Generalized Poisson Model Research Articles

Fast Bayesian Inference for Spatial Mean-Parameterized Conway–Maxwell–Poisson Models

Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are currently two classes of models that allow for these features—the mode-parameterized Conway–Maxwell–Poisson (COMP) distribution and the generalized Poisson model. However both require the use of either constraints on the parameter space or a parameterization that leads to challenges in interpretability. We propose spatial mean-parameterized COMP models that retain the flexibility of these models while resolving the above issues. We use a Bayesian spatial filtering approach in order to efficiently handle high-dimensional spatial data and we use reversible-jump MCMC to automatically choose the basis vectors for spatial filtering. The COMP distribution poses two additional computational challenges—an intractable normalizing function in the likelihood and no closed-form expression for the mean. We propose a fast computational approach that addresses these challenges by, respectively, introducing an efficient auxiliary variable algorithm and pre-computing key approximations for fast likelihood evaluation. We illustrate the application of our methodology to simulated and real datasets, including Texas HPV-cancer data and US vaccine refusal data. Supplementary materials for this article are available online.

SpVC for the detection and interpretation of spatial gene expression variation

Spatially resolved transcriptomics technologies have opened new avenues for understanding gene expression heterogeneity in spatial contexts. However, existing methods for identifying spatially variable genes often focus solely on statistical significance, limiting their ability to capture continuous expression patterns and integrate spot-level covariates. To address these challenges, we introduce spVC, a statistical method based on a generalized Poisson model. spVC seamlessly integrates constant and spatially varying effects of covariates, facilitating comprehensive exploration of gene expression variability and enhancing interpretability. Simulation and real data applications confirm spVC’s accuracy in these tasks, highlighting its versatility in spatial transcriptomics analysis.

Impacts of Livestock Production on Grassland Grasshopper Disasters

Grasshopper disasters threaten grassland animal husbandry, and overgrazing is widely recognized as one of the main causes of locust infestation in grassland regions. However, the impact of overgrazing on grasshopper disasters remains unclear. To address this knowledge gap, this study interviewed 541 households living in locust-prone areas in Inner Mongolia, China. The generalized Poisson model and OLS regression examined the relationship between herders’ production behavior and locust disasters. The results showed that 42% of the herders had suffered from locusts more than three times over the past 15 years, with an average of 49 ha of grassland damaged per household. In addition, with the increase in grazing rates, the scale of locust disasters decreased before it increased. The results also showed that operating grassland areas and feeding forage reduced locust disasters significantly, while renting grassland areas and grazing rates worked oppositely. These results suggest that grazing intensity can make a significant difference in the occurrence of locust disasters.

Mapping QTL controlling count traits with excess zeros and ones using a zero-and-one-inflated generalized Poisson regression model.

The research on the quantitative trait locus (QTL) mapping of count data has aroused the wide attention of researchers. There are frequent problems in applied research that limit the application of the conventional Poisson model in the analysis of count phenotypes, which include the overdispersion and excess zeros and ones. In this article, a novel model, that is, the zero-and-one-inflated generalized Poisson (ZOIGP) model, is proposed to deal with these problems. Based on the proposed model, a score test is performed for the inflation parameter, in which the ZOIGP model with a constant proportion of excess zeros and ones is compared with a standard generalized Poisson model. To illustrate the practicability of the ZOIGP model, we extend it to the QTL interval mapping application that underpins count phenotype with excess zeros and excess ones. The genetic effects are estimated utilizing the expectation-maximization algorithm embedded with the Newton-Raphson algorithm, and the genome-wide scan and likelihood ratio test is performed to map and test the potential QTLs. The statistical properties exhibited by the proposed method are investigated through simulation. Finally, a real data analysis example is used to illustrate the utility of the proposed method for QTLmapping.

