Zero-inflation Research Articles

Utilisation of Hospital Outpatient Services by Diabetes Mellitus Sufferers, Analysis of BPJS Kesehatan Sample Data

Diabetes mellitus is a catastrophic disease that burdens the financing of the National Health Insurance or Jaminan Kesehatan Nasional Program, and sufferers continue to increase. Specific participant segments still widely use access for participants with diabetes mellitus to utilise health services at advanced-level referral health facilities. Various factors also influence access to health services at advanced-level referral health facilities. This research aims to analyse utilisation based on membership type and examine the factors that affect the utilisation of advanced outpatient services by JKN participants with DM. This research uses secondary data from the 2022 DM contextual BPJS Health sample data. The data was analysed univariately, bivariately, and multivariately with the Zero Inflated Negative Binomial regression model. The results of statistical tests showed that in outpatient care, age, type of participant, gender, treatment class, and province of participants were significantly different in terms of health service utilisation. The influence of the type of participation in the JKN program significantly affects the utilisation of services in outpatient care; the utilisation of non-recipients of contribution assistance participants is 1.16 times greater than that of the recipient of contribution assistance participants in outpatient care.

A deep neural network to de-noise single-cell RNA sequencing data.

Single-cell RNA sequencing (scRNA-seq), a powerful technique for investigating the transcriptome of individual cells, enables the discovery of heterogeneous cell populations, rare cell types, and transcriptional dynamics in separate cells. Yet, scRNA-seq data analysis is limited by the problem of measurement dropouts, i.e., genes displaying zero expression levels. We introduce ZiPo, a deep artificial neural network for rate estimation and library size prediction in scRNA-seq data which incorporates adjustable zero inflation in the distribution to capture the dropouts. ZiPo builds upon established concepts, including using deep autoencoders and adopting the Poisson and negative binomial distributions, by taking advantage of novel strategies, including library size prediction and residual connections, to improve the overall performance. A significant innovation of ZiPo is the introduction of a scale-invariant loss term, making the weights sparse and, hence, the model biologically more interpretable. ZiPo quickly handles vast singular and mixed datasets, with the processing time directly proportional to the number of cells. In this paper, we demonstrate the power of ZiPo on three datasets and show its advantages over other current techniques. The code used to produce the results in this manuscript is available at https://bitbucket.org/habilzare/alzheimer/src/master/code/deep/ZiPo/.

Matrix Factorization and Prediction for High-Dimensional Co-Occurrence Count Data via Shared Parameter Alternating Zero Inflated Gamma Model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

The impact of frailty on the use of social services, medication and mortality risk: a cross-sectional study

BackgroundFrailty is a common condition in older people, and its prevalence increases with age. With an ageing population, the adverse consequences of frailty cause an increasing appeal to the health care system. The impact of frailty on population level is often assessed using adverse health outcomes, such as mortality and medication use. Use of community nursing services and services offered through the Social Support Act are hardly used in assessing the impact of frailty. However, these services are important types of care use, especially in relation to ageing in place. In this cross-sectional study, we aimed to assess the impact of frailty on use of Social Support Act services, use of community nursing services, medication use, and mortality.MethodsWe used a frailty index, the FI-HM37, that was based on data from the Dutch Public Health Monitor 2016, for which respondents ≥ 65 years of age were included (n = 233,498). The association between frailty, the use of Social Support Act services, community nursing services and medication use was assessed using the Zero Inflated Poisson (ZIP) regression method. Survival analysis using Cox proportional hazards regression was conducted to estimate the hazard ratios for the association between frailty and mortality.ResultsThe ZIP regression with a final sample size of 181,350 showed that frailty affected care use even after correcting for several covariates mentioned in the literature. For each unit increase in frailty index (FI) score, the relative probability of using zero Social Support services decreased with 7.7 (p < 0.001). The relative chance of zero community nursing services decreased with 4.0 (p < 0.001) for each unit increase in FI score. Furthermore, for each unit increase in FI score, the likelihood of zero medication use decreased with 2.9 (p < 0.001). Finally, for each unit increase in FI score, the mortality risk was 3.8 times higher (CI = 3.4–4.3; p < 0.001).ConclusionsWe demonstrated that frailty negatively affects the use of Social Support Act services, the use of community nursing services, medication use, and mortality risk. This study is the first to demonstrate the impact of frailty on Social Support Act services and community nursing services in the Netherlands. Findings emphasize the importance of frailty prevention for older people and public health policy.

