Correlation structure and model selection for negative binomial distribution in GEE

A new model selection criterion, termed as the “quasi-likelihood under the independence model criterion” (QIC), was proposed by Pan (2001) for GEE models. Cui (2007) developed a general computing program to implement the QIC method for a range of statistical distributions. However, only a special case of the negative binomial distribution was considered in Cui (2007), where the dispersion parameter equals to unity. This article introduces a new computing program that can be applied for the general negative binomial model, where the dispersion parameter can be any fixed value. An example is also given in this article.

Earthquake fatalities : the interaction of nature and political economy

To say that the level of fatalities resulting from an earthquake is inversely related to a country's per capita level of income is hardly novel. What makes our approach novel is that we relate fatalities to both per capita income and the level of inequality that exists within a country through their joint impact on the likelihood of collective action being taken to mitigate the destructive potential of quakes. We first develop a theoretical model which offers an explanation as to why, in some environments, different segments of society prove incapable of arriving at what all parties perceive to be an agreeable distribution of the burden of the necessary collective action, causing the relatively wealthy simply to self-insure against the disaster while leaving the relatively poor to its mercy. Following this, we test our theoretical model by evaluating 269 large earthquakes occurring worldwide, between 1960 and 2002, taking into account other factors that influence a quake's destructiveness such as its magnitude, depth and proximity to population centers. Using a Negative Binomial estimation strategy with both random and fixed estimators, we find strong evidence of the theoretical model's predictions. That is, while earthquakes themselves are natural phenomena beyond the reach of humankind, our collective inaction with respect to items like the creation and enforcement of building codes, failure to retrofit structures and to enact quake-sensitive zoning clearly plays a part in determining the actual toll that a given quake takes. And, it is through these and other examples of collective inaction that limited per capita income and inequality couple together with a given quake's natural destructive power in determining the actual fatalities resulting from a quake.

Acute rheumatic fever associated with household crowding in a developed country

Background: Acute rheumatic fever (ARF) and its sequelae, chronic rheumatic heart disease, remain important causes of morbidity and mortality worldwide, but there is little recent information about risk factors. The aim of this study was to examine the association between ARF and household crowding in New Zealand between 1996 and 2005.

Methods: This ecologic study used hospitalization data and census data to calculate incidence rates by census area unit (CAU). Rates of ARF were examined in relation to individual factors (age, ethnicity) and area factors based on the CAU of home address (household crowding, New Zealand deprivation index, household income, and proportion of children aged 5–14 years). The multivariate relationship between ARF incidence and CAU-based variables was assessed using a zero-inflated negative binomial model.

Results: This study included 1249 new cases of ARF between 1996 and 2005. At the univariate level, ARF rates were associated with household crowding across all age groups and ethnicities. ARF rates were significantly and positively related to household crowding after controlling for age, ethnicity, household income, and the density of children in the neighborhood. The incidence rate ratio was 1.065 (95% confidence interval, 1.052–1.079) for the total population.

Conclusions: In New Zealand, ARF rates are associated with household crowding at the CAU level. This finding supports action to reduce household crowding to improve health and reduce health inequalities. Our conclusion could be further investigated using a case-control study.

Positive association between ambient temperature and salmonellosis notifications in New Zealand, 1965-2006

Objective: To investigate the temporal relationship between the monthly count of salmonellosis notifications and the monthly average temperature in New Zealand during the period 1965–2006.

Methods: A negative binomial regression model was used to analyse monthly average ambient temperature and salmonellosis notifications in New Zealand between 1965 and 2006.

Results: A 1°C increase in monthly average ambient temperature was associated with a 15% increase in salmonellosis notifications within the same month (IRR 1.15; 95% CI 1.07 – 1.24).

Conclusion: The positive association found in this study between temperature and salmonellosis notifications in New Zealand is consistent with the results of studies conducted in other countries. New Zealand is projected to experience an increase in temperature due to climate change. Therefore, all other things being equal, climate change could increase salmonellosis notifications in New Zealand.

