Excess Zeros Research Articles

The Association between Frailty and Healthcare Expenditure among Chinese Older Adults

ObjectivesThe purpose of this study was to examine whether frailty could explain variability in healthcare expenditure beyond multimorbidity and disability among Chinese older adults. DesignCross-sectional. Setting and ParticipantsParticipants were 5300 community-dwelling adults age at least 60 years from the China Health and Retirement Longitudinal Study. MethodsFrailty was identified by the physical frailty phenotype approach that has been created and validated among Chinese older adults. Five criteria were used: slowness, weakness, exhaustion, inactivity, and shrinking. Persons were classified as “nonfrail” (0 criteria), “prefrail” (1‒2 criteria), or “frail” (3‒5 criteria). Healthcare expenditure was measured based on participants’ self-report and was classified into 3 types: outpatient expenditure, inpatient expenditure, and self-treatment expenditure. The association of frailty and healthcare expenditure was analyzed using a 2-part regression model to account for excessive zero expenditures. ResultsFrailty was associated with higher odds of incurring outpatient, inpatient, and self-treatment expenditure. Among persons with non-zero expenditure, prefrail and frail persons, on average, had US $30.62 [95% confidence interval (CI) 8.41, 52.82] and US $60.60 (95% CI 5.84, 115.36) higher outpatient expenditure than the nonfrail, adjusting for sociodemographics, multimorbidity, and disability. After adjustment for all covariates, prefrail persons, on average, had US $3.34 (95% CI 0.54, 6.13) higher self-treatment expenditure than the nonfrail. Conclusions and ImplicationsFrailty is an independent predictor of higher healthcare expenditure among older adults. These findings suggest that timely screening and recognition of frailty are important to reduce healthcare expenditure among older adults.

Sparse semiparametric canonical correlation analysis for data of mixed types.

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern datasets due to high-dimensionality and mixed data types (continuous/binary/zero-inflated). We propose a new approach for sparse canonical correlation analysis of mixed data types that does not require explicit parametric assumptions. Our main contribution is the use of truncated latent Gaussian copula to model the data with excess zeroes, which allows us to derive a rank-based estimator of latent correlation matrix without the estimation of marginal transformation functions. The resulting semiparametric sparse canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, and application to the analysis of association between gene expression and micro RNA data of breast cancer patients.

A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros

Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley distributions are special cases. Several statistical properties of the proposed distribution are presented. The dispersion index for the proposed distribution is derived and based on the index, it is clear that the proposed distribution can adequately fit the data with properties of overdispersion or underdispersion depending on the choice of the parameters. The proposed distribution is fitted to three overdispersed datasets with large proportion of zeros. The best fitted model is selected based on the values of AIC, mean absolute error and root mean squared error. From the model fittings, it can be concluded that the proposed distribution outperforms Poisson and negative binomial distributions in fitting the count data with overdispersion and large number of zeros.

Copula-based Markov zero-inflated count time series models with application

ABSTRACT Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway–Maxwell–Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data.

Prediction of the days in hospital for next year using ensemble learning

There are many difficulties in predicting problems in real life with an individual model. In order to solve these problems, we use combined these models using an ensemble learning. Combined models can be applied to the prediction of the number of days in hospital. In this paper, we use the 2011 National Sample Cohort Database to construct a combined model using an ensemble learning and predict the number of days in hospital in 2013. Also, we consider the zero inflated poisson models and hurdle poisson models considering that the days in hospital as the response variable have excess zeros. For the problem of overdispersion, we consider the zero inflated negative binomial models and hurdle negative binomial models. As baseline models, we consider the generalized additive models and the generalized linear models using the poisson and negative binomial distributions. Finally, we consider the combined models using ensemble learning. We use the National Sample Cohort Database by National Health Insurance Service and apply eight models to this data. Finally, we suggest the best prediction model by the accuracy criterion of the root mean squared logarithmic error which penalizes an under-predicted estimate greater than an over-predicted estimate.