Socio-environmental predictors of diabetes incidence disparities in Tanzania mainland: a comparison of regression models for count data

BackgroundDiabetes is one of the top four non-communicable diseases that cause death and illness to many people around the world. This study aims to use an efficient count data model to estimate socio-environmental factors associated with diabetes incidences in Tanzania mainland, addressing lack of evidence on the efficient count data model for estimating factors associated with disease incidences disparities.MethodsThis study analyzed diabetes counts in 184 Tanzania mainland councils collected in 2020. The study applied generalized Poisson, negative binomial, and Poisson count data models and evaluated their adequacy using information criteria and Pearson chi-square values.ResultsThe data were over-dispersed, as evidenced by the mean and variance values and the positively skewed histograms. The results revealed uneven distribution of diabetes incidence across geographical locations, with northern and urban councils having more cases. Factors like population, GDP, and hospital numbers were associated with diabetes counts. The GP model performed better than NB and Poisson models.ConclusionThe occurrence of diabetes can be attributed to geographical locations. To address this public health issue, environmental interventions can be implemented. Additionally, the generalized Poisson model is an effective tool for analyzing health information system count data across different population subgroups.

Modeling Zero-inflated Count Data Using Generalized Poisson and Ordinal Logistic Regression Models in Medical Research.

In medical research, the study's design and statistical methods are pivotal, as they guide interpretation and conclusion. Selecting appropriate statistical models hinges on the distribution of the outcome measure. Count data, frequently used in medical research, often exhibit over-dispersion or zero inflation. Occasionally, count data are considered ordinal (with a maximum outcome value of 5), and this calls for the application of ordinal regression models. Various models exist for analyzing over-dispersed data such as negative binomial, generalized Poisson (GP), and ordinal regression model. This study aims to examine whether the GP model is a superior alternative to the ordinal logistic regression (OLR) model, specifically in the context of zero-inflated Poisson models using both simulated and real-time data. Simulated data were generated with varied estimates of regression coefficients, sample sizes, and various proportions of zeros. The GP and OLR models were compared using fit statistics. Additionally, comparisons were made using real-time datasets. The simulated results consistently revealed lower bias and mean squared error values in the GP model compared to the OLR model. The same trend was observed in real-time datasets, with the GP model consistently demonstrating lower standard errors. Except when the sample size was 1000 and the proportions of zeros were 30% and 40%, the Bayesian information criterion consistently favored the GP model over the OLR model. This study establishes that the proposed GP model offers a more advantageous alternative to the OLR model. Moreover, the GP model facilitates easier modeling and interpretation when compared to the OLR model.

Implementation of Continuous Pegasparaginase Dosing without an Asparaginase-Free Interval Reduces Hypersensitivity in Children with Newly Diagnosed Acute Lymphoblastic Leukemia: Results of the DCOG ALL11 Pegasparaginase Randomization

