Particulate air pollution is associated with increased mortality. There is a need for European results from multicountry databases concerning cause-specific mortality to obtain more accurate effect estimates. We report the estimated effects of ambient particle concentrations (black smoke and particulate matter less than 10 μm [PM10]) on cardiovascular and respiratory mortality, from 29 European cities, within the Air Pollution and Health: a European Approach (APHEA2) project. We applied a 2-stage hierarchical modeling approach assessing city-specific effects first and then overall effects. City characteristics were considered as potential effect modifiers. An increase in PM10 by 10 μg/m3 (lag 0 + 1) was associated with increases of 0.76% (95% confidence interval = 0.47 to 1.05%) in cardiovascular deaths and 0.58% (0.21 to 0.95%) in respiratory deaths. The same increase in black smoke was associated with increases of 0.62% (0.35 to 0.90%) and 0.84% (0.11 to 1.57%), respectively. These effect estimates are appropriate for health impact assessment and standard-setting procedures.

Multivariate count data occur in several different disciplines. However, existing models do not offer great flexibility for dependence modeling. Models based on copulas nowadays are widely used for continuous data dependence modeling. Modeling count data via copulas is still in its infancy; see the recent article of Genest and Nešlehová ( 2007 Genest , C. , Nešlehová , J. ( 2007 ). A primer on copulas for count data . The Astin Bulletin 37 : 475 – 515 . [Crossref], [Web of Science ®] [Google Scholar] ). A series of different copula models providing various residual dependence structures are considered for vectors of count response variables whose marginal distributions depend on covariates through negative binomial regressions. A real data application related to the number of purchases of different products is provided.

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.