Spatio-temporal patterns of northern gannet abundance in a migratory and wintering area

In marine ecosystems, seabird populations are well monitored, thus allowing their use as indicators of system fluctuations at multiple spatio-temporal scales. Population abundance estimates are essential features of any conservation and management measures and initiatives. Population abundances can be used to delineate the distribution range and foraging grounds of species during both breeding and non-breeding periods, with multi-annual monitoring allowing for the inspection of the temporal variability within key marine areas. Taking advantage of long-term monitoring schemes, we examined the annual abundance patterns of the northern gannet Morus bassanus in its southern European migratory flyway. Here, the presence of a topographical feature (i.e. a submarine canyon system) could influence physical processes (e.g. upwelling, alongshore currents, and riverine inputs), thus oceanographically differentiating canyon and shelf ecosystems within a spatially restricted marine area. We assessed seasonal and long-term trend fluctuations of monthly northern gannet abundance using Generalized Additive Mixed Models, yielding only a strong seasonal effect. Moreover, we jointly tested the effect of the phenology and the spatial domain (canyon versus shelf) on northern gannet abundance using Generalised Linear Mixed Models, accounting for the excess of zeros. Northern gannet abundance was higher during the pre-winter and post-winter migration, corresponding to its southward and northward movements in the NE Atlantic, respectively. The effect of the canyon was only detected during the post-winter migration. By age, adult northern gannets were more abundant in some periods of the year (from October to March, including the pre-winter migration, the wintering and the post-winter migration), whereas juveniles and immatures were especially abundant during the pre-winter period. Our results could provide quantitative baseline information of northern gannet spatio-temporal patterns in a migratory and wintering area important for both research and conservation efforts, given the high conservation value of the area within the Natura 2000 network.

Modelling the cone yields of Korean pine

Korean pine is the most important plantation tree species in northeast China. Besides timber, it produces edible seeds. Economic comparisons between alternative management schedules of Korean pine plantations require information on tree growth but also on seed yields since Korean pine seeds generate significant economic returns. This study developed models for the cone yields of Korean pine. Data were collected from 24 permanent sample plots during 2004–2018. Model types suitable for modelling count data with a high proportion of zero counts, namely zero-inflated and hurdle models, were tested as alternatives to those types of Poisson and negative binomial models that did not include a sub-model for the excess of zeros. Correlations between observations collected from the same plot and tree were taken into account by fitting mixed-effects models. There was much annual variation in seed production, which was modelled by using indicator variables for different years. The other predictors of the cone models were tree diameter at the breast height, stand basal area, competitive position of the tree in the stand (basal area in larger trees) and site index. It was concluded that the best model types for predicting cone yields in simulation and optimization studies were negative binomial hurdle model and Poisson hurdle model. The same models were evaluated to be the most recommendable also in cases where probabilistic predictions are needed, for instance in stochastic optimization.

Inequalities in participation and time spent in moderate-to-vigorous physical activity: a pooled analysis of the cross-sectional health surveys for England 2008, 2012, and 2016

