Discrete Distribution Based on Compound Sum to Model Dental Caries Count Data

Methods for analysing dental caries and associated risk indicators have evolved considerably in recent decades. The use of zero-inflated or hurdle models is increasing so as to take account of the decayed, missing, and filled teeth (DMFT) distribution, which is positively skewed and has a high proportion of zero scores. However, there is a need to develop new statistical models that involve pragmatic biological considerations on dental caries in epidemiological surveys. In this paper, we show that the zero-inflated and the hurdle models can both be expressed as a compound sum. Using the same compound sum, we then present the generalized negative binomial (GNB) distribution for dental caries count data, and provide a numerical application using the data of the EPIPAP study. The GNB model generates the best score functions while handling the lifetime dental caries disease process better. In conclusion, the GNB model suits the nature of some count data, in particular when structural zeros are unlikely to occur and when several latent spells can lead to new countable events. For these reasons, the use of the GNB distribution appears to be relevant for the modelling of dental caries count data.

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A comparison of zero-inflated and hurdle models for modeling zero-inflated count data

Journal of Statistical Distributions and Applications ◽

10.1186/s40488-021-00121-4 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Cindy Xin Feng

Keyword(s):

Health Services ◽

Count Data ◽

Goodness Of Fit ◽

Negative Binomial ◽

Simulation Studies ◽

Final Choice ◽

Hurdle Models ◽

Count Distribution ◽

Careful Assessment

AbstractCounts data with excessive zeros are frequently encountered in practice. For example, the number of health services visits often includes many zeros representing the patients with no utilization during a follow-up time. A common feature of this type of data is that the count measure tends to have excessive zero beyond a common count distribution can accommodate, such as Poisson or negative binomial. Zero-inflated or hurdle models are often used to fit such data. Despite the increasing popularity of ZI and hurdle models, there is still a lack of investigation of the fundamental differences between these two types of models. In this article, we reviewed the zero-inflated and hurdle models and highlighted their differences in terms of their data generating processes. We also conducted simulation studies to evaluate the performances of both types of models. The final choice of regression model should be made after a careful assessment of goodness of fit and should be tailored to a particular data in question.

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Using Count Data Models to Predict Epiphytic Bryophyte Recruitment in Schima superba Gardn. et Champ. Plantations in Urban Forests

Forests ◽

10.3390/f11020174 ◽

2020 ◽

Vol 11 (2) ◽

pp. 174

Author(s):

Dexian Zhao ◽

Zhenkai Sun ◽

Cheng Wang ◽

Zezhou Hao ◽

Baoqiang Sun ◽

...

Keyword(s):

Count Data ◽

Human Disturbance ◽

Negative Binomial ◽

Urban Environments ◽

Tree Planting ◽

Count Data Models ◽

Urban Tree ◽

Schima Superba ◽

Hurdle Models ◽

Positive Effects

Epiphytic bryophytes are known to perform essential ecosystem functions, but their sensitivity to environmental quality and change makes their survival and development vulnerable to global changes, especially habitat loss in urban environments. Fortunately, extensive urban tree planting programs worldwide have had a positive effect on the colonization and development of epiphytic bryophytes. However, how epiphytic bryophytes occur and grow on planted trees remain poorly known, especially in urban environments. In the present study, we surveyed the distribution of epiphytic bryophytes on tree trunks in a Schima superba Gardn. et Champ. urban plantation and then developed count data models, including tree characteristics, stand characteristics, human disturbance, terrain factors, and microclimate to predict the drivers on epiphytic bryophyte recruitment. Different counting models (Poisson, Negative binomial, Zero-inflated Poisson, Zero-inflated negative binomial, Hurdle-Poisson, Hurdle-negative binomial) were compared for a data analysis to account for the zero-inflated data structure. Our results show that (i) the shaded side and base of tree trunks were the preferred locations for bryophytes to colonize in urban plantations, (ii) both hurdle models performed well in modeling epiphytic bryophyte recruitment, and (iii) both hurdle models showed that the tree height, diameter at breast height (DBH), leaf area index (LAI), and altitude (ALT) promoted the occurrence of epiphytic bryophytes, but the height under branch and interference intensity of human activities opposed the occurrence of epiphytic bryophytes. Specifically, DBH and LAI had positive effects on the species richness recruitment count; similarly, DBH and ALT had positive effects on the abundance recruitment count, but slope had a negative effect. To promote the occurrence and growth of epiphytic bryophytes in urban tree planting programs, we suggest that managers regulate suitable habitats by cultivating and protecting large trees, promoting canopy closure, and controlling human disturbance.