C-ziptf: stable tensor factorization for zero-inflated multi-dimensional genomics data.

In the past two decades, genomics has advanced significantly, with single-cell RNA-sequencing (scRNA-seq) marking a pivotal milestone. ScRNA-seq provides unparalleled insights into cellular diversity and has spurred diverse studies across multiple conditions and samples, resulting in an influx of complex multidimensional genomics data. This highlights the need for robust methodologies capable of handling the complexity and multidimensionality of such genomics data. Furthermore, single-cell data grapples with sparsity due to issues like low capture efficiency and dropout effects. Tensor factorizations (TF) have emerged as powerful tools to unravel the complex patterns from multi-dimensional genomics data. Classic TF methods, based on maximum likelihood estimation, struggle with zero-inflated count data, while the inherent stochasticity in TFs further complicates result interpretation and reproducibility. Our paper introduces Zero Inflated Poisson Tensor Factorization (ZIPTF), a novel method for high-dimensional zero-inflated count data factorization. We also present Consensus-ZIPTF (C-ZIPTF), merging ZIPTF with a consensus-based approach to address stochasticity. We evaluate our proposed methods on synthetic zero-inflated count data, simulated scRNA-seq data, and real multi-sample multi-condition scRNA-seq datasets. ZIPTF consistently outperforms baseline matrix and tensor factorization methods, displaying enhanced reconstruction accuracy for zero-inflated data. When dealing with high probabilities of excess zeros, ZIPTF achieves up to better accuracy. Moreover, C-ZIPTF notably enhances the factorization's consistency. When tested on synthetic and real scRNA-seq data, ZIPTF and C-ZIPTF consistently uncover known and biologically meaningful gene expression programs. Access our data and code at: https://github.com/klarman-cell-observatory/scBTF and https://github.com/klarman-cell-observatory/scbtf_experiments .

Zero-Inflated Binary Classification Model with Elastic Net Regularization

Zero inflation and overfitting can reduce the accuracy rate of using machine learning models for characterizing binary data sets. A zero-inflated Bernoulli (ZIBer) model can be the right model to characterize zero-inflated binary data sets. When the ZIBer model is used to characterize zero-inflated binary data sets, overcoming the overfitting problem is still an open question. To improve the overfitting problem for using the ZIBer model, the minus log-likelihood function of the ZIBer model with the elastic net regularization rule for an overfitting penalty is proposed as the loss function. An estimation procedure to minimize the loss function is developed in this study using the gradient descent method (GDM) with the momentum term as the learning rate. The proposed estimation method has two advantages. First, the proposed estimation method can be a general method that simultaneously uses L1- and L2-norm terms for penalty and includes the ridge and least absolute shrinkage and selection operator methods as special cases. Second, the momentum learning rate can accelerate the convergence of the GDM and enhance the computation efficiency of the proposed estimation procedure. The parameter selection strategy is studied, and the performance of the proposed method is evaluated using Monte Carlo simulations. A diabetes example is used as an illustration.

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.

Learning to quantify uncertainty in off-target activity for CRISPR guide RNAs.

CRISPR-based genome editing technologies have revolutionised the field of molecular biology, offering unprecedented opportunities for precise genetic manipulation. However, off-target effects remain a significant challenge, potentially leading to unintended consequences and limiting the applicability of CRISPR-based genome editing technologies in clinical settings. Current literature predominantly focuses on point predictions for off-target activity, which may not fully capture the range of possible outcomes and associated risks. Here, we present crispAI, a neural network architecture-based approach for predicting uncertainty estimates for off-target cleavage activity, providing a more comprehensive risk assessment and facilitating improved decision-making in single guide RNA (sgRNA) design. Our approach makes use of the count noise model Zero Inflated Negative Binomial (ZINB) to model the uncertainty in the off-target cleavage activity data. In addition, we present the first-of-its-kind genome-wide sgRNA efficiency score, crispAI-aggregate, enabling prioritization among sgRNAs with similar point aggregate predictions by providing richer information compared to existing aggregate scores. We show that uncertainty estimates of our approach are calibrated and its predictive performance is superior to the state-of-the-art in silico off-target cleavage activity prediction methods. The tool and the trained models are available at https://github.com/furkanozdenn/crispr-offtarget-uncertainty.