BackgroundEvidence is unclear on whether inequalities in average levels of moderate-to-vigorous physical activity (MVPA) reflect differences in participation, differences in the amount of time spent active, or both. Using self-reported data from 24,882 adults (Health Survey for England 2008, 2012, 2016), we examined gender-specific inequalities in these separate aspects for total and domain-specific MVPA.MethodsHurdle models accommodate continuous data with excess zeros and positive skewness. Such models were used to assess differences between income groups in three aspects: (1) the probability of doing any MVPA, (2) the average hours/week spent in MVPA, and (3) the average hours/week spent in MVPA conditional on participation (MVPA-active). Inequalities were summarised on the absolute scale using average marginal effects (AMEs) after confounder adjustment.ResultsInequalities were robust to adjustment in each aspect for total MVPA and for sports/exercise. Differences between adults in high-income versus low-income households in sports/exercise MVPA were 2.2 h/week among men (95% confidence interval (CI): 1.6, 2.8) and 1.7 h/week among women (95% CI: 1.3, 2.1); differences in sports/exercise MVPA-active were 1.3 h/week (95% CI: 0.4, 2.1) and 1.0 h/week (95% CI: 0.5, 1.6) for men and women, respectively. Heterogeneity in associations was evident for the other domains. For example, adults in high-income versus low-income households were more likely to do any walking (men: 13.0% (95% CI: 10.3, 15.8%); women: 10.2% (95% CI: 7.6, 12.8%)). Among all adults (including those who did no walking), the average hours/week spent walking showed no difference by income. Among those who did any walking, adults in high-income versus low-income households walked on average 1 h/week less (men: − 0.9 h/week (95% CI: − 1.7, − 0.2); women: − 1.0 h/week (95% CI: − 1.7, − 0.2)).ConclusionsParticipation and the amount of time that adults spend in MVPA typically favours those in high-income households. Monitoring inequalities in MVPA requires assessing different aspects of the distribution within each domain. Reducing inequalities in sports/exercise requires policy actions and interventions to move adults in low-income households from inactivity to activity, and to enable those already active to do more. Measures to promote walking should focus efforts on reducing the sizeable income gap in the propensity to do any walking.

Powmic: an R package for power assessment in microbiome case-control studies.

Power analysis is essential to decide the sample size of metagenomic sequencing experiments in a case-control study for identifying differentially abundant (DA) microbes. However, the complexity of microbial data characteristics, such as excessive zeros, over-dispersion, compositionality, intrinsically microbial correlations and variable sequencing depths, makes the power analysis particularly challenging because the analytical form is usually unavailable. Here, we develop a simulation-based power assessment strategy and R package powmic, which considers the complexity of microbial data characteristics. A real data example demonstrates the usage of powmic. powmic R package and online tutorial are available at https://github.com/lichen-lab/powmic. chen61@iu.edu. Supplementary data are available at Bioinformatics online.

A study of alternative approaches to non-normal latent trait distributions in item response theory models used for health outcome measurement.

It is often unrealistic to assume normally distributed latent traits in the measurement of health outcomes. If normality is violated, the item response theory (IRT) models that are used to calibrate questionnaires may yield parameter estimates that are biased. Recently, IRT models were developed for dealing with specific deviations from normality, such as zero-inflation (“excess zeros”) and skewness. However, these models have not yet been evaluated under conditions representative of item bank development for health outcomes, characterized by a large number of polytomous items. A simulation study was performed to compare the bias in parameter estimates of the graded response model (GRM), polytomous extensions of the zero-inflated mixture IRT (ZIM-GRM), and Davidian Curve IRT (DC-GRM). In the case of zero-inflation, the GRM showed high bias overestimating discrimination parameters and yielding estimates of threshold parameters that were too high and too close to one another, while ZIM-GRM showed no bias. In the case of skewness, the GRM and DC-GRM showed little bias with the GRM showing slightly better results. Consequences for the development of health outcome measures are discussed.

A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes

Quantile regression models are typically used for modeling non-Gaussian outcomes, and such models allow quantile-specific inference. While there exists a vast literature on conditional quantile regression (where the model parameters are estimated precisely for one prefixed quantile level), relatively less work has been reported on joint quantile regression. The challenge in joint quantile regression is to avoid quantile crossing while estimating multiple quantiles simultaneously. In this article, we propose a semi-parametric approach of handling non-Gaussian zero-inflated and incomplete longitudinal outcomes. We use a two-part model for handling the excess zeros, and propose a dynamic joint quantile regression model for the nonzero outcomes. A multinomial probit model is used for modeling the missingness. We develop a Bayesian joint estimation method where the model parameters are estimated through Markov Chain Monte Carlo. The unknown distribution of the outcome can be constructed based on the estimated quantiles. We analyze data from the health and retirement study and model the out-of-pocket medical expenditure through the proposed joint quantile regression method. Simulation studies are performed to assess the practical usefulness and efficiency of the proposed approach compared to the existing methods.

