Clustered Count Data Research Articles

Modeling clustered count data using mixed effect discrete Weibull regression model with cubic splines

This paper investigates the use of mixed-effect discrete Weibull (DW) regression model with cubic splines for clustered count data. DW regression model can be used for both over and under-dispersed data thus, it can be an appropriate choice for researchers to use without having the risk to violate assumptions for using a particular model distribution. We used a cubic spline function to model the non-linear relationship between the outcome variable and the covariate. The proposed model is applied to a clustered dataset from the eighth Korean National Health and Nutrition Examination Survey (KNHANES VIII) from 2019 to assess the factors influencing the amount of alcohol drink in 17 different regions. We compared the results with our proposed model with those of Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models in the presence of spline function. The results show that using DW regression model with cubic spline gives the best fit. We also held a simulation study to investigate the performance and the robustness of DW with a spline function. It turns out that DW regression model with a spline function can flexibly model clustered count data with various dispersion and data with many zeros.

Sexual and Reproductive Health Outcomes Among Adolescent Females During the COVID-19 Pandemic.

Coronavirus disease 2019 (COVID-19) posed a significant threat to adolescents' sexual and reproductive health. In this study, we examined population-level pregnancy and sexual health-related care utilization among adolescent females in Ontario, Canada during the pandemic and evaluated relationships between these outcomes and key sociodemographic characteristics. This was a population-based, repeated cross-sectional study of >630 000 female adolescents (12-19 years) during the prepandemic (January 1, 2018-February 29, 2020) and COVID-19 pandemic (March 1, 2020-December 31, 2022) periods. Primary outcome was pregnancy; secondary outcomes were contraceptive management visits, contraception prescription uptake, and sexually transmitted infection (STI) management visits. Poisson models with generalized estimating equations for clustered count data were used to model pre-COVID-19 trends and forecast expected rates during the COVID-19 period. Absolute rate differences between observed and expected outcome rates for each pandemic month were calculated overall and by urbanicity, neighborhood income, immigration status, and region. During the pandemic, lower-than-expected population-level rates of adolescent pregnancy (rate ratio 0.87; 95% confidence interval [CI]:0.85-0.88), and encounters for contraceptive (rate ratio 0.82; 95% CI:0.77-0.88) and STI management (rate ratio 0.52; 95% CI:0.51-0.53) were observed. Encounter rates did not return to pre-pandemic rates by study period end, despite health system reopening. Pregnancy rates among adolescent subpopulations with the highest pre-pandemic pregnancy rates changed least during the pandemic. Population-level rates of adolescent pregnancy and sexual health-related care utilization were lower than expected during the COVID-19 pandemic, and below-expected care utilization rates persist. Pregnancy rates among more structurally vulnerable adolescents demonstrated less decline, suggesting exacerbation of preexisting inequities.

Sample size calculations for clustered count data based on zero-inflated discrete Weibull regression models

Sample size calculations for clustered count data based on zero-inflated discrete Weibull regression models

Regression analysis of clustered panel count data with additive mean models

Regression analysis of clustered panel count data with additive mean models

Modeling clustered count data with discrete weibull regression model

Modeling clustered count data with discrete weibull regression model

Addressing overdispersion and zero-inflation for clustered count data via new multilevel heterogenous hurdle models

ABSTRACT Unobserved heterogeneity causing overdispersion and the excessive number of zeros take a prominent place in the methodological development on count modeling. An insight into the mechanisms that induce heterogeneity is required for better understanding of the phenomenon of overdispersion. When the heterogeneity is sourced by the stochastic component of the model, the use of a heterogenous Poisson distribution for this part encounters as an elegant solution. Hierarchical design of the study is also responsible for the heterogeneity as the unobservable effects at various levels also contribute to the overdispersion. Zero-inflation, heterogeneity and multilevel nature in the count data present special challenges in their own respect, however the presence of all in one study adds more challenges to the modeling strategies. This study therefore is designed to merge the attractive features of the separate strand of the solutions in order to face such a comprehensive challenge. This study differs from the previous attempts by the choice of two recently developed heterogeneous distributions, namely Poisson–Lindley (PL) and Poisson–Ailamujia (PA) for the truncated part. Using generalized linear mixed modeling settings, predictive performances of the multilevel PL and PA models and their hurdle counterparts were assessed within a comprehensive simulation study in terms of bias, precision and accuracy measures. Multilevel models were applied to two separate real world examples for the assessment of practical implications of the new models proposed in this study.

