed a Bayesian regression model to characterize local mean-variance trends in data, to estimate measurement uncertainty and hyperparameters for the decision model. A key contribution is the development of a new gamma regression model that describes the mean-variance dependency as a mixture of a common and a latent trend—allowing for localized trend estimates. We then evaluate the performance of Baldur, limma-trend, and t test on six benchmark datasets: five total proteomics and one post-translational modification dataset. We find that Baldur drastically improves the decision in noisier post-translational modification data over limma-trend and t test. In addition, we see significant improvements using Baldur over the other methods in the total proteomics datasets. Finally, we analyzed Baldur’s performance when increasing the number of replicates and found that the method always increases precision with sample size, while showing robust control of the false positive rate. We conclude that our model vastly improves over popular data analysis methods (limma-trend and t test) in several spike-in datasets by achieving a high true positive detection rate, while greatly reducing the false-positive rate.

Generalized linear model based gamma control chart

AbstractTraditional monitoring techniques are frequently used for monitoring a response variable, while ignoring the other important variables. A simple linear regression model to introduce covariates‐based charts has received a lot of attention in the recent publications. When the response variable belongs to the exponential family, the generalized linear model (GLM) is a flexible approach to model a phenomenon. This study uses gamma distribution to introduce GLM‐based Shewhart‐type control charts. The monitoring statistic is developed using the Pearson residuals (PRs) obtained from the gamma regression model. The suggested charts' performance is evaluated using the run‐length properties and extensive Monte Carlo simulations. A comparison of Pearson‐residual to the deviance‐residual charts is also discussed in this article. Finally, to emphasize the significance of the study, the proposed control charts are implemented on a real‐life data set.

Relationship Between Residents’ Physiological Stress and Faculty Leadership Skills in a Department of Surgery

Leadership skills of team leaders can impact the functioning of their teams. It is unknown whether attending surgeons' leadership skills impact residents' physiological stress. This study sought to (1) assess the relationship between attending surgeons' leadership skills and residents' physiological stress and (2) to characterize lifestyle behaviors associated with resident physiological stress. We hypothesized that strong attending leadership skills would be associated with low resident physiological stress. This prospective observational cohort study was conducted at a single urban, academic medical center in the US, over 12 months. Residents were enrolled during their rotation of 1 to 2 months on the Trauma and ICU services. The primary predictor was the attending surgeons' leadership skills that were measured using a weekly survey filled out by residents, using the Surgeons' Leadership Inventory (SLI). The SLI uses a 4-point Likert scale to measure surgeons' leadership skills across eight domains. The primary outcome was residents' physiological stress, which was measured by their Heart Rate Variability (HRV). We recorded the residents' HRV with a WHOOP strap that was continuously worn on the wrist or the bicep. We used multivariate repeated measures gamma regression to assess the relationship between attending leadership skills and residents' physiological stress, adjusting for hours of sleep, age, and service. Sixteen residents were enrolled over 12 months. The median attending surgeons' leadership score was 3.8 (IQR: 3.2-4.0). The median residents' percent of maximal HRV was 70.8% (IQR: 56.7-83.7). Repeated measure gamma regression model demonstrated a minimal nonsignificant increase of 1.6 % (95% CI: -5.6, 8.9; p-value = 0.65) in the percent of maximal HRV (less resident physiological stress) for every unit increase in leadership score. There was an increase of 2.9% (95% CI= 1.6, 4.2; p-value < 0.001) in the percent of maximal HRV per hour increase in sleep and a significant decrease of 10.9% (95% CI= -16.8, -5.2; < 0.001) in the percent of HRV when working in the ICU compared to the Trauma service. This study revealed that more residents' sleep was associated with lower physiological stress. Attending surgeons' leadership skills were not associated with residents' physiological stress.