Between spaces: Unravelling motives and distances in internal migration

AbstractDistance, economic disparities and housing market conditions are considered key moderators of internal migration. Existing research has used panels and surveys to establish the drivers of and barriers to domestic moves. This research employs administrative data on all Slovak internal migrants in 1997–2022 (2.38 million moves). The individual migrant data are associated with regional characteristics such as wages, unemployment rates, business activity, housing construction, the ethnic composition of the population, and connections to trans‐European transport network (TEN‐T) motorway networks. Zero‐inflated (ZI) regression models help to identify the key moderators of internal moves through reported migration motives and major structural barriers to migration. Gravity models distinguish between long‐distance moves motivated by human capital considerations and short‐distance moves informed by housing and family motives. Motives related to housing, following family, marriage, divorcee and health accounted for 75.4% of the total moves in the 1997–2022 period. Migration distance, followed by education, population mass and housing, proved to be key moderators of internal moves.

Exponentially weighted moving average chart using zero-inflated negative binomial distribution

Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts that leads to excess variance besides inflation of zeros in the data using a more flexible model than the zero-inflated Poisson model, a zero-inflated negative binomial (ZINB) is suggested. In the present study, Shewhart and exponentially weighted moving average (EWMA) control charts are suggested to monitor the ZINB data. The charts are compared using the average run length and standard deviation of run length by using extensive Monte Carlo simulations. Besides a comprehensive simulation study assuming different settings of parameters of ZINB, a real data set is used to show the practicality of the proposed charts. The results indicate that the EWMA chart is better than the Shewhart chart.

HANDLING OF OVERDISPERSION CASES IN MORBIDITY DATA IN SELUMA REGENCY

The problem of overdispersion as a violation of the assumption of equidispersion in Poisson regression is generally caused by sources of unobserved heterogeneity, missing observations on predictor variables, outliers in the data, errors in the specification of the bridging function, and many observed values that are zero. The purpose of this study is to find out the right model and the variables that affect data that occurs overdispersion and excess zero in the case of the number of days of disruption at work, school, or other daily activities due to health complaints. The methods used were Poisson Regression, Negative Binomial Regression, Hurdle Poisson Regression, Zero Inflated Poisson Regression, Zero Inflated Negative Binomial Regression, and Hurdle Negative Binomial Regression. The data used were morbidity taken from data on the number of days of disruption at work, school or other daily activities due to health complaints in Seluma district, Bengkulu Province. It was found that the best model is Zero Inflated Negative Poisson with the smallest Akaike Information Criterion (AIC) value of 1620.609 and the variables that have a significant effect on the log model and the logit model are marital status and work variables.

Measurement error models with zero inflation and multiple sources of zeros, with applications to hard zeros.

We consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to fit it. Simulations and data analyses are used to illustrate our methods. Extensions to parametric models and survival analysis are discussed briefly.

Determination of Zero Inflation Instrument, Commodity Supercycle and Sustainability Impact by Velocity Cryptocurrency to Support Digital Assets Management Trend: An Empirical Report From Digital Asset Commodity Transactions in Indonesia

Determination of Zero Inflation Instrument, Commodity Supercycle and Sustainability Impact by Velocity Cryptocurrency to Support Digital Assets Management Trend: An Empirical Report From Digital Asset Commodity Transactions in Indonesia

On Designing a New Control Chart Using the Generalized Conway–Maxwell–Poisson Distribution to Monitor Count Data

Many researchers employed Poisson distribution-based control charts to monitor count data. Nevertheless, these charts can handle count data that deviate from the Poisson assumption of equal mean and variance. This paper suggests a new control chart (CC) that uses the generalized Conway–Maxwell–Poisson (GCOMP) distribution, which can deal with count data that have different levels of dispersion and zero-inflation (ZI). The proposed chart is designed considering the total number of counts. The main advantage of this study is that it pays attention to the tails of the count data when monitoring the process. The performance is measured by the average run length using L control limits at different sample sizes and parametric settings. The findings demonstrate that, for count data with varying tail behaviors, the proposed chart performs better compared to existing CCs. ZI count data can also be monitored with the proposed chart. The proposed chart can be applied in a variety of fields, as verified by the examples provided in this paper.