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Geometric Regression for Modelling Count Data on the Time-to-First Antenatal Care Visit

Journal of Statistics Advances in Theory and Applications ◽

10.18642/jsata_7100122148 ◽

2020 ◽

Vol 23 (1) ◽

pp. 35-57

Author(s):

Zainab Mohammed Darwish Al-Balushi ◽

◽

M. Mazharul Islam ◽

Keyword(s):

Antenatal Care ◽

Regression Model ◽

Count Data ◽

Negative Binomial ◽

Geometric Distribution ◽

Discrete Distribution ◽

Mass Function ◽

Probability Mass Function ◽

Antenatal Care Visit ◽

Care Visit

Geometric distribution belongs to the family of discrete distribution that deals with the count of trail needed for first occurrence or success of any event. However, little attention has been paid in applying the GLM for the geometric distribution, which has a very simple form for its probability mass function with a single parameter. In this study, an attempt has been made to introduce geometric regression for modelling the count data. We have illustrated the suitability of the geometric regression model for analyzing the count data on time to first antenatal care visit that displayed under-dispersion, and the results were compared with Poisson and negative binomial regressions. We conclude that the geometric regression model may provide a flexible model for fitting count data sets which may present over-dispersion or under-dispersion, and the model may serve as an alternative model to the very familiar Poisson and negative binomial models for modelling count data.

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Dental Caries Thresholds among Adolescents in England, Wales and Northern Ireland, 2013 at 12, and 15 years: Implications for Epidemiology and Clinical Care

10.21203/rs.3.rs-109208/v1 ◽

2020 ◽

Author(s):

Xiaozhe Wang ◽

Eduardo Bernabe ◽

Nigel Pitts ◽

Shuguo Zheng ◽

Jennifer Gallagher

Keyword(s):

Dental Caries ◽

Northern Ireland ◽

Negative Binomial ◽

Clinical Care ◽

Caries Experience ◽

Area Deprivation ◽

School Type ◽

Clinical Criteria ◽

Enamel Caries ◽

Epidemiological Surveys

Abstract BackgroundDental caries is the most prevalent condition globally. Despite improvements over the past few decades, there remains a significant disease burden in childhood. Epidemiological surveys provide insight to disease patterns and trends, have traditionally focused on obvious decay which are inconsistent with contemporary clinical criteria. This study examined the distribution of dental caries in 12- and 15-year-olds in England, Wales and Northern Ireland, by severity threshold, at surface, tooth and child level and explored its association with socioeconomic, psychological and behavioural factors. MethodsData from 12- and 15-year-olds in the 2013 Children’s Dental Health Survey (CDHS 2013) were analysed at three levels, taking account of dental caries thresholds which involved recording both clinical decay (visual enamel caries (AV) and above) and obvious decay (non-cavitated dentine lesions (2V) and above). Negative binomial regression was used to identify factors associated with dental caries experience at both thresholds. Results The prevalence and severity of dental caries experience was higher among 15-year-olds at all levels. Lesions in AV were by far the most common stage of caries recorded in both ages. The average number of surfaces with obvious decay experience, which has been the traditional epidemiological threshold, in 12- and 15-year-olds was 2.3 and 3.9 respectively. The corresponding values under the clinical decay threshold were higher, at 3.9 and 5.9 respectively. Visualisation of the distribution of dental caries at surface/tooth-level exhibited left:right symmetry and to a lesser extent upper:lower. In the adjusted models for both ages, country/region, school type, area deprivation, high frequency sugar consumption and irregular dental attendance were associated with greater caries experience in both groups. Dental anxiety was inversely associated with caries experience among 15-year-olds. ConclusionThis research highlights the importance of recognising dental caries patterns by surface, tooth and child-level amongst adolescents and the value of reporting dental caries distribution by threshold in epidemiological surveys and its relevance for clinical care. Inclusion of enamel caries reveals the extent of caries management required at a point when non-invasive care is possible, emphasising the importance of prevention in primary care.

