Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Optimal designs for mixed effects poisson regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.

The use of Poisson regression in the sociological study of suicide

This paper explains how Poisson regression can be used in studies in which the dependent variable describes the number of occurrences of some rare event such as suicide. After pointing out why ordinary linear regression is inappropriate for treating dependent variables of this sort, we go on to present the basic Poisson regression model and show how it fits in the broad class of generalized linear models. Then we turn to discussing a major problem of Poisson regression known as overdispersion and suggest possible solutions, including the correction of standard errors and negative binomial regression. The paper ends with a detailed empirical example, drawn from our own research on suicide.

Predictors of temporary and permanent work disability in patients with inflammatory bowel disease: results of the swiss inflammatory bowel disease cohort study.

BACKGROUND: Inflammatory bowel disease can decrease the quality of life and induce work disability. We sought to (1) identify and quantify the predictors of disease-specific work disability in patients with inflammatory bowel disease and (2) assess the suitability of using cross-sectional data to predict future outcomes, using the Swiss Inflammatory Bowel Disease Cohort Study data. METHODS: A total of 1187 patients were enrolled and followed up for an average of 13 months. Predictors included patient and disease characteristics and drug utilization. Potential predictors were identified through an expert panel and published literature. We estimated adjusted effect estimates with 95% confidence intervals using logistic and zero-inflated Poisson regression. RESULTS: Overall, 699 (58.9%) experienced Crohn's disease and 488 (41.1%) had ulcerative colitis. Most important predictors for temporary work disability in patients with Crohn's disease included gender, disease duration, disease activity, C-reactive protein level, smoking, depressive symptoms, fistulas, extraintestinal manifestations, and the use of immunosuppressants/steroids. Temporary work disability in patients with ulcerative colitis was associated with age, disease duration, disease activity, and the use of steroids/antibiotics. In all patients, disease activity emerged as the only predictor of permanent work disability. Comparing data at enrollment versus follow-up yielded substantial differences regarding disability and predictors, with follow-up data showing greater predictor effects. CONCLUSIONS: We identified predictors of work disability in patients with Crohn's disease and ulcerative colitis. Our findings can help in forecasting these disease courses and guide the choice of appropriate measures to prevent adverse outcomes. Comparing cross-sectional and longitudinal data showed that the conduction of cohort studies is inevitable for the examination of disability.

Health care usage among immigrants and native-born elderly populations in eleven European countries: results from SHARE

Differences in health care utilization of immigrants 50 years of age and older relative to the native-born populations in eleven European countries are investigated. Negative binomial and zero-inflated Poisson regression are used to examine differences between immigrants and native-borns in number of doctor visits, visits to general practitioners, and hospital stays using the 2004 Survey of Health, Ageing, and Retirement in Europe database. In the pooled European sample and in some individual countries, older immigrants use from 13 to 20% more health services than native-borns after demographic characteristics are controlled. After controlling for the need for health care, differences between immigrants and native-borns in the use of physicians, but not hospitals, are reduced by about half. These are not changed much with the incorporation of indicators of socioeconomic status and extra insurance coverage. Higher country-level relative expenditures on health, paying physicians a fee-for-service, and physician density are associated with higher usage of physician services among immigrants.

Predictors of temporary and permanent work disability in patients with inflammatory bowel disease: results of the swiss inflammatory bowel disease cohort study

BACKGROUND Inflammatory bowel disease can decrease the quality of life and induce work disability. We sought to (1) identify and quantify the predictors of disease-specific work disability in patients with inflammatory bowel disease and (2) assess the suitability of using cross-sectional data to predict future outcomes, using the Swiss Inflammatory Bowel Disease Cohort Study data. METHODS A total of 1187 patients were enrolled and followed up for an average of 13 months. Predictors included patient and disease characteristics and drug utilization. Potential predictors were identified through an expert panel and published literature. We estimated adjusted effect estimates with 95% confidence intervals using logistic and zero-inflated Poisson regression. RESULTS Overall, 699 (58.9%) experienced Crohn's disease and 488 (41.1%) had ulcerative colitis. Most important predictors for temporary work disability in patients with Crohn's disease included gender, disease duration, disease activity, C-reactive protein level, smoking, depressive symptoms, fistulas, extraintestinal manifestations, and the use of immunosuppressants/steroids. Temporary work disability in patients with ulcerative colitis was associated with age, disease duration, disease activity, and the use of steroids/antibiotics. In all patients, disease activity emerged as the only predictor of permanent work disability. Comparing data at enrollment versus follow-up yielded substantial differences regarding disability and predictors, with follow-up data showing greater predictor effects. CONCLUSIONS We identified predictors of work disability in patients with Crohn's disease and ulcerative colitis. Our findings can help in forecasting these disease courses and guide the choice of appropriate measures to prevent adverse outcomes. Comparing cross-sectional and longitudinal data showed that the conduction of cohort studies is inevitable for the examination of disability.