Implications: This association between temperature and salmonellosis should be considered when developing public health plans and climate change adaptation policies. Strategically, existing food safety programs to prevent salmonellosis could be intensified during warmer periods. As the association was strongest within the same month, focusing on improving food handling and storage during this time period may assist in climate change adaptation in New Zealand.

Tuberculosis associated with household crowding in a developed country

Background: Tuberculosis (TB) remains an important infectious disease in New Zealand (NZ) and globally, but risk factors for transmission are still poorly understood. This research aimed to identify whether household crowding contributes to TB transmission in NZ.

Methods: This ecological study used TB surveillance and census data to calculate TB incidence rates by census area unit (CAU). Census data were used to determine CAU characteristics including proportion of household crowding (a bedroom deficit of one or more), proportion of population who are migrants born in high-TB-incidence countries, median household income, and deprivation level. A negative binomial regression model was used to estimate the association between TB incidence and household crowding.

Results: The analysis included 1898 notified TB cases for the 2000–4 period. Univariate analysis showed TB incidence at the CAU level was associated with household crowding, for the total population and for all ethnic and age groups. After adjusting for the covariates of household income, existing TB burden, and proportion of migrants from high-TB-incidence countries, multivariate analysis showed statistically significant associations between TB incidence and household crowding. The incidence rate ratio (IRR) was 1.05 (95% CI 1.02 to 1.08) in the total population and 1.08 (95% CI 1.04 to 1.12) for NZ-born people <40 years.

Conclusion: At the CAU level, TB incidence in NZ is associated with household crowding. An individual-based study (e.g. case–control) in recently infected cases (detected by molecular epidemiology techniques) is suggested to complement these findings. Reducing or eliminating household crowding could decrease TB incidence in NZ and globally.

The impact of climate variability and change on cryptosporidiosis and giardiasis rates in New Zealand

Aim: To investigate the spatial relationship between climate variability and cryptosporidiosis and giardiasis notifications in New Zealand between 1997 and 2006.

Methods: Negative binomial regression was used to analyse spatial relationships between cryptosporidiosis and giardiasis notifications in New Zealand between 1997 and 2006, and climatological average rainfall and temperature at the Census Area Unit (CAU) level. The quality of domestic water supplies, urban-rural status and deprivation were included as covariates.

Main results: Giardiasis: There was a positive association between rainfall and giardiasis and between temperature and giardiasis.

Cryptosporidiosis: There was a positive association between rainfall and cryptosporidiosis and a negative association between temperature and cryptosporidiosis. The effect of rainfall was modified by the quality of the domestic water supply.

Conclusions: These findings suggest that climate variability affects protozoan disease rates in New Zealand. However, predicting the effect of climate change from this study is difficult, as these results suggest that the projected increases in temperature and rainfall may have opposing effects on cryptosporidiosis rates. Nevertheless, water supply quality appeared to modify the impact of increased rainfall on cryptosporidiosis rates. This finding suggests that improving water supply quality in New Zealand could reduce vulnerability to the impact of climate change on protozoan diseases.

Population biology of swift (Apus apus) ectoparasites in relation to host reproductive success

1We censused ectoparasite populations of adult and nestling swifts over the course of the host's breeding season. Nearly all of the birds were infested with chewing lice and two-thirds of the nests were infested with louse flies. Feather mites were observed but not quantified.2Lice and louse flies both showed aggregated distributions among hosts. Louse eggs, hatched lice and adult louse flies had negative binomial distributions, whereas the aggregated distribution of louse fly pupae was not adequately described by negative binomial or Poisson models.3Transmission of lice from parents to offspring was documented. A comparison of the age structure of lice on parents and offspring indicated that most transmission was by nymphal lice.4Host reproductive success and survival appeared to be independent of the number of lice or louse flies. Neither parasite correlated with the number, body mass, or date of fledging of young birds, nor with the overwinter survival of adults. We caution, however, that experimental manipulations of parasite load are required for a definitive test of the impact of ectoparasites on evolutionary fitness components.