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Extended negative binomial hurdle models

Statistical Methods in Medical Research ◽

10.1177/0962280218766567 ◽

2018 ◽

Vol 28 (5) ◽

pp. 1540-1551

Author(s):

Maengseok Noh ◽

Youngjo Lee

Keyword(s):

Count Data ◽

Negative Binomial ◽

Random Effect ◽

Random Effect Model ◽

Real Data ◽

Hurdle Models ◽

Poisson Models ◽

Effect Model ◽

Zero Rate ◽

General Statistical

Poisson models are widely used for statistical inference on count data. However, zero-inflation or zero-deflation with either overdispersion or underdispersion could occur. Currently, there is no available model for count data, that allows excessive occurrence of zeros along with underdispersion in non-zero counts, even though there have been reported necessity of such models. Furthermore, given an excessive zero rate, we need a model that allows a larger degree of overdispersion than existing models. In this paper, we use a random-effect model to produce a general statistical model for accommodating such phenomenon occurring in real data analyses.

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Matching the Statistical Model to the Research Question for Dental Caries Indices with Many Zero Counts

Caries Research ◽

10.1159/000452675 ◽

2017 ◽

Vol 51 (3) ◽

pp. 198-208 ◽

Cited By ~ 4

Author(s):

John S. Preisser ◽

D. Leann Long ◽

John W. Stamm

Keyword(s):

Clinical Trial ◽

Dental Caries ◽

Statistical Model ◽

Randomized Clinical Trial ◽

Count Data ◽

Treatment Effects ◽

Negative Binomial ◽

Research Question ◽

Model Class ◽

Zero Counts

Marginalized zero-inflated count regression models have recently been introduced for the statistical analysis of dental caries indices and other zero-inflated count data as alternatives to traditional zero-inflated and hurdle models. Unlike the standard approaches, the marginalized models directly estimate overall exposure or treatment effects by relating covariates to the marginal mean count. This article discusses model interpretation and model class choice according to the research question being addressed in caries research. Two data sets, one consisting of fictional dmft counts in 2 groups and the other on DMFS among schoolchildren from a randomized clinical trial comparing 3 toothpaste formulations to prevent incident dental caries, are analyzed with negative binomial hurdle, zero-inflated negative binomial, and marginalized zero-inflated negative binomial models. In the first example, estimates of treatment effects vary according to the type of incidence rate ratio (IRR) estimated by the model. Estimates of IRRs in the analysis of the randomized clinical trial were similar despite their distinctive interpretations. The choice of statistical model class should match the study's purpose, while accounting for the broad decline in children's caries experience, such that dmft and DMFS indices more frequently generate zero counts. Marginalized (marginal mean) models for zero-inflated count data should be considered for direct assessment of exposure effects on the marginal mean dental caries count in the presence of high frequencies of zero counts.