Zero-inflated Bell scan: A more flexible spatial scan statistic

Spatial scan statistic has been widely employed in spatial disease surveillance and spatial cluster detection. However, the over-dispersion and excess of zeros are often presented in real-world data, causing not only the violation of likelihood assumption for the Poisson model, but also excessive Type I error or false alarms. In this paper, we propose the Bell scan and the zero-inflated Bell scan statistics which cover the over-dispersion and/or excess of zeros in the data. The proposed scan methods can be potentially applied to the event data in a simple way. Considering zero-inflated models, we compare the Bell, Poisson and binomial scan statistics based on relative risk bias, precision, recall of cluster detection, and power. By our simulations, we show that the Bell scan is a robust and a powerful alternative in comparison with the traditional scan models. We finally illustrate the new methodology with two real data scan analyses.

Two-part hidden Markov models for semicontinuous longitudinal data with nonignorable missing covariates.

This study develops a two-part hidden Markov model (HMM) for analyzing semicontinuous longitudinal data in the presence of missing covariates. The proposed model manages a semicontinuous variable by splitting it into two random variables: a binary indicator for determining the occurrence of excess zeros at all occasions and a continuous random variable for examining its actual level. For the continuous longitudinal response, an HMM is proposed to describe the relationship between the observation and unobservable finite-state transition processes. The HMM consists of two major components. The first component is a transition model for investigating how potential covariates influence the probabilities of transitioning from one hidden state to another. The second component is a conditional regression model for examining the state-specific effects of covariates on the response. A shared random effect is introduced to each part of the model to accommodate possible unobservable heterogeneity among observation processes and the nonignorability of missing covariates. A Bayesian adaptive least absolute shrinkage and selection operator (lasso) procedure is developed to conduct simultaneous variable selection and estimation. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative dataset. New insights into the pathology of Alzheimer's disease and its potential risk factors are obtained.

A robust Bayesian mixed effects approach for zero inflated and highly skewed longitudinal count data emanating from the zero inflated discrete Weibull distribution.

This article proposes a Bayesian mixed effects zero inflated discrete Weibull (ZIDW) regression model for zero inflated and highly skewed longitudinal count data, as an alternative to mixed effects regression models that are based on the negative binomial, zero inflated negative binomial, and conventional discrete Weibull (DW) distributions. The mixed effects ZIDW regression model is an extension of a recently introduced model based on the DW distribution and uses the log-link function to specify the relationship between the linear predictors and the median counts. The ZIDW approach offers a more robust characteristic of central tendency, compared to the mean count, when there is skewness in the data. A matrix generalized half-t (MGH-t) prior distribution is specified for the random effects covariance matrix as an alternative to the widely used Wishart prior distribution. The methodology is applied to a longitudinal dataset from an epilepsy clinical trial. In a data contamination simulation study, we show that the mixed effect ZIDW regression model is more robust than the competing mixed effects regression models when the data contain excess zeros or outliers. The performance of the ZIDW regression model is also assessed in a simulation study under the specification of, respectively, the MGH-t and Wishart prior distributions for the random effects covariance matrix. It turns out that the highest posterior density intervals under the MGH-t prior for the fixed effects maintain nominal coverage when the true variability between random slopes over time is small, whereas those under the Wishart prior are generally conservative.

CMF-Impute: an accurate imputation tool for single-cell RNA-seq data.