A Flexible Mixed Model for Clustered Count Data

Clustered count data are commonly modeled using Poisson regression with random effects to account for the correlation induced by clustering. The Poisson mixed model allows for overdispersion via the nature of the within-cluster correlation, however, departures from equi-dispersion may also exist due to the underlying count process mechanism. We study the cross-sectional COM-Poisson regression model—a generalized regression model for count data in light of data dispersion—together with random effects for analysis of clustered count data. We demonstrate model flexibility of the COM-Poisson random intercept model, including choice of the random effect distribution, via simulated and real data examples. We find that COM-Poisson mixed models provide comparable model fit to well-known mixed models for associated special cases of clustered discrete data, and result in improved model fit for data with intermediate levels of over- or underdispersion in the count mechanism. Accordingly, the proposed models are useful for capturing dispersion not consistent with commonly used statistical models, and also serve as a practical diagnostic tool.

Sample size for clustered count data based on discrete Weibull regression model

In this study we consider the problem of sample size determination for clustered count data based on clustered discrete Weibull regression model. Many papers that deal with sample size calculation for clustered count data have a strong assumption about the dispersion type of the data. Poisson, negative binomial are widely used models however their assumptions are hard to be met in real life. Here we propose to use discrete Weibull regression model which can handle both under and over dispersed type of data for clustered count data when calculating the sample size. We incorporate a random intercept to consider the correlation between the subjects in each cluster. We used the h-likelihood method and Monte Carlo simulation to estimate the required sample size for clustered count data. Extensive simulation study is also performed to examine the effect of the skewness of the data, variance of the random effect and the number of the clusters on calculating the required sample calculation.

Use of between-within degrees of freedom as an alternative to the Kenward–Roger method for small-sample inference in generalized linear mixed modeling of clustered count data

Clustered count data, common in health-related research, are routinely analyzed using generalized linear mixed models. There are two well-known challenges in small-sample inference in mixed modeling: bias in the naïve standard error approximation for the empirical best linear unbiased estimator, and lack of clearly defined denominator degrees of freedom. The Kenward–Roger method was designed to address these issues in linear mixed modeling, but neither it nor the simpler option of using between-within denominator degrees of freedom has been thoroughly examined in generalized linear mixed modeling. We compared the Kenward–Roger and between-within methods in two simulation studies. For simulated cluster-randomized trial data, coverage rates for both methods were generally close to the nominal 95% level and never outside 93-97%, even for 5 clusters with an average of 3 observations each. For autocorrelated longitudinal data, between-within intervals were more accurate overall, and under some conditions both the original and improved Kenward–Roger methods behaved erratically. Overall, coverage for Kenward–Roger and between-within intervals was generally adequate, if often conservative. Based on the scenarios examined here, use of between-within degrees of freedom may be a suitable or even preferable alternative to the Kenward–Roger method in some analyses of clustered count data with simple covariance structures.

The Poisson Inverse Gaussian Regression Model in the Analysis of Clustered Counts Data

We explore the possibility of modeling clustered count data using the Poisson Inverse Gaussian distribution. We develop a regression model, which relates the number of mastitis cases in a sample of dairy farms in Ontario, Canada, to various farm level covariates, to illustrate the method ology. Residual plots are constructed to explore the quality of the fit. We compare the results with a negative binomial regression model using max imum likelihood estimation, and to the generalized linear mixed regression model fitted in SAS.

Spatially clustered count data provide more efficient search strategies in invasion biology and disease control.