Background: Asparaginase is key in the treatment of pediatric acute lymphoblastic leukemia (ALL). Hypersensitivity is one of its major side effects and hamper its use. Most hypersensitivity reactions occur after an asparaginase-free interval, as neutralizing anti-drug antibodies increase during these intervals. Thus we hypothesized that a continuous PEGasparaginase dosing schedule (without an asparaginase-free interval) would result in less hypersensitivity to PEGasparaginase compared to the standard non-continuous PEGasparaginase dosing schedule. Methods: Medium risk (MR) patients (aged 1-18 yrs) with ALL enrolled in the DCOG ALL11 protocol, were randomized to receive 14 individualized PEGasparaginase doses after an asparaginase-free interval of 3 months or to continue PEGasparaginase treatment following the first 3 doses in induction (EudraCT:2012-000067-25; Dutch Trial Register NL3227). Hypersensitivity included allergies, allergic-like reactions, and silent inactivations, where inactivating hypersensitivity reactions comprised the sum of allergies and silent inactivations. Secondary endpoints included other asparaginase-related adverse event (AEs) (CTCAE >grade 3), such as febrile neutropenia, infection, a thromboembolic event, pancreatitis, and avascular necrosis, as well as antibody levels and treatment outcome. Cumulative incidence of relapse (CIR), cumulative incidence of death (CID) in CR1 and disease-free survival (DFS) were compared between both treatment arms. Results: 312 MR patients were randomized to receive PEGasparaginase in a continuous (n=155) and non-continuous (n=157) dosing schedule. Hypersensitivity reactions occurred in 4 out of 155 (2.6%) patients in the continuous treatment arm versus 17 out of 157 (10.8%) patients in the non-continuous treatment arm (P<0.01), of which 2 (1.3%) versus 13 (8.3%) were inactivating reactions (Figure 1; P<0.01). Patients in de continuous treatment arm were significantly less likely to get an inactivating hypersensitivity reaction (odds ratio: 0.15 (0.032-0.653), P=0.012). Antibody levels were significantly lower in the continuous arm compared to the non-continuous arm (P<0.01). Without the asparaginase-free interval, the antibody levels slightly increased by 1.1-fold between dose 3 and 4 whereas antibody levels in the non-continuous arm increased by 2.5-fold during the asparaginase-free interval. We did not find any significant differences in the total number of asparaginase-associated AEs between the treatment arms (Figure 1). However, the generalized Poisson model analysis revealed that the occurrence of specific AEs, such as a thromboembolic event and pancreatitis, was influenced by both treatment phase and arm. These correlations can be attributed to the timing of asparaginase administrations, since at start of randomization asparaginase treatment was interrupted in the non-continuous arm but uninterrupted in the continuous arm. Consequently, thromboembolic events and pancreatitis occurred more frequently at the beginning of randomization in the continuous arm compared to the non-continuous arm (Table 1). This pattern reversed when the non-continuous arm resumed asparaginase treatment after the asparaginase-free period, while the continuous arm concluded their treatment. The occurrence of infections was not associated with treatment phase and treatment arm. The median duration of treatment phases was comparable between the two arms, with the exception of a longer duration of protocol M in the continuous versus non-continuous arm (median 10.3 versus 9.4 weeks respectively instead of the planned 9 weeks; P<0.01) Estimated median follow-up time was 57.2 months (95%-CI 51.9-61.3). The 5-yr CIR, CID in CR1 and DFS were 5.6% (SE 2.1%), 1.9% (SE 1.1%) and 91.9% (SE 2.4%) for continuous treatment vs 4.0% (SE 1.8%), 0.6% (SE 0.6%) and 95.3% (SE 1.9%) for non-continuous treatment (P=0.710; P=0.308; P=0.289), respectively. Conclusion: A continuous dosing schedule of PEGasparaginase resulted in a 7 times lower incidence of inactivating hypersensitivity reactions and lower anti-drug antibody levels compared with a non-continuous dosing schedule with an asparaginase-free interval. The continuous schedule of asparaginase treatment did not increase toxicity but changed the timing of toxicities and did not affect the efficacy of the therapy.

Testing latent classes in gut microbiome data using generalized Poisson regression models.

Human microbiome research has gained increasing importance due to its critical roles in comprehending human health and disease. Within the realm of microbiome research, the data generated often involves operational taxonomic unit counts, which can frequently present challenges such as over-dispersion and zero-inflation. To address dispersion-related concerns, the generalized Poisson model offers a flexible solution, effectively handling data characterized by over-dispersion, equi-dispersion, and under-dispersion. Furthermore, the realm of zero-inflated generalized Poisson models provides a strategic avenue to simultaneously tackle both over-dispersion and zero-inflation. The phenomenon of zero-inflation frequently stems from the heterogeneous nature of study populations. It emerges when specific microbial taxa fail to thrive in the microbial community of certain subjects, consequently resulting in a consistent count of zeros for these individuals. This subset of subjects represents a latent class, where their zeros originate from the genuine absence of the microbial taxa. In this paper, we introduce a novel testing methodology designed to uncover such latent classes within generalized Poisson regression models. We establish a closed-form test statistic and deduce its asymptotic distribution based on estimating equations. To assess its efficacy, we conduct an extensive array of simulation studies, and further apply the test to detect latent classes in human gut microbiome data from the Bogalusa Heart Study.