Single-cell RNA-sequencing (scRNA-seq) technology provides a powerful tool for investigating cell heterogeneity and cell subpopulations by allowing the quantification of gene expression at single-cell level. However, scRNA-seq data analysis remains challenging because of various technical noises such as dropout events (i.e. excessive zero counts in the expression matrix). By taking consideration of the association among cells and genes, we propose a novel collaborative matrix factorization-based method called CMF-Impute to impute the dropout entries of a given scRNA-seq expression matrix. We test CMF-Impute and compare it with the other five state-of-the-art methods on six popular real scRNA-seq datasets of various sizes and three simulated datasets. For simulated datasets, CMF-Impute outperforms other methods in imputing the closest dropouts to the original expression values as evaluated by both the sum of squared error and Pearson correlation coefficient. For real datasets, CMF-Impute achieves the most accurate cell classification results in spite of the choice of different clustering methods like SC3 or T-SNE followed by K-means as evaluated by both adjusted rand index and normalized mutual information. Finally, we demonstrate that CMF-Impute is powerful in reconstructing cell-to-cell and gene-to-gene correlation, and in inferring cell lineage trajectories. CMF-Impute is written as a Matlab package which is available at https://github.com/xujunlin123/CMFImpute.git. Supplementary data are available at Bioinformatics online.

Modelling heavy-tailedness in count time series

Count data frequently exhibit overdispersion, zero inflation and even heavy-tailedness (the tail probabilities are non-negligible or decrease very slowly) in practical applications. Many models have been proposed for modelling count data with overdispersion and zero inflation, but heavy-tailedness is less considered. The proposed model, a new integer-valued autoregressive process with generalized Poisson-inverse Gaussian innovations, is capable of capturing these features. The generalized Poisson-inverse Gaussian family is very flexible, which includes Poisson distribution, Poisson inverse Gaussian distribution, discrete stable distribution and so on. Stationarity and ergodicity of this model are investigated and the expressions of marginal mean and variance are provided. Conditional maximum likelihood is used for estimating the parameters, and consistency and asymptotic normality for the estimators are presented. Further, we consider the h-step forecast and diagnostics for the proposed model. The proposed model is applied to three real data examples. In the first example, we consider the monthly number of cases of Polio, which validates that the proposed model can take into account count data with excessive zeros. Then, we illustrate the use of the proposed model through an application to the numbers of National Science Foundation fundings. Finally, we apply the proposed model to the numbers of transactions in 5-min intervals for the stock traded at Empire District Electric Company. The second and third examples show that the proposed model has a good performance in modelling heavy-tailed count data.

Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models

When modelling insurance claim count data, the actuary often observes overdispersion and an excess of zeros that may be caused by unobserved heterogeneity. A common approach to accounting for overdispersion is to consider models with some overdispersed distribution as opposed to Poisson models. Zero-inflated, hurdle and compound frequency models are typically applied to insurance data to account for such a feature of the data. However, a natural way to deal with unobserved heterogeneity is to consider mixtures of a simpler models. In this paper, we consider k-finite mixtures of some typical regression models. This approach has interesting features: first, it allows for overdispersion and the zero-inflated model represents a special case, and second, it allows for an elegant interpretation based on the typical clustering application of finite mixture models. k-finite mixture models are applied to a car insurance claim dataset in order to analyse whether the problem of unobserved heterogeneity requires a richer structure for risk classification. Our results show that the data consist of two subpopulations for which the regression structure is different.

Modelling the number of antenatal care visits in Bangladesh to determine the risk factors for reduced antenatal care attendance.

The existence of excess zeros in the distribution of antenatal care (ANC) visits in Bangladesh raises the research question of whether there are two separate generating processes in taking ANC and the frequency of ANC. Thus the main objective of this study is to identify a proper count regression model for the number of ANC visits by pregnant women in Bangladesh covering the issues of overdispersion, zero-inflation, and intra-cluster correlation with an additional objective of determining risk factors for ANC use and its frequency. The data have been extracted from the nationally representative 2014 Bangladesh Demographic and Health Survey, where 22% of the total 4493 women did not take any ANC during pregnancy. Since these zero ANC visits can be either structural or sampling zeros, two-part zero-inflated and hurdle regression models are investigated along with the standard one-part count regression models. Correlation among response values has been accounted for by incorporating cluster-specific random effects in the models. The hurdle negative binomial regression model with cluster-specific random intercepts in both the zero and the count part is found to be the best model according to various diagnostic tools including likelihood ratio and uniformity tests. The results show that women who have poor education, live in poor households, have less access to mass media, or belong to the Sylhet and Chittagong regions are less likely to use ANC and also have fewer ANC visits. Additionally, women who live in rural areas, depend on family members' decisions to take health care, and have unintended pregnancies had fewer ANC visits. The findings recommend taking both cluster-specific random effects and overdispersion and zero-inflation into account in modelling the ANC data of Bangladesh. Moreover, safe motherhood programmes still need to pay particular attention to disadvantaged and vulnerable subgroups of women.