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Dental caries thresholds among adolescents in England, Wales, and Northern Ireland, 2013 at 12, and 15 years: implications for epidemiology and clinical care

BMC Oral Health ◽

10.1186/s12903-021-01507-1 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Xiaozhe Wang ◽

Eduardo Bernabe ◽

Nigel Pitts ◽

Shuguo Zheng ◽

Jennifer E. Gallagher

Keyword(s):

Dental Caries ◽

Northern Ireland ◽

Negative Binomial ◽

Clinical Care ◽

Caries Experience ◽

Area Deprivation ◽

School Type ◽

Clinical Criteria ◽

Enamel Caries ◽

Epidemiological Surveys

Abstract Background Dental caries is the most prevalent condition globally. Despite improvements over the past few decades, there remains a significant disease burden in childhood. Epidemiological surveys provide insight to disease patterns and trends, and have traditionally focused on obvious decay which are inconsistent with contemporary clinical criteria. This study examined the distribution of dental caries in 12- and 15-year-olds in England, Wales and Northern Ireland, by severity threshold, at surface, tooth and child level and explored its association with socioeconomic, psychological and behavioural factors. Methods Data from 12- and 15-year-olds in the 2013 Children’s Dental Health Survey (CDHS 2013) were analysed at three levels, taking account of dental caries thresholds which involved recording both clinical decay [visual enamel caries (AV) and above] and obvious decay [non-cavitated dentine lesions (2V) and above]. Negative binomial regression was used to identify factors associated with dental caries experience at both thresholds. Results The prevalence and severity of dental caries experience was higher among 15-year-olds at all levels. Visual change in enamel (AV) was by far the most common stage of caries recorded in both ages. The average number of surfaces with obvious decay experience, which has been the traditional epidemiological threshold, in 12- and 15-year-olds was 2.3 and 3.9 respectively. The corresponding values under the clinical decay threshold were higher, at 3.9 and 5.9 respectively. Visualisation of the distribution of dental caries at surface/tooth-level exhibited horizontal symmetry and to a lesser extent vertical symetry. In the adjusted models for both ages, country/region, school type, area deprivation, high frequency sugar consumption and irregular dental attendance were associated with greater caries experience in both groups. Dental anxiety was inversely associated with caries experience among 15-year-olds. Conclusion This research highlights the importance of recognising dental caries patterns by surface, tooth and child-level amongst adolescents and the value of reporting dental caries distribution by threshold in epidemiological surveys, including its relevance for clinical care. Inclusion of enamel caries reveals the extent of caries management required at a point when non-invasive care is possible, emphasising the importance of prevention through contemporary primary care, which includes supporting self-care.

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Spatiotemporal hurdle models for zero-inflated count data: Exploring trends in emergency department visits

Statistical Methods in Medical Research ◽

10.1177/0962280214527079 ◽

2016 ◽

Vol 25 (6) ◽

pp. 2558-2576 ◽

Cited By ~ 11

Author(s):

Brian Neelon ◽

Howard H Chang ◽

Qiang Ling ◽

Nicole S Hastings

Keyword(s):

Emergency Department ◽

Random Effects ◽

Count Data ◽

Negative Binomial ◽

Emergency Department Visits ◽

Emergency Department Use ◽

Generalized Poisson ◽

Hurdle Models ◽

Spatiotemporal Trends ◽

Temporal Smoothing

Motivated by a study exploring spatiotemporal trends in emergency department use, we develop a class of two-part hurdle models for the analysis of zero-inflated areal count data. The models consist of two components—one for the probability of any emergency department use and one for the number of emergency department visits given use. Through a hierarchical structure, the models incorporate both patient- and region-level predictors, as well as spatially and temporally correlated random effects for each model component. The random effects are assigned multivariate conditionally autoregressive priors, which induce dependence between the components and provide spatial and temporal smoothing across adjacent spatial units and time periods, resulting in improved inferences. To accommodate potential overdispersion, we consider a range of parametric specifications for the positive counts, including truncated negative binomial and generalized Poisson distributions. We adopt a Bayesian inferential approach, and posterior computation is handled conveniently within standard Bayesian software. Our results indicate that the negative binomial and generalized Poisson hurdle models vastly outperform the Poisson hurdle model, demonstrating that overdispersed hurdle models provide a useful approach to analyzing zero-inflated spatiotemporal data.