Marketing data security and privacy protection based on federated gamma in cloud computing environment

This study aims to address the existing data security and user privacy vulnerabilities in the “cloud” environment, which is essential for ensuring the safety and integrity of data in the era of big data and cloud computing. To achieve this purpose, we propose a novel approach that combines the logit link function with a longitudinal joint learning framework for the gamma regression model. This approach enhances the application of the model and the loss function, providing a robust solution for data security and user privacy in cloud-based systems. While cloud computing technology has greatly improved the convenience of work and life, it has also introduced significant challenges related to data security and user privacy. This study leverages semantic web technology and blockchain technology to establish a distributed and credit-guaranteed product quality and safety traceability application. By designing a concept verification system and ensuring data integrity at each stage of the product supply chain, this approach addresses these challenges effectively. The distributed network architecture employed in our technical design ensures overall system stability, reliability, and sustainability, with no single point of failure.

Profile monitoring of residuals control charts under gamma regression model

The statistical control chart is considered one of the superlative tools in quality control. Currently, control charts are being widely used in various areas, one of them being manufacturing processes. They are essential instruments that can impart crucial insights to quality controllers for maintaining productivity. The quality of a product or process can be characterized by a relationship between two or more variables, which is typically referred to as a profile. Also, public health surveillance is considered another important area that widely used control charts. In this regard, they are very useful and reliable tools for detecting outbreaks of infectious diseases. On the other hand, the gamma regression model (GRM) is a popular model considered in medical and other fields. It is applied when the response variable is continuous and positively skewed and well fitted to the gamma distribution. This paper presents a scheme for monitoring the profile. Based upon the generalized linear model (GLM) in the case of two link functions: identity and log link function. Exponentially weighted moving average control charts (EWMA) are proposed using deviance residuals and Pearson residuals for detecting any disturbance in the control variable of the gamma regression model. A detailed simulation study is designed to scrutinize and evaluate the performance of the control charts in phase I analysis and in phase II under parametric maximum likelihood estimation (MLE) using the average run length (ARL) measure. It turns out that using deviance residuals under the identity link function seems more suitable than Pearson residuals. Also, with increasing the sample size, the percentages of out-of-control (OC) samples increased which is theoretically acceptable

Kibria‐Lukmantype estimator for gamma regression model

SummaryThe gamma regression model explores the relationship between a skewed response variable and one or more independent variables. The method of maximum likelihood is popularly adopted to model the relationship. However, the method performance drops when linear dependency exists among the predictors (multicollinearity). In this article, we develop a new method to account for multicollinearity in gamma regression model. The proposed estimator theoretically dominates the existing estimators. The simulation studies and real‐life application supports the theoretical findings.

On the Bayesian Mixture of Generalized Linear Models with Gamma-Distributed Responses

This paper proposes enhanced studies on a model consisting of a finite mixture framework of generalized linear models (GLMs) with gamma-distributed responses estimated using the Bayesian approach coupled with the Markov Chain Monte Carlo (MCMC) method. The log-link function, which relates the mean and linear predictors of the model, is implemented to ensure non-negative values of the predicted gamma-distributed responses. The simulation-based inferential processes related to the Bayesian-MCMC method is carried out using the Gibbs sampler algorithm. The performance of proposed model is conducted through two real data applications on the gross domestic product per capita at purchasing power parity and the annual household income per capita. Graphical posterior predictive checks are carried out to verify the adequacy of the fitted model for the observed data. The predictive accuracy of this model is compared with other Bayesian models using the widely applicable information criterion (WAIC). We find that the Bayesian mixture of GLMs with gamma-distributed responses performs properly when the appropriate prior distributions are applied and has better predictive accuracy than the Bayesian mixture of linear regression model and the Bayesian gamma regression model.

ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESIS MODEL GEOGRAPHICALLY WEIGHTED GENERALIZED GAMMA REGRESSION

Each location has unique characteristics, which are different from other locations which give rise to spatial effects between locations. Therefore, the Generalized Gamma Regression (GGR) model is not suitable to be applied to this problem. The solution is to use a Geographically Weighted Generalized Gamma Regression (GWGGR) model which produces different parameters for each observation location. This study aims to estimate GWGGR parameters using the Berndt-Hall-Hall-Hausman (BHHH) algorithm. After parameter estimation is performed, the hypothesis testing procedure is used to test the similarity of parameters between the generalized gamma regression and GWGGR and to test the significance of the independent variables in the model, either simultaneously using the Maximum Likelihood Ratio Test (MLRT) or partially using the Z-test. Keywords: BHHH, Generalized Gamma, GGR, GWGGR, MLRT.