Geographic profiling, a mathematical model originally developed in criminology, is increasingly being used in ecology and epidemiology. Geographic profiling boasts a wide range of applications, such as finding source populations of invasive species or breeding sites of vectors of infectious disease. The model provides a cost-effective approach for prioritizing search strategies for source locations and does so via simple data in the form of the positions of each observation, such as individual sightings of invasive species or cases of a disease. In doing so, however, classic geographic profiling approaches fail to make the distinction between those areas containing observed absences and those areas where no data were recorded. Absence data are generated via spatial sampling protocols but are often discarded during the inference process. Here we construct a geographic profiling model that resolves these issues by making inferences via count data, analyzing a set of discrete sentinel locations at which the number of encounters has been recorded. Crucially, in our model this number can be zero. We verify the ability of this new model to estimate source locations and other parameters of practical interest via a Bayesian power analysis. We also measure model performance via real-world data in which the model infers breeding locations of mosquitoes in bromeliads in Miami-Dade County, Florida, USA. In both cases, our novel model produces more efficient search strategies by shifting focus from those areas containing observed absences to those with no data, an improvement over existing models that treat these areas equally. Our model makes important improvements upon classic geographic profiling methods, which will significantly enhance real-world efforts to develop conservation management plans and targeted interventions.

A multilevel zero-inflated Conway–Maxwell type negative binomial model for analysing clustered count data

Basic negative binomial models can only capture over-dispersed count responses, because the variance of the distribution is always greater than the mean value. So, they are not the best selection when the data are under-dispersed or have less dispersion than the negative binomial. Over the last years, a variety of new distributions that can account a wide range of dispersion in count data, have been introduced. One of these novel distributions is Conway–Maxwell type negative binomial distribution. In biomedical studies, it is common to demonstrate excess zeros and a pattern of dispersion in count data. Also, the observations may be correlated in clusters or longitudinally. Here, we propose a multilevel zero-inflated Conway–Maxwell type negative binomial model. Statistical inference is employed via an expectation-maximization algorithm for the parameter estimation. The model performance is illustrated by simulation studies and with a real data set.

Developing a goodness of fit test for a joint model of clustered survival and count data

Mixed responses within clusters are becoming an increasingly popular phenomenon. However, this scenario is a complex one. This research is based on survival and count response data which occur frequently in medical studies. In the literature, there is no satisfactory goodness of fit test for a joint model of these two responses within a cluster setting. Therefore, the main objective of this study is to develop a GOF test for this scenario. Simulation studies were used to examine the type I error rate and the power of the test. An example was used to display the practicality of the test.

Three-level zero-inflated Conway–Maxwell–Poisson regression model for analyzing dispersed clustered count data with extra zeros

The count response variables are usually included of extra zeros. A useful tool for modeling such data is zero-inflated regression models. In the last decade, the Conway–Maxwell–Poisson model is applied for analyzing count data that can handle under- and over-dispersed data, besides that can encompass the Poisson and negative binomial. Sometimes, due to the sampling design or the data collection procedure, the data simultaneously are clustered or correlated with extra zeros and under- or over-dispersion. We applied a three-level zero-inflated Conway–Maxwell–Poisson regression model to overcome these problems. An expectation-maximization algorithm is used to estimate the model parameters of an appropriate penalized log-likelihood function. Model flexibility and finite-sample properties of this methodology have been investigated by extensive simulation study. The method has been illustrated with an application on real data in the health survey. Furthermore, we compared the results of the model with a three-level zero-inflated negative binomial regression model.

GEE-based zero-inflated generalized Poisson model for clustered over or under-dispersed count data

ABSTRACTThe zero-inflated regression models such as zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) or zero-inflated generalized Poisson (ZIGP) regression models can model the count data with excess zeros. The ZINB model can handle over-dispersed and the ZIGP model can handle the over or under-dispersed count data with excess zeros as well. Moreover, the count data may be correlated because of data collection procedure or special study design. The clustered sampling approach is one of the examples in which the correlation among subjects could be defined. In such situations, a marginal model using generalized estimating equation (GEE) approach can incorporate these correlations and lead up to the relationships at the population level. In this study, the GEE-based zero-inflated generalized Poisson regression model was proposed to fit over and under-dispersed clustered count data with excess zeros.

Fast two-stage estimator for clustered count data with overdispersion

ABSTRACTClustered count data are commonly analysed by the generalized linear mixed model (GLMM). Here, the correlation due to clustering and some overdispersion is captured by the inclusion of cluster-specific normally distributed random effects. Often, the model does not capture the variability completely. Therefore, the GLMM can be extended by including a set of gamma random effects. Routinely, the GLMM is fitted by maximizing the marginal likelihood. However, this process is computationally intensive. Although feasible with medium to large data, it can be too time-consuming or computationally intractable with very large data. Therefore, a fast two-stage estimator for correlated, overdispersed count data is proposed. It is rooted in the split-sample methodology. Based on a simulation study, it shows good statistical properties. Furthermore, it is computationally much faster than the full maximum likelihood estimator. The approach is illustrated using a large dataset belonging to a network of Belgian general practices.