ALTERNATIVE MODELS IN OVERCOMING THE PROBLEM OF OVERDISPERSION IN POISSON REGRESSION

This study aims to compare various alternative models in overcoming the problem of overdispersion in Poisson regression modeling. The comparative modeling is the Generalized Poisson model, Negative Binomial, and Generalized Negative Binomial. Modeling is applied to modeling the number of poor people in Central Java in 2021 with unemployment, HDI, and GRDP as independent variables. The results obtained by Generalized Poison are better than Negative Binomial and Generalized Negative Binomial because of the smaller AIC and BIC values ??and the larger R2. For simultaneous tests, it can be concluded that unemployment, HDI, and GRDP significantly affect the number of poor people. Only unemployment and HDI variables partially affect the number of poor people in Central Java. On the other hand, there is not enough evidence that GRDP affects some poor people. There is a need for comprehensive and relevant policies to overcome the number of poor people in an area.

A generalized Poisson model to predict host-seeking female Aedes aegypti marked by dusted Metarhizium anisopliae-exposed males.

We developed a biological control method directed toward Aedes aegypti using the release of Metarhizium anisopliae-contaminated males to spread the fungus to wild females. A generalized Poisson model was used to relate Ae. aegypti marked females (MKF) to M. anisopliae-exposed males (FEM). In a mark-recapture parallel arm trial, FEM release was a better predictor than unexposed male (UM) releases to forecast MKF by FEM. Total females (TF), marked males (MKM), and wild males (WM) as predictors were counted in human-landings in 15 households treated with 40 FEM each, vs 40 UM released/household/week in 15 households for eight weeks. Fit of MKF to standard, generalized Poisson (GP), and negative binomial models/arm built by TF, MKM, WM, and interactions as predictors were computed. In both arms, MKF was better modeled by GP, which in treated, all but one of the eight observed data fell within the confidence intervals predicted by the model. However, the control GP had two outliers and MKM as a single predictor. Likewise, the pseudo-R2 measures of 95% and 46% for treated and control groups also showed that the GP with FEM was more suitable to predict MKF. It should thus be possible to use the GP model to indirectly estimate that an increase of one TF or one fungus-exposed male would increase the number of marked-females by 8% or 9%, respectively, while wild males were an irrelevant predictor to the model.

Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms

Under-dispersed count data often appear in clinical trials, medical studies, demography, actuarial science, ecology, biology, industry and engineering. Although the generalized Poisson (GP) distribution possesses the twin properties of under- and over-dispersion, in the past 50 years, many authors only treat the GP distribution as an alternative to the negative binomial distribution for modeling over-dispersed count data. To our best knowledge, the issues of calculating maximum likelihood estimates (MLEs) of parameters in GP model without covariates and with covariates for the case of under-dispersion were not solved up to now. In this paper, we first develop a new minimization–maximization (MM) algorithm to calculate the MLEs of parameters in the GP distribution with under-dispersion, and then we develop another new MM algorithm to compute the MLEs of the vector of regression coefficients for the GP mean regression model for the case of under-dispersion. Three hypothesis tests (i.e., the likelihood ratio, Wald and score tests) are provided. Some simulations are conducted. The Bangladesh demographic and health surveys dataset is analyzed to illustrate the proposed methods and comparisons with the existing Conway–Maxwell–Poisson regression model are also presented.

BAYESIAN MODELLING OF TUBERCULOSIS PREVALENCE IN SOUTH AFRICA. AN OVER-DISPERSION STUDIES

Introduction: To account for over-dispersion in the impact of population density, number of schools, and average household size on tuberculosis prevalence in South Africa’s Eastern Cape Province, this study compared robust count regression models with a Poisson regression model. Methods: The prevalence of tuberculosis in the province of Eastern Cape in South Africa in 2022 served as the basis for this study’s data. Various models, including the Poisson regression model; Summed up Poisson and Negative Binomial Relapse were used within the sight of over-scattering. Results: It was seen that Poisson Relapse models couldn’t deal with over-scattering present in the South Africa’s Eastern Cape Region Tuberculosis dataset. Modeling with Negative Binomial Regression (NBR) and Generalized Binomial Regression (GBR) was used to solve the over-dispersion issue because both approaches can accommodate the dispersion parameter. Based on both selection criteria, the Negative Binomial model performed slightly better than the Generalized Poisson model. The findings indicated that population density has a positive and significant impact on tuberculosis prevalence in South Africa, that the number of schools in the province has a negative but significant impact, and that the average household has no significant impact. Conclusions: The Eastern Cape Province of South Africa’s government ought to intensify its efforts to combat the spread and prevalence of tuberculosis by identifying, isolating, and treating tuberculosis early in the population and in schools.