More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications

The Gamma ridge regression estimator (GRRE) is commonly used to solve the problem of multicollinearity, when the response variable follows the gamma distribution. Estimation of the ridge parameter estimator is an important issue in the GRRE as well as for other models. Numerous ridge parameter estimators are proposed for the linear and other regression models. So, in this study, we generalized these estimators for the Gamma ridge regression model. A Monte Carlo simulation study and two real-life applications are carried out to evaluate the performance of the proposed ridge regression estimators and then compared with the maximum likelihood method and some existing ridge regression estimators. Based on the simulation study and real-life applications results, we suggest some better choices of the ridge regression estimators for practitioners by applying the Gamma regression model with correlated explanatory variables.

Hospital treatment costs associated with incident complications in patients with type 2 diabetes\u2014real-world study based on electronic patient information systems

BackgroundType 2 diabetes (T2D) and its complications cause a significant public health and economic challenge. To enable the optimal resource allocation across different prevention and treatment policies for the management of T2D-related complications, detailed cost estimates related to the complications of T2D are needed. Therefore, the objective of the study was to provide reliable and sufficiently detailed real-world estimates of costs associated with different T2D complications in a Finnish university hospital setting.MethodsA cohort of T2D patients living in the catchment area of a university hospital during 2012 and 2016 was identified from the comprehensive national FinDM diabetes database for longitudinal assessment of T2D associated complication treatment costs. Data on patient-level events were extracted from the FinDM data and complemented with all accountable services and related detailed costing data gathered from the university hospital’s electronic patient information systems by using unique personal identity codes. Patients were screened for their first diagnoses of complications using the same national quality registry definitions as in the FinDM database. Multivariable gamma regression model with a log link function was applied to study the association between baseline factors and complication costs. In addition, an interactive online tool was developed to create predicted costs for complication costs with selected baseline factors.ResultsA total of 27 255 prevalent and incident patients with T2D were identified from the national FinDM register. Finally, a total of 16 148 complication episodes for 7 895 patients were included in the cost analyses. The mean estimated one-year hospital treatment costs of T2D-related complication varied from 6 184 to 24 507 euros per complication. Regression analyses showed that coexisting conditions are significantly associated with initial and recurrent complication costs.ConclusionsThe study shows updated Finnish cost estimates and their main cost drivers for T2D-related complications treated in the university hospital setting. The results of our study highlight the significance of guideline implementation, effective preventive treatments for T2D, as well as the importance of treatment adherence to avoid these costly complications.

Handgrip Strength-Related Factors in a Colombian Hypertensive Population: A Cross-Sectional Study.

(1) Background: This study determined the factors associated with manual grip strength in people with high blood pressure (HBP); (2) Methods: 219 subjects participated in this cross-sectional study, which evaluated muscle strength (manual dynamometer), sociodemographic factors, clinical characteristics, level of physical activity (International Physical Activity Questionnaire-IPAQ score), and depression (Zung’s Depression Self-Rating Scale); (3) Results: The bivariate analysis found that handgrip strength in people with HPB was associated with sex (p = 0.000), age (p = 0.000), ethnicity (p = 0.019), smoking habits (p = 0.037), alcohol consumption (p = 0.004), diastolic blood pressure (p = 0.012), weight (p = 0.000), height (p = 0.000), measurement of waist circumference (p = 0.002), depression (p = 0.041), and IPAQ score (p = 0.000). Regardless of being male or female, handgrip strength was associated with age (p = 0.009), IPAQ (p = 0.000), weight (p = 0.038), height (p = 0.000), DPB units (p = 0.043), and depression (p = 0.020). The multivariate generalized linear gamma regression model showed that the coefficient with the greatest weight, regardless of sex, was age (p = 0.043), level of physical activity (24% more at high level than at low level, p = 0.031), and depression (moderate/severe depression level) associated with lower handgrip strength (p = 0.025); (4) Conclusions: Handgrip strength showed an association with level of physical activity, age, and level of depression in a middle-aged population with HBP.