Regression Models with Heteroscedasticity using Bayesian Approach

In this paper, we compare the performance of two statistical approaches for the analysis of data obtained from the social research area. In the first approach, we use normal models with joint regression modelling for the mean and for the variance heterogeneity. In the second approach, we use hierarchical models. In the first case, individual and social variables are included in the regression modelling for the mean and for the variance, as explanatory variables, while in the second case, the variance at level 1 of the hierarchical model depends on the individuals (age of the individuals), and in the level 2 of the hierarchical model, the variance is assumed to change according to socioeconomic stratum. Applying these methodologies, we analyze a Colombian tallness data set to find differences that can be explained by socioeconomic conditions. We also present some theoretical and empirical results concerning the two models. From this comparative study, we conclude that it is better to jointly modelling the mean and variance heterogeneity in all cases. We also observe that the convergence of the Gibbs sampling chain used in the Markov Chain Monte Carlo method for the jointly modeling the mean and variance heterogeneity is quickly achieved.

The hierarchical model of branch planning with random coefficients

We consider the management branch model where the random resources of the subsystem are given by the exponential distributions. The determinate equivalent is a block structure problem of quadratic programming. It is solved effectively by means of the decomposition method, which is based on iterative aggregation. The aggregation problem of the upper level is resolved analytically. This overcomes all difficulties concerning the large dimension of the main problem.

A Bayesian nonparametric model for Taguchi's on-line quality monitoring procedure for attributes

A Bayesian nonparametric model for Taguchi's on-line quality monitoring procedure for attributes is introduced. The proposed model may accommodate the original single shift setting to the more realistic situation of gradual quality deterioration and allows the incorporation of an expert's opinion on the production process. Based on the number of inspections to be carried out until a defective item is found, the Bayesian operation for the distribution function that represents the increasing sequence of defective fractions during a cycle considering a mixture of Dirichlet processes as prior distribution is performed. Bayes estimates for relevant quantities are also obtained. © 2012 Elsevier B.V.

Severity of Brazilian sickle cell disease patients: severity scores and feasibility of the Bayesian network model use

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Bayesian nonparametric model for Taguchi's on-line quality monitoring procedure for attributes

A Bayesian nonparametric model for Taguchi's on-line quality monitoring procedure for attributes is introduced. The proposed model may accommodate the original single shift setting to the more realistic situation of gradual quality deterioration and allows the incorporation of an expert's opinion on the production process. Based on the number of inspections to be carried out until a defective item is found, the Bayesian operation for the distribution function that represents the increasing sequence of defective fractions during a cycle considering a mixture of Dirichlet processes as prior distribution is performed. Bayes estimates for relevant quantities are also obtained. (C) 2012 Elsevier B.V. All rights reserved.

Why Are Women With Cervical Cancer Not Being Diagnosed in Preinvasive Phase? An Analysis of Risk Factors Using a Hierarchical Model

Objective: To assess the risk factors for delayed diagnosis of uterine cervical lesions. Materials and Methods: This is a case-control study that recruited 178 women at 2 Brazilian hospitals. The cases (n = 74) were composed of women with a late diagnosis of a lesion in the uterine cervix (invasive carcinoma in any stage). The controls (n = 104) were composed of women with cervical lesions diagnosed early on (low-or high-grade intraepithelial lesions). The analysis was performed by means of logistic regression model using a hierarchical model. The socioeconomic and demographic variables were included at level I (distal). Level II (intermediate) included the personal and family antecedents and knowledge about the Papanicolaou test and human papillomavirus. Level III (proximal) encompassed the variables relating to individuals' care for their own health, gynecologic symptoms, and variables relating to access to the health care system. Results: The risk factors for late diagnosis of uterine cervical lesions were age older than 40 years (odds ratio [OR] = 10.4; 95% confidence interval [CI], 2.3-48.4), not knowing the difference between the Papanicolaou test and gynecological pelvic examinations (OR, = 2.5; 95% CI, 1.3-4.9), not thinking that the Papanicolaou test was important (odds ratio [OR], 4.2; 95% CI, 1.3-13.4), and abnormal vaginal bleeding (OR, 15.0; 95% CI, 6.5-35.0). Previous treatment for sexually transmissible disease was a protective factor (OR, 0.3; 95% CI, 0.1-0.8) for delayed diagnosis. Conclusions: Deficiencies in cervical cancer prevention programs in developing countries are not simply a matter of better provision and coverage of Papanicolaou tests. The misconception about the Papanicolaou test is a serious educational problem, as demonstrated by the present study.