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Comparing Zero-inflated Poisson, Zero-inflated Negative Binomial and Zero-inflated Geometric in Count Data with Excess Zero

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2019/v4i230113 ◽

2019 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

M. I. Adarabioyo ◽

R. A. Ipinyomi

Keyword(s):

Count Data ◽

Negative Binomial ◽

Likelihood Estimation ◽

Information Criterion ◽

Skewed Distribution ◽

Hurdle Models ◽

Mean And Variance ◽

Over Dispersion ◽

Mean Vector ◽

Inflation Parameter

Count data often violate the assumptions of a normal distribution due to the fact that they are bounded by their lowest value which is zero. The Poison distribution is sometimes suggested but when the assumption of equal mean and variance is violated due to over-dispersion and presence of zeros we tend to look in the direction of other models. Zero-inflated data falls in this category. The zero-inflated and hurdle models have been found to fit this scenario. The proportions of zero in the data often affect the choice of the models. Our study used the Monte Carlo design to sample 1000 cases from positively skewed distribution with 1.25 as mean vector and 0.10 as zero-inflation parameter. The data was analysed using the method of the maximum likelihood estimation. The Zero-Inflated Poisson, Zero-Inflated Negative Binomial and Zero-Inflated Geometric were fitted; the standard error and Akaike Information Criterion were obtained as measures of model validation with ZIP outperformed ZINB and ZIG.

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Trend on dental caries status and its risk indicators in children aged 12 years in China: a multilevel analysis based on the repeated national cross-sectional surveys in 2005 and 2015

BMC Public Health ◽

10.1186/s12889-021-12262-x ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Fei Li ◽

Si-Cheng Wu ◽

Zhi-Yuan Zhang ◽

Edward Chin Man Lo ◽

Wen-Jia Gu ◽

...

Keyword(s):

Oral Health ◽

Dental Caries ◽

Negative Binomial ◽

Dental Fluorosis ◽

Dental Pain ◽

Risk Indicators ◽

World Health ◽

Negative Binomial Regression Model ◽

Sociodemographic Characteristics ◽

Health Related

Abstract Background This study aimed to explore the trend and risk indicators for dental caries of children aged 12 years in China based on national oral health survey data in 2005 and 2015. Methods Research data were from the two latest national oral health surveys conducted in mainland China, including 30 and 31 provinces, autonomous regions, and municipalities in 2005 and 2015, respectively. Children aged 12 years were clinically examined for dental caries and dental fluorosis according to the World Health Organization criteria. Sociodemographic characteristics and oral health-related behaviours were collected using questionnaires. Multilevel zero-inflated negative binomial regression model was used to investigate the association between dental caries severity and dental fluorosis, sociodemographic characteristics, and oral health-related behaviours. Results The final analyses included 12,350 and 27,818 children surveyed in 2005 and 2015, respectively. The standardized prevalence of dental caries increased from 27.05% (95% confidence interval [CI], 24.25-28.85) in 2005 to 37.92% (95% CI, 34.94-40.90) in 2015, and the respective standardized mean decayed, missing, filled teeth (DMFT) index scores increased from 0.50 (standard deviation [SD], 1.04) to 0.83 (SD, 1.45) (P < 0.001). Fujian province had the highest increase in dental caries, followed by Liaoning, Heilongjiang, Hainan, and Yunnan. Results revealed that children who were girls, more frequently experienced dental pain, and had more recent dental visits, had significantly higher DMFT scores after adjusting for the survey year and other variables (all P < 0.05). Conclusions Dental caries of 12-year-old children in China deteriorated from 2005 to 2015, particularly in the northeast and southwest regions. Dental caries was associated with sex, dental pain, and dental service utilization.

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