Oral health outcomes and shift working among male workers: A cross-sectional survey.

Working time outside routine daily working hours is known as shift working. Studies have shown adverse effects of shift working such as stress, obesity, and diabetes on the workers' health. The aim of the present study was to compare aspects of oral health in shift workers and non-shift workers of a cement factory in Shahroud, Iran. Study population comprised of 180 male workers of the factory in the year 2015. Convenience sampling was continued until recruiting 180 subjects of shift- and non-shift workers. Data collection included oral health questionnaire, health and safety executive (HSE) questionnaire, and clinical oral examination. The Chi-square test, Pearson correlation coefficient, and generalized Poisson model were employed for statistical evaluation. Mean age of the workers was 39.19 (±9.48); 53% had educational level of less than diploma. Their mean DMFT was 12.89 (±5.75) which correlated with number of years in shift work schedule (Pearson correlation coefficient: 0.41; p<0.001) but not correlated with job stress (Pearson correlation coefficient: -0.11; p = 0.12). Mean number of deep periodontal pockets among the workers was 5.03 (±1.84) that showed correlation with number of years in shift work schedule (Pearson correlation coefficient: 0.33; p<0.001) but no correlation with job stress (Pearson correlation coefficient: -0.03; p = 0.68). Adherence to various oral health behaviors was reported by less than half of the workers. Positive correlation of dental caries and periodontal diseases with shift working partly signals negative impact of working conditions on oral health among this group of workers which calls for modifications in their working environment to facilitate health practices.

Modelling Underdispersed Count Data: Relative Performance of Poisson Model and its Alternatives

Count data are common in many fields and often modelled with the Poisson model. However, the equidispersion assumption (variance = mean) related to the Poisson model is often violated in practice. While much research has focused on modelling overdispersed count data, underdispersion has received relatively little attention. Alternative models are therefore needed to handle overdispersion (variance &gt; mean) and underdispersion (variance &lt; mean). This study assessed the relative performance of the Poisson model and its alternatives (COM-Poisson, Generalized Poisson Regression, Double Poisson and Gamma Count) to model underdispersed count data. Using a Monte Carlo experiment, the simulation plan considered various underdispersion levels (k (variance/mean) = 0.2, 0.5 and 0.81), k=1 as a control, and sample sizes (n=20, 50, 100, 300 and 500). Results showed that the Poisson model is not robust to handle underdispersion but it is the best performer when k=1. The COM-Poisson model best fitted severe underdispersed data (k=0.2). It is also the best performer model for moderate underdispersed count data (k=0.81). However, when k=0.5, the Double Poisson model and Generalized Poisson model outperformed other models for relatively large sample sizes (n=100, 300 and 500). Our finding suggests that none of the models suits all situations. Therefore, in practice, several of these models need to be tested to select the best one.

Trivariate compound generalized poisson model for corticotropin-releasing hormone effects on human pregnant and nonpregnant

In this paper, we apply a new approach to uterine contractions to a large panel of human pregnant non pregnant myometrial strips, treated or not by corticotropin releasing hormone (CRH). This model is based on a fine analysis of the contraction curves.This analysis yield four mathematical parameters beta, theta, tau1 and tau2 related to excitability, duration of plateau phase, and time constants for relaxation describing respectively, the different portions of the contraction cycle. This leads to specific differences in spontaneous contractile activity between pregnant and nonpregnant states. In the present study, we compare nonpregant and pregnant women close to the term vitro CRH myometrial responsiveness, to describe uterine contractile activity during a parturition. We have a Trivariate compound generalized Poisson model for uterine contraction to a pregnant and nonpregnant myometrial strips, treated or not treated by corticotrophin- releasing hormone (CRH). Although, the biochemical signification of these results remains to be elucidated, we contribute to emphasize CRH action at the myometrical level. The results reveal highly significant differences between pregnant and nonpregnant myometrium as well as in their response to CRH.