Rainfall spatial predictions: a two-part model and its assessment

Spatial prediction of hourly rainfall via radar calibration is addressed. The change of support problem (COSP), arising when the spatial supports of different data sources do not coincide, is faced in a non-Gaussian setting; in fact, hourly rainfall in Emilia-Romagna region, in Italy, is characterized by abundance of zero values and right-skeweness of the distribution of positive amounts. Rain gauge direct measurements on sparsely distributed locations and hourly cumulated radar grids are provided by the ARPA-SIMC Emilia-Romagna. We propose a three-stage Bayesian hierarchical model for radar calibration, exploiting rain gauges as reference measure. Rain probability and amounts are modeled via linear relationships with radar in the log scale; spatial correlated Gaussian effects capture the residual information. We employ a probit link for rainfall probability and Gamma distribution for rainfall positive amounts; the two steps are joined via a two-part semicontinuous model. Three model specifications differently addressing COSP are presented; in particular, a stochastic weighting of all radar pixels, driven by a latent Gaussian process defined on the grid, is employed. Estimation is performed via MCMC procedures implemented in C, linked to R software. Communication and evaluation of probabilistic, point and interval predictions is investigated. A non-randomized PIT histogram is proposed for correctly assessing calibration and coverage of two-part semicontinuous models. Predictions obtained with the different model specifications are evaluated via graphical tools (Reliability Plot, Sharpness Histogram, PIT Histogram, Brier Score Plot and Quantile Decomposition Plot), proper scoring rules (Brier Score, Continuous Rank Probability Score) and consistent scoring functions (Root Mean Square Error and Mean Absolute Error addressing the predictive mean and median, respectively). Calibration is reached and the inclusion of neighbouring information slightly improves predictions. All specifications outperform a benchmark model with incorrelated effects, confirming the relevance of spatial correlation for modeling rainfall probability and accumulation.

A BAYESIAN SHRINKAGE MODEL FOR INCOMPLETE LONGITUDINAL BINARY DATA WITH APPLICATION TO THE BREAST CANCER PREVENTION TRIAL

We consider inference in randomized studies, in which repeatedly measured outcomes may be informatively missing due to drop out. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and posit an exponential tilt model that links non-identifiable and identifiable distributions. This model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated and applied to data from the Breast Cancer Prevention Trial.

Reduced Bayesian Hierarchical Models: Estimating Health Effects of Simultaneous Exposure to Multiple Pollutants

Quantifying the health effects associated with simultaneous exposure to many air pollutants is now a research priority of the US EPA. Bayesian hierarchical models (BHM) have been extensively used in multisite time series studies of air pollution and health to estimate health effects of a single pollutant adjusted for potential confounding of other pollutants and other time-varying factors. However, when the scientific goal is to estimate the impacts of many pollutants jointly, a straightforward application of BHM is challenged by the need to specify a random-effect distribution on a high-dimensional vector of nuisance parameters, which often do not have an easy interpretation. In this paper we introduce a new BHM formulation, which we call "reduced BHM", aimed at analyzing clustered data sets in the presence of a large number of random effects that are not of primary scientific interest. At the first stage of the reduced BHM, we calculate the integrated likelihood of the parameter of interest (e.g. excess number of deaths attributed to simultaneous exposure to high levels of many pollutants). At the second stage, we specify a flexible random-effect distribution directly on the parameter of interest. The reduced BHM overcomes many of the challenges in the specification and implementation of full BHM in the context of a large number of nuisance parameters. In simulation studies we show that the reduced BHM performs comparably to the full BHM in many scenarios, and even performs better in some cases. Methods are applied to estimate location-specific and overall relative risks of cardiovascular hospital admissions associated with simultaneous exposure to elevated levels of particulate matter and ozone in 51 US counties during the period 1999-2005.