Correlation and association analyses in microbiome study integrating multiomics in health and disease.

Correlation and association analyses are one of the most widely used statistical methods in research fields, including microbiome and integrative multiomics studies. Correlation and association have two implications: dependence and co-occurrence. Microbiome data are structured as phylogenetic tree and have several unique characteristics, including high dimensionality, compositionality, sparsity with excess zeros, and heterogeneity. These unique characteristics cause several statistical issues when analyzing microbiome data and integrating multiomics data, such as large p and small n, dependency, overdispersion, and zero-inflation. In microbiome research, on the one hand, classic correlation and association methods are still applied in real studies and used for the development of new methods; on the other hand, new methods have been developed to target statistical issues arising from unique characteristics of microbiome data. Here, we first provide a comprehensive view of classic and newly developed univariate correlation and association-based methods. We discuss the appropriateness and limitations of using classic methods and demonstrate how the newly developed methods mitigate the issues of microbiome data. Second, we emphasize that concepts of correlation and association analyses have been shifted by introducing network analysis, microbe-metabolite interactions, functional analysis, etc. Third, we introduce multivariate correlation and association-based methods, which are organized by the categories of exploratory, interpretive, and discriminatory analyses and classification methods. Fourth, we focus on the hypothesis testing of univariate and multivariate regression-based association methods, including alpha and beta diversities-based, count-based, and relative abundance (or compositional)-based association analyses. We demonstrate the characteristics and limitations of each approaches. Fifth, we introduce two specific microbiome-based methods: phylogenetic tree-based association analysis and testing for survival outcomes. Sixth, we provide an overall view of longitudinal methods in analysis of microbiome and omics data, which cover standard, static, regression-based time series methods, principal trend analysis, and newly developed univariate overdispersed and zero-inflated as well as multivariate distance/kernel-based longitudinal models. Finally, we comment on current association analysis and future direction of association analysis in microbiome and multiomics studies.

Modeling Zero Inflation and Over-Dispersion in Domestic Package Insurance Claims Portfolio: A Case of Madison Insurance Company-Kenya

The standard Poisson distribution is widely used as a mechanism for regression modeling of count data outcomes. However, the suitability of this modeling technique is only limited to equi-dispersed count data outcomes. This is due to the fact that this modeling technique does not take into account the problems associated with over dispersion and excess zeros in many data sets as with insurance claims data. The study objective is to model domestic package insurance claims frequency using zero inflated and hurdle models since insurance portfolios are characterized by the non-occurrence of claims over a given time interval. This non-occurrence of claims over a given time interval usually leads to the Zero-Inflation and Dispersion associated with insurance claims data. The study consequently evaluates the performance of the Poisson, Zero Inflated Poisson (ZIP) and Hurdle Poisson (HP) models in determining the model that best models the domestic package insurance claims data. This is then used to estimate, predict and determine the heterogeneity of occurrence of the aforementioned insurance claims. The statistical Hosmer-Lemeshow tests is used to define the suitability of the fitted model to estimate the zero-inflation and over-dispersion characteristic of the data. To determine the presence of outliers and the distribution of residuals, the Residual Pearson and Deviance statistics are used. Data on a number of claims for domestic package insurance policy from Madison Insurance ltd, Kenya spanning from 2014 to 2018 (261 weeks) is used in the study.