Weighted zero-inflated Poisson mixed model with an application to Medicaid utilization data

In medical or public health research, it is common to encounter clustered or longitudinal count data that exhibit excess zeros. For example, health care utilization data often have a multi-modal distribution with excess zeroes as well as a multilevel structure where patients are nested within physicians and hospitals. To analyze this type of data, zero-inflated count models with mixed effects have been developed where a count response variable is assumed to be distributed as a mixture of a Poisson or negative binomial and a distribution with a point mass of zeros that include random effects. However, no study has considered a situation where data are also censored due to the finite nature of the observation period or follow-up. In this paper, we present a weighted version of zero-inflated Poisson model with random effects accounting for variable individual follow-up times. We suggested two different types of weight function. The performance of the proposed model is evaluated and compared to a standard zero-inflated mixed model through simulation studies. This approach is then applied to Medicaid data analysis.

A Bayesian approach for analyzing zero-inflated clustered count data with dispersion.

In practice, count data may exhibit varying dispersion patterns and excessive zero values; additionally, they may appear in groups or clusters sharing a common source of variation. We present a novel Bayesian approach for analyzing such data. To model these features, we combine the Conway-Maxwell-Poisson distribution, which allows both overdispersion and underdispersion, with a hurdle component for the zeros and random effects for clustering. We propose an efficient Markov chain Monte Carlo sampling scheme to obtain posterior inference from our model. Through simulation studies, we compare our hurdle Conway-Maxwell-Poisson model with a hurdle Poisson model to demonstrate the effectiveness of our Conway-Maxwell-Poisson approach. Furthermore, we apply our model to analyze an illustrative dataset containing information on the number and types of carious lesions on each tooth in a population of 9-year-olds from the Iowa Fluoride Study, which is an ongoing longitudinal study on a cohort of Iowa children that began in 1991.

A search for sterile neutrinos with the latest cosmological observations

We report the result of a search for sterile neutrinos with the latest cosmological observations. Both cases of massless and massive sterile neutrinos are considered in the Lambda CDM cosmology. The cosmological observations used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev–Zeldovich cluster counts data, the Planck lensing data, and the cosmic shear data. We find that the current observational data give a hint of the existence of massless sterile neutrino (as dark radiation) at the 1.44sigma level, and the consideration of an extra massless sterile neutrino can indeed relieve the tension between observations and improve the cosmological fit. For the case of massive sterile neutrino, the observations give a rather tight upper limit on the mass, which implies that actually a massless sterile neutrino is more favored. Our result is consistent with the recent result of neutrino oscillation experiment done by the Daya Bay and MINOS collaborations, as well as the recent result of cosmic ray experiment done by the IceCube collaboration.

Analyzing clustered count data with a cluster-specific random effect zero-inflated Conway–Maxwell–Poisson distribution

ABSTRACTCount data analysis techniques have been developed in biological and medical research areas. In particular, zero-inflated versions of parametric count distributions have been used to model excessive zeros that are often present in these assays. The most common count distributions for analyzing such data are Poisson and negative binomial. However, a Poisson distribution can only handle equidispersed data and a negative binomial distribution can only cope with overdispersion. However, a Conway–Maxwell–Poisson (CMP) distribution [4] can handle a wide range of dispersion. We show, with an illustrative data set on next-generation sequencing of maize hybrids, that both underdispersion and overdispersion can be present in genomic data. Furthermore, the maize data set consists of clustered observations and, therefore, we develop inference procedures for a zero-inflated CMP regression that incorporates a cluster-specific random effect term. Unlike the Gaussian models, the underlying likelihood is computationally challenging. We use a numerical approximation via a Gaussian quadrature to circumvent this issue. A test for checking zero-inflation has also been developed in our setting. Finite sample properties of our estimators and test have been investigated by extensive simulations. Finally, the statistical methodology has been applied to analyze the maize data mentioned before.