Comparison of Bayesian and frequentist approaches in clinical outcomes between hospitals

Many public health agencies and researchers are interested in comparing hospital outcomes, for example, morbidity, mortality, and hospitalization across areas and hospitals. However, since there is variation of rates in clinical trials among hospitals because of several biases, we are interested in controlling for the bias and assessing real differences in clinical practices. In this study, we compared the variations between hospitals in rates of severe Intraventricular Haemorrhage (IVH) infant using Frequentist statistical approach vs. Bayesian hierarchical model through simulation study. The template data set for simulation study was included the number of severe IVH infants of 24 intensive care units in Australian and New Zealand Neonatal Network from 1995 to 1997 in severe IVH rate in preterm babies. We evaluated the rates of severe IVH for 24 hospitals with two hierarchical models in Bayesian approach comparing their performances with the shrunken rates in Frequentist method. Gamma-Poisson (BGP) and Beta-Binomial (BBB) were introduced into Bayesian model and the shrunken estimator of Gamma-Poisson (FGP) hierarchical model using maximum likelihood method were calculated as Frequentist approach. To simulate data, the total number of infants in each hospital was kept and we analyzed the simulated data for both Bayesian and Frequentist models with two true parameters for severe IVH rate. One was the observed rate and the other was the expected severe IVH rate by adjusting for five predictors variables for the template data. The bias in the rate of severe IVH infant estimated by both models showed that Bayesian models gave less variable estimates than Frequentist model. We also discussed and compared the results from three models to examine the variation in rate of severe IVH by 20th centile rates and avoidable number of severe IVH cases. ^

E-service quality:development of a hierarchical model

Using survey data from 358 online customers, the study finds that the e-service quality construct conforms to the structure of a third-order factor model that links online service quality perceptions to distinct and actionable dimensions, including (1) website design, (2) fulfilment, (3) customer service, and (4) security/privacy. Each dimension is found to consist of several attributes that define the basis of e-service quality perceptions. A comprehensive specification of the construct, which includes attributes not covered in existing scales, is developed. The study contrasts a formative model consisting of 4 dimensions and 16 attributes against a reflective conceptualization. The results of this comparison indicate that studies using an incorrectly specified model overestimate the importance of certain e-service quality attributes. Global fit criteria are also found to support the detection of measurement misspecification. Meta-analytic data from 31,264 online customers are used to show that the developed measurement predicts customer behavior better than widely used scales, such as WebQual and E-S-Qual. The results show that the new measurement enables managers to assess e-service quality more accurately and predict customer behavior more reliably.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

National, regional, and global trends in fasting plasma glucose and diabetes prevalence since 1980: systematic analysis of health examination surveys and epidemiological studies with 370 country-years and 2·7 million participants.

BACKGROUND: Data for trends in glycaemia and diabetes prevalence are needed to understand the effects of diet and lifestyle within populations, assess the performance of interventions, and plan health services. No consistent and comparable global analysis of trends has been done. We estimated trends and their uncertainties in mean fasting plasma glucose (FPG) and diabetes prevalence for adults aged 25 years and older in 199 countries and territories. METHODS: We obtained data from health examination surveys and epidemiological studies (370 country-years and 2·7 million participants). We converted systematically between different glycaemic metrics. For each sex, we used a Bayesian hierarchical model to estimate mean FPG and its uncertainty by age, country, and year, accounting for whether a study was nationally, subnationally, or community representative. FINDINGS: In 2008, global age-standardised mean FPG was 5·50 mmol/L (95% uncertainty interval 5·37-5·63) for men and 5·42 mmol/L (5·29-5·54) for women, having risen by 0·07 mmol/L and 0·09 mmol/L per decade, respectively. Age-standardised adult diabetes prevalence was 9·8% (8·6-11·2) in men and 9·2% (8·0-10·5) in women in 2008, up from 8·3% (6·5-10·4) and 7·5% (5·8-9·6) in 1980. The number of people with diabetes increased from 153 (127-182) million in 1980, to 347 (314-382) million in 2008. We recorded almost no change in mean FPG in east and southeast Asia and central and eastern Europe. Oceania had the largest rise, and the highest mean FPG (6·09 mmol/L, 5·73-6·49 for men; 6·08 mmol/L, 5·72-6·46 for women) and diabetes prevalence (15·5%, 11·6-20·1 for men; and 15·9%, 12·1-20·5 for women) in 2008. Mean FPG and diabetes prevalence in 2008 were also high in south Asia, Latin America and the Caribbean, and central Asia, north Africa, and the Middle East. Mean FPG in 2008 was lowest in sub-Saharan Africa, east and southeast Asia, and high-income Asia-Pacific. In high-income subregions, western Europe had the smallest rise, 0·07 mmol/L per decade for men and 0·03 mmol/L per decade for women; North America had the largest rise, 0·18 mmol/L per decade for men and 0·14 mmol/L per decade for women. INTERPRETATION: Glycaemia and diabetes are rising globally, driven both by population growth and ageing and by increasing age-specific prevalences. Effective preventive interventions are needed, and health systems should prepare to detect and manage diabetes and its sequelae. FUNDING: Bill & Melinda Gates Foundation and WHO.