A penalized likelihood approach for dealing with separation in count data regression model

Separation or monotone likelihood can be observed in fitting process of both Poisson or generalized Poisson (GP) regression, particularly in case of small and/or sparse count data, using maximum likelihood estimation (MLE) when one or more regression coefficients diverge to infinity. The study investigates the consequence of separation in the MLE based standard Poisson or GP model and addressed the problems by introducing a penalized likelihood approach. The penalized likelihood function is derived by adding a penalty term to the standard maximum likelihood function, which was originally proposed by Firth (1993) for reducing first order bias in MLE. The corresponding penalized likelihood score equation has shown to achieve convergence and provide finite estimate of the regression coefficient, which was not possible for the maximum likelihood method score equation. The simulation study, with different forms of separation, showed that penalized Poisson model or penalized GP outperform the standard Poisson and even the Zero-inflated Poisson (ZIP) in the presence of complete or quasi-complete separation by achieving convergence and providing finite estimate of the regression coefficients. Even in the presence of near-to-quasi-complete separation, which is very common in practice, the penalized method showed better results than the standard Poisson, GP and ZIP in all simulation scenarios. The method was illustrated using antenatal care data extracted from database of the Bangladesh demographic health survey 2018.

Generalized Poisson Hurdle Model for Count Data and Its Application in Ear Disease.

For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

Letalidad peatonal en Ciudad de México: análisis general desde una perspectiva de racionalidad limitada

Considering a theoretical perspective of bounded rationality of drivers and pedestrians in pedestrian collisions, a research was carried out about pedes-trian lethality rate in Mexico City considering attribu-table causes to persons or other causes, place (intersections and non-intersections of roads), time of the day, day, month, local municipalities and year of the accident from 1997 to 2017. To the analysis was estimated a Generalized Poisson Model. With the model results, the relative risk of pedestrian death after being run over was analyzed. There are three remarkable results: Lethality and relative risk of deaths increased due to non-attributable causes of the agents. Secondly, that lethality is higher in non-intersections and that the relative risk of deaths in intersections is lower in percentage terms concer-ning non-intersections. Third, that lethality and the relative risk of deaths are greater in attributable causes of pedestrians than in attributable causes of drivers. These results may constitute part of the un-certainty and information constraints that describe bounded rationality. The conclusion is that crossing pedestrians at non-interference crossings can in-crease lethality and increase death's relative risk. Also, it was observed that causes unrelated to agent’s actions (pedestrians and drivers) cause mo-re pedestrian deaths.

Zero-Inflated Generalized Poisson Regression Model with an Application to Domestic Violence Data

The generalized Poisson regression model has been used to model dispersed count data. It is a good competitor to the negative binomial regression model when the count data is over-dispersed. Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for the situations where the data generating process results into too many zeros. In this paper, we propose a zero-inflated generalized Poisson (ZIGP) regression model to model domestic violence data with too many zeros. Estimation of the model parameters using the method of maximum likelihood is provided. A score test is presented to test whether the number of zeros is too large for the generalized Poisson model to adequately fit the domestic violence data

Models for Overdispersion Count Data with Generalized Distribution: An Application to Parasites Intensity

The Poisson regression model is widely used for count data. This model assumes equidispersion. In practice, equidispersion is seldom reflected in data. However, in real-life data, the variance usually exceeds the mean. This situation is known as overdispersion. Negative binomial distribution and other Poisson mix models are often used to model overdispersion count data. Another extension of the negative binomial distribution in another model for count data is the univariate generalized Waring. In addition, the model developed by Famoye can be used in the analysis of count data. When the count data contains a large number of zeros, it is necessary to use zero-inflated models. In this study, different generalized regression models are emphasized for the analysis of excessive zeros count data. For this purpose, a real data set was analysed with the generalized Poisson model, generalized negative binomial model, generalized negative binomial Famoye, generalized Waring model, and the foregoing zero-inflated models. Log-likelihood, Akaike information criterion, Bayes information criterion, Vuong statistics were used for model comparisons.