Assessing the impacts of grazing levels on bird density in woodland habitat: a Bayesian approach using expert opinion

Many studies on birds focus on the collection of data through an experimental design, suitable for investigation in a classical analysis of variance (ANOVA) framework. Although many findings are confirmed by one or more experts, expert information is rarely used in conjunction with the survey data to enhance the explanatory and predictive power of the model. We explore this neglected aspect of ecological modelling through a study on Australian woodland birds, focusing on the potential impact of different intensities of commercial cattle grazing on bird density in woodland habitat. We examine a number of Bayesian hierarchical random effects models, which cater for overdispersion and a high frequency of zeros in the data using WinBUGS and explore the variation between and within different grazing regimes and species. The impact and value of expert information is investigated through the inclusion of priors that reflect the experience of 20 experts in the field of bird responses to disturbance. Results indicate that expert information moderates the survey data, especially in situations where there are little or no data. When experts agreed, credible intervals for predictions were tightened considerably. When experts failed to agree, results were similar to those evaluated in the absence of expert information. Overall, we found that without expert opinion our knowledge was quite weak. The fact that the survey data is quite consistent, in general, with expert opinion shows that we do know something about birds and grazing and we could learn a lot faster if we used this approach more in ecology, where data are scarce. Copyright (c) 2005 John Wiley & Sons, Ltd.

Glycemic control: Risk factors, quality of life, workforce participation, and mortality among US adults with type 2 diabetes

Despite research showing the benefits of glycemic control, it remains suboptimal among adults with diabetes in the United States. Possible reasons include unaddressed risk factors as well as lack of awareness of its immediate and long term consequences. The objectives of this study were to, using cross-sectional data, (1) ascertain the association between suboptimal (Hemoglobin A1c (HbA1c) .7%), borderline (HbA1c 7-8.9%), and poor (HbA1c .9%) glycemic control and potentially new risk factors (e.g. work characteristics), and (2) assess whether aspects of poor health and well-being such as poor health related quality of life (HRQOL), unemployment, and missed-work are associated with glycemic control; and (3) using prospective data, assess the relationship between mortality risk and glycemic control in US adults with type 2 diabetes. Data from the 1988-1994 and 1999-2004 National Health and Nutrition Examination Surveys were used. HbA1c values were used to create dichotomous glycemic control indicators. Binary logistic regression models were used to assess relationships between risk factors, employment status and glycemic control. Multinomial logistic regression analyses were conducted to assess relationships between glycemic control and HRQOL variables. Zero-inflated Poisson regression models were used to assess relationships between missed work days and glycemic control. Cox-proportional hazard models were used to assess effects of glycemic control on mortality risk. Using STATA software, analyses were weighted to account for complex survey design and non-response. Multivariable models adjusted for socio-demographics, body mass index, among other variables. Results revealed that being a farm worker and working over 40 hours/week were risk factors for suboptimal glycemic control. Having greater days of poor mental was associated with suboptimal, borderline, and poor glycemic control. Having greater days of inactivity was associated with poor glycemic control while having greater days of poor physical health was associated with borderline glycemic control. There were no statistically significant relationships between glycemic control, self-reported general health, employment, and missed work. Finally, having an HbA1c value less than 6.5% was protective against mortality. The findings suggest that work-related factors are important in a person’s ability to reach optimal diabetes management levels. Poor glycemic control appears to have significant detrimental effects on HRQOL.^

Glycemic Control: Risk Factors, Quality of Life, Workforce Participation, and Mortality Among US Adults with Type 2 Diabetes

Despite research showing the benefits of glycemic control, it remains suboptimal among adults with diabetes in the United States. Possible reasons include unaddressed risk factors as well as lack of awareness of its immediate and long term consequences. The objectives of this study were to, using cross-sectional data, 1) ascertain the association between suboptimal (Hemoglobin A1c (HbA1c) ≥7%), borderline (HbA1c 7-8.9%), and poor (HbA1c ≥9%) glycemic control and potentially new risk factors (e.g. work characteristics), and 2) assess whether aspects of poor health and well-being such as poor health related quality of life (HRQOL), unemployment, and missed-work are associated with glycemic control; and 3) using prospective data, assess the relationship between mortality risk and glycemic control in US adults with type 2 diabetes. Data from the 1988-1994 and 1999-2004 National Health and Nutrition Examination Surveys were used. HbA1c values were used to create dichotomous glycemic control indicators. Binary logistic regression models were used to assess relationships between risk factors, employment status and glycemic control. Multinomial logistic regression analyses were conducted to assess relationships between glycemic control and HRQOL variables. Zero-inflated Poisson regression models were used to assess relationships between missed work days and glycemic control. Cox-proportional hazard models were used to assess effects of glycemic control on mortality risk. Using STATA software, analyses were weighted to account for complex survey design and non-response. Multivariable models adjusted for socio-demographics, body mass index, among other variables. Results revealed that being a farm worker and working over 40 hours/week were risk factors for suboptimal glycemic control. Having greater days of poor mental was associated with suboptimal, borderline, and poor glycemic control. Having greater days of inactivity was associated with poor glycemic control while having greater days of poor physical health was associated with borderline glycemic control. There were no statistically significant relationships between glycemic control, self-reported general health, employment, and missed work. Finally, having an HbA1c value less than 6.5% was protective against mortality. The findings suggest that work-related factors are important in a person’s ability to reach optimal diabetes management levels. Poor glycemic control appears to have significant detrimental effects on HRQOL.