Increasing prevalence of gastroschisis in Europe 1980-2002: a phenomenon restricted to younger mothers?

Gastroschisis is an abdominal wall defect more prevalent in offspring of young mothers. It is known to be increasing in prevalence despite the general decrease in the proportion of births to young European women. We investigated whether the increase in prevalence was restricted to the high-risk younger mothers. We analysed 936 cases of gastroschisis from 25 population-based registries in 15 European countries, 1980-2002. We fitted a Bayesian Hierarchical Model which allowed us to estimate trend, to estimate which registries were significantly different from the common distribution, and to adjust simultaneously for maternal age, time (in grouped years) and the random variation between registries. The maternal age-standardised prevalence (standardised to the year 2000 European maternal age structure) increased almost fourfold from 0.54 [95% Credible Interval (CrI) 0.37, 0.75] per 10,000 births in 1980-84 to 2.12 [95% CrI 1.85, 2.40] per 10,000 births in 2000-02. The relative risk of gastroschisis for mothers <20 years of age in 1995-2002 was 7.0 [95% CrI 5.6, 8.7]. There were geographical differences within Europe, with higher rates of gastroschisis in the UK, and lower rates in Italy after adjusting for maternal age. After standardising for regional variation, our results showed that the increase in risk over time was the same for mothers of all ages--the increase for mothers <20 years was 3.96-fold compared with an increase of 3.95-fold for mothers in the other age groups. These findings indicate that the phenomenon of increasing gastroschisis prevalence is not restricted to younger mothers only.

Worldwide trends in diabetes since 1980: a pooled analysis of 751 population-based studies with 4.4 million participants.

One of the global targets for non-communicable diseases is to halt, by 2025, the rise in the age-standardised adult prevalence of diabetes at its 2010 levels. We aimed to estimate worldwide trends in diabetes, how likely it is for countries to achieve the global target, and how changes in prevalence, together with population growth and ageing, are affecting the number of adults with diabetes. We pooled data from population-based studies that had collected data on diabetes through measurement of its biomarkers. We used a Bayesian hierarchical model to estimate trends in diabetes prevalence-defined as fasting plasma glucose of 7.0 mmol/L or higher, or history of diagnosis with diabetes, or use of insulin or oral hypoglycaemic drugs-in 200 countries and territories in 21 regions, by sex and from 1980 to 2014. We also calculated the posterior probability of meeting the global diabetes target if post-2000 trends continue. We used data from 751 studies including 4,372,000 adults from 146 of the 200 countries we make estimates for. Global age-standardised diabetes prevalence increased from 4.3% (95% credible interval 2.4-7.0) in 1980 to 9.0% (7.2-11.1) in 2014 in men, and from 5.0% (2.9-7.9) to 7.9% (6.4-9.7) in women. The number of adults with diabetes in the world increased from 108 million in 1980 to 422 million in 2014 (28.5% due to the rise in prevalence, 39.7% due to population growth and ageing, and 31.8% due to interaction of these two factors). Age-standardised adult diabetes prevalence in 2014 was lowest in northwestern Europe, and highest in Polynesia and Micronesia, at nearly 25%, followed by Melanesia and the Middle East and north Africa. Between 1980 and 2014 there was little change in age-standardised diabetes prevalence in adult women in continental western Europe, although crude prevalence rose because of ageing of the population. By contrast, age-standardised adult prevalence rose by 15 percentage points in men and women in Polynesia and Micronesia. In 2014, American Samoa had the highest national prevalence of diabetes (>30% in both sexes), with age-standardised adult prevalence also higher than 25% in some other islands in Polynesia and Micronesia. If post-2000 trends continue, the probability of meeting the global target of halting the rise in the prevalence of diabetes by 2025 at the 2010 level worldwide is lower than 1% for men and is 1% for women. Only nine countries for men and 29 countries for women, mostly in western Europe, have a 50% or higher probability of meeting the global target. Since 1980, age-standardised diabetes prevalence in adults has increased, or at best remained unchanged, in every country. Together with population growth and ageing, this rise has led to a near quadrupling of the number of adults with diabetes worldwide. The burden of diabetes, both in terms of prevalence and number of adults affected, has increased faster in low-income and middle-income countries than in high-income countries. Wellcome Trust.