Assessing and Addressing Zero Inflation in Intensive Longitudinal Data

Assessing and Addressing Zero Inflation in Intensive Longitudinal Data

A maximum likelihood and regenerative bootstrap approach for estimation and forecasting of INAR(p) processes with zero-inflated innovations

In this work, we study a class of p-order non-negative integer-valued autoregressive (INAR(p)) processes, with innovations following zero-inflated (ZI) distributions called ZI-INAR(p) processes. Based on the EM algorithm, we present an estimation procedure of parameters model. We also develop a regenerative bootstrap method to construct confidence intervals for the parameters as well as to estimate the forecasting distributions for future values. We discuss asymptotic properties of the regenerative bootstrap method. The performance of the proposed methods is evaluated considering the analysis of two simulation studies and a real dataset.

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.

Effective multi-modal clustering method via skip aggregation network for parallel scRNA-seq and scATAC-seq data.

In recent years, there has been a growing trend in the realm of parallel clustering analysis for single-cell RNA-seq (scRNA) and single-cell Assay of Transposase Accessible Chromatin (scATAC) data. However, prevailing methods often treat these two data modalities as equals, neglecting the fact that the scRNA mode holds significantly richer information compared to the scATAC. This disregard hinders the model benefits from the insights derived from multiple modalities, compromising the overall clustering performance. To this end, we propose an effective multi-modal clustering model scEMC for parallel scRNA and Assay of Transposase Accessible Chromatin data. Concretely, we have devised a skip aggregation network to simultaneously learn global structural information among cells and integrate data from diverse modalities. To safeguard the quality of integrated cell representation against the influence stemming from sparse scATAC data, we connect the scRNA data with the aggregated representation via skip connection. Moreover, to effectively fit the real distribution of cells, we introduced a Zero Inflated Negative Binomial-based denoising autoencoder that accommodates corrupted data containing synthetic noise, concurrently integrating a joint optimization module that employs multiple losses. Extensive experiments serve to underscore the effectiveness of our model. This work contributes significantly to the ongoing exploration of cell subpopulations and tumor microenvironments, and the code of our work will be public at https://github.com/DayuHuu/scEMC.

Using zero-inflated and hurdle regression models to analyze schistosomiasis data of school children in the southern areas of Ghana.

Schistosomiasis is a neglected disease prevalent in tropical and sub-tropical areas of the world, especially in Africa. Detecting the presence of the disease is based on the detection of the parasites in the stool or urine of children and adults. In such studies, typically, data collected on schistosomiasis infection includes information on many negative individuals leading to a high zero inflation. Thus, in practice, counts data with excessive zeros are common. However, the purpose of this analysis is to apply statistical models to the count data and evaluate their performance and results. This is a secondary analysis of previously collected data. As part of a modelling process, a comparison of the Poisson regression, negative binomial regression and their associated zero inflated and hurdle models were used to determine which offered the best fit to the count data. Overall, 94.1% of the study participants did not have any schistosomiasis eggs out of 1345 people tested, resulting in a high zero inflation. The performance of the negative binomial regression models (hurdle negative binomial (HNB), zero inflated negative binomial (ZINB) and the standard negative binomial) were better than the Poisson-based regression models (Poisson, zero inflated Poisson, hurdle Poisson). The best models were the ZINB and HNB and their performances were indistinguishable according to information-based criteria test values. The zero-inflated negative binomial and hurdle negative binomial models were found to be the most satisfactory fit for modelling the over-dispersed zero inflated count data and are recommended for use in future statistical modelling analyses.

Modelling of Poor Household in East Kalimantan Using Zero Inflated Ordered Probit (ZIOP) Approach

Discrete ordinal response variables often exhibit an “excess” of zeros, which can be attributed to two different data conditions. Conventional ordinal probit models are limited in their ability to explain these excess zeros. The Zero Inflated Ordered Probit (ZIOP) model, which combines binary probit and ordinal probit regression, can be used to address this limitation. This study reviews the empirical analysis of the factors that contribute to poor household levels in East Kalimantan. The goodness-of-fit of the ZIOP and ordinal probit models was assessed using the Vuong test.