Distribution of physical activity facilities in Scotland by small area measures of deprivation and urbanicity

Background The aim of this study was to examine the distribution of physical activity facilities by area-level deprivation in Scotland, adjusting for differences in urbanicity, and exploring differences between and within the four largest Scottish cities. Methods We obtained a list of all recreational physical activity facilities in Scotland. These were mapped and assigned to datazones. Poisson and negative binomial regression models were used to investigate associations between the number of physical activity facilities relative to population size and quintile of area-level deprivation. Results The results showed that prior to adjustment for urbanicity, the density of all facilities lessened with increasing deprivation from quintiles 2 to 5. After adjustment for urbanicity and local authority, the effect of deprivation remained significant but the pattern altered, with datazones in quintile 3 having the highest estimated mean density of facilities. Within-city associations were identified between the number of physical activity facilities and area-level deprivation in Aberdeen and Dundee, but not in Edinburgh or Glasgow. Conclusions In conclusion, area-level deprivation appears to have a significant association with the density of physical activity facilities and although overall no clear pattern was observed, affluent areas had fewer publicly owned facilities than more deprived areas but a greater number of privately owned facilities.

Predicting future purchases with the Poisson log-normal model

The negative binomial distribution (NBD) has been widely used in marketing for modeling purchase frequency counts, particularly in packaged goods contexts. A key managerially relevant use of this model is Conditional Trend Analysis (CTA)—a method of benchmarking future sales utilizing the NBD conditional expectation. CTA allows brand managers to identify whether the sales change in a second period is accounted for by previous non-, light, or heavy buyers of the brand. Although a useful tool, the conditional prediction of the NBD suffers from a bias: it under predicts what the period-one non-buyer class will do in period two and over predicts the sales contribution of existing buyers. In addition, the NBD's assumption of a gamma-distributed mean purchase rate lacks theoretical support—it is not possible to explain why a gamma distribution should hold. This paper therefore proposes an alternative model using a log-normal distribution in place of the gamma distribution, hence creating a Poisson log-normal (PLN) distribution. The PLN distribution has a stronger theoretical grounding than the NBD as it has a natural interpretation relying on the central limit theorem. Empirical analysis of brands in multiple categories shows that the PLN distribution gives better predictions than the NBD.

Disease mapping and regression with count data in the presence of overdispersion and spatial autocorrelation: a Bayesian model averaging approach

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

Statistical approaches used to assess the equity of access to food outlets: a systematic review

Abstract: Background Inequalities in eating behaviours are often linked to the types of food retailers accessible in neighbourhood environments. Numerous studies have aimed to identify if access to healthy and unhealthy food retailers is socioeconomically patterned across neighbourhoods, and thus a potential risk factor for dietary inequalities. Existing reviews have examined differences between methodologies, particularly focussing on neighbourhood and food outlet access measure definitions. However, no review has informatively discussed the suitability of the statistical methodologies employed; a key issue determining the validity of study findings. Our aim was to examine the suitability of statistical approaches adopted in these analyses.
Methods: Searches were conducted for articles published from 2000–2014. Eligible studies included objective measures of the neighbourhood food environment and neighbourhood-level socio-economic status, with a statistical analysis of the association between food outlet access and socio-economic status.
Results Fifty four papers were included. Outlet accessibility was typically defined as the distance to the nearest outlet from the neighbourhood centroid, or as the numberof food outlets within a neighbourhood (or buffer). To assess if these measures were linked to neighbourhood disadvantage, common statistical methods included ANOVA, correlation, and Poisson or negative binomial regression. Although all studies involved spatial data, few considered spatial analysis techniques or spatial autocorrelation.
Conclusions: With advances in GIS software, sophisticated measures of neighbourhood outlet accessibility can be considered. However, approaches to statistical analysis often appear less sophisticated. Care should be taken to consider assumptions underlying the analysis and the possibility of spatially correlated residuals which could affect the results.

Occupational class differences in suicide: evidence of changes over time and during the global financial crisis in Australia

BACKGROUND: Previous research showed an increase in Australian suicide rates during the Global Financial Crisis (GFC). There has been no research investigating whether suicide rates by occupational class changed during the GFC. The aim of this study was to investigate whether the GFC-associated increase in suicide rates in employed Australians may have masked changes by occupational class.

