Background/Aims Age-related macular degeneration (AMD) is the main cause of visual impairment and blindness in Europe. A further increase in the number of affected persons is expected and current European data are needed for healthcare resource planning. Methods We performed a systematic review on the prevalence and incidence of AMD based on the meta-analysis of observational studies in epidemiology guideline. Meta-analysis and meta-regression on time-trends, age, countries, regions, sex and classification systems for AMD were performed. Based on Eurostat population projections, the pooled prevalence estimates were extrapolated to the year 2050. Results Twenty-two prevalence and four incidence studies published since 1996 were included. Our pooled prevalence estimate of early or intermediate AMD and any late AMD in those 60 years and older was 25.3% (95% CI 18.0% to 34.4%) and 2.4% (95% CI 1.8% to 3.3%), respectively. A significant increase in prevalence was seen in older populations. In the meta-analysis of incidence, the pooled annual incidence of any late AMD was 1.4 per 1 000 individuals (95% CI 0.8 to 2.6). Overall, the number of EU inhabitants with any late AMD is expected to increase from 67 to 77 million until 2050. Incident late AMD is estimated to increase from 400 000 per year today to 700 000 per year in 2050. Conclusions Approximately 67 million people in the EU are currently affected by any AMD and, due to population ageing, this number is expected to increase by 15% until 2050. Monitoring and treatment of people with advanced disease stages will require additional healthcare resources and thorough healthcare planning in the years and decades to come.

Purpose: To examine the prevalence and incidence of rhegmatogenous retinal detachment (RRD) in Europe. Methods: A systematic review of the prevalence and incidence of RRD in Europe according to the meta-analyses of observational studies in epidemiology (MOOSE) guidelines was performed using the databases PubMed, Embase, and Web of Science followed by a meta-analysis of incidence data. Results: 658 studies were identified, 76 full-text articles were assessed, and 5 studies were eligible for meta-analysis. Random-effects pooled mean annual incidence of RRD in Europe was 13.3 cases per 100,000 inhabitants (95% CI: 11.3–15.6) based on the examination of 95,765 individuals from the 5 incidence studies. No European studies reporting prevalence of retinal detachment were identified. Conclusion: Published articles on the prevalence and incidence of RRD in Europe are limited. Further epidemiological research is needed for adequate healthcare planning.

Summary: A popular modeling approach for competing risks analysis in longitudinal studies is the proportional subdistribution hazards model by Fine and Gray (1999. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association94, 496–509). This model is widely used for the analysis of continuous event times in clinical and epidemiological studies. However, it does not apply when event times are measured on a discrete time scale, which is a likely scenario when events occur between pairs of consecutive points in time (e.g., between two follow-up visits of an epidemiological study) and when the exact lengths of the continuous time spans are not known. To adapt the Fine and Gray approach to this situation, we propose a technique for modeling subdistribution hazards in discrete time. Our method, which results in consistent and asymptotically normal estimators of the model parameters, is based on a weighted ML estimation scheme for binary regression. We illustrate the modeling approach by an analysis of nosocomial pneumonia in patients treated in hospitals.

Statistical modeling of ecological data is often faced with a large number of variables as well as possible nonlinear relationships and higher-order interaction effects.Gradient boosted trees(GBT) have been successful in addressing these issues and have shown a good predictive performance in modeling nonlinear relationships, in particular in classification settings with a categorical response variable. They also tend to be robust against outliers. However, their black-box nature makes it difficult to interpret these models. We introduce several recently developed statistical tools to the environmental research community in order to advance interpretation of these black-box models. To analyze the properties of the tools, we applied gradient boosted trees to investigate biological health of streams within the contiguous USA, as measured by a benthic macroinvertebrate biotic index. Based on these data and a simulation study, we demonstrate the advantages and limitations ofpartial dependence plots(PDP),individual conditional expectation(ICE) curves andaccumulated local effects(ALE) in their ability to identify covariate–response relationships. Additionally, interaction effects were quantified according to interaction strength (IAS) and Friedman’s $$H^2$$H2 statistic. Interpretable machine learning techniques are useful tools to open the black-box of gradient boosted trees in the environmental sciences. This finding is supported by our case study on the effect of impervious surface on the benthic condition, which agrees with previous results in the literature. Overall, the most important variables were ecoregion, bed stability, watershed area, riparian vegetation and catchment slope. These variables were also present in most identified interaction effects. In conclusion, graphical tools (PDP, ICE, ALE) enable visualization and easier interpretation of GBT but should be supported by analytical statistical measures. Future methodological research is needed to investigate the properties of interaction tests. Supplementary materials accompanying this paper appear on-line.