METHODS: Negative binomial regression models were used to investigate Rate Ratios (RRs) in suicide by occupational class. Years of the GFC (2007, 2008, 2009) were compared to the baseline years 2001-2006.

RESULTS: There were widening disparities between a number of the lower class occupations and the highest class occupations during the years 2007, 2008, and 2009 for males, but less evidence of differences for females.

CONCLUSIONS: Occupational disparities in suicide rates widened over the GFC period. There is a need for programs to be responsive to economic downturns, and to prioritise the occupational groups most affected.

An investigation of neighborhood-level social, economic and physical factors for railway suicide in Victoria, Australia

BACKGROUND: This study investigates the associations between railway suicide and neighborhood social, economic, and physical determinants using postcode-level data. It also examines whether the associations are influenced by having high concentration of high-risk individuals in a neighborhood area. METHODS: Railway suicide cases from Victoria, Australia for the period of 2001-2012, their age, sex, year of death, usual residential address and suicide location were obtained from the National Coronial Information System. Univariate negative binomial regression models were used to estimate the association between railway suicide and neighborhood-level social, economic and physical factors. Variables which were significant in these univariate models were then assessed in a multivariate model, controlling for age and sex of the deceased and other known confounders. RESULTS: Findings from the multivariate analysis indicate that an elevated rate of railway suicide was strongly associated with neighborhood exposure of higher number of railway stations (IRR=1.30 95% CI=1.16-1.46). Other significant neighborhood risk factors included patronage volume (IRR=1.06, 95% CI=1.02-1.11) and train frequency (IRR=1.02, 95% CI=1.01-1.04). An increased number of video surveillance systems at railway stations and carparks was significantly associated with a modest reduction in railway suicide risk (IRR=0.93, 95% CI=0.88-0.98). These associations were independent of concentration of high-risk individuals. LIMITATIONS: Railway suicide may be under-reported in Australia. CONCLUSIONS: Interventions to prevent railway suicide should target vulnerable individuals residing in areas characterized by high station density, patronage volume and train frequency.

Barroom aggression among Australian tradesmen: associations with heavy episodic drinking, trait aggression, and conformity to masculine norms

Objective: Past research associates heavy episodic drinking (HED), trait aggression, and conformity to masculine norms with increased risk of barroom aggression (BA) perpetration by men. Such studies have mostly employed university samples, limiting the generalizability of these findings to other male groups. This study assessed the association of HED, trait aggression, and masculine norms with BA perpetration in a sample of male tradespeople. Method: Australian tradesmen aged 18–35 years (N = 221, Mage = 21.92, SDage = 4.08, 81.5% apprentices) completed an individual interview at their place of work or training, assessing past-month HED and past-year verbal and physical BA perpetrations, as well as the short Buss-Perry Aggression Questionnaire and items from the Conformity to Masculine Norms Inventory-46. Results: Participants reported high levels of verbal (35.1%) and physical (27%) BA perpetration. Negative binomial regression analyses found that HED, trait aggression, and Winning, Risk-taking, and Playboy norms predicted increased risk of both verbal and physical BA perpetrations, while Violence was negatively associated with verbal BA perpetration. Conclusions: Trait aggression was the strongest predictor of both verbal and physical BA perpetrations. Dispositional aggression, HED, and norms endorsing competitiveness, risk-taking, and promiscuity increase the risk of male tradespeople engaging in BA.

Optimistic bias for negative and positive events.

Presents results of an investigation into the occurrence of optimistic bias in relation to both positive and negative events, using absolute judgements to assess perceived risk for each of six events. Participants were asked why they offered different ratings for themselves and for others. The results showed that optimistic bias is a pervasive phenomenon that occurs for both positive and negative events. It occurred for all six events when comparisons were made with an unspecified person of the same age and sex, and occurred for three of six events when comparisons were made with the same-sex best friend. Participants could provide information about their own behaviour that they felt justified their positive outlook; however, they implicitly assumed that the comparison target did not engage in the same behaviour. Concludes that risk-reduction education needs to be made personally relevant to the target audience.