Background In an era of shifting global agendas and expanded emphasis on non-communicable diseases and injuries along with communicable diseases, sound evidence on trends by cause at the national level is essential. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) provides a systematic scientific assessment of published, publicly available, and contributed data on incidence, prevalence, and mortality for a mutually exclusive and collectively exhaustive list of diseases and injuries.Methods GBD estimates incidence, prevalence, mortality, years of life lost (YLLs), years lived with disability (YLDs), and disability-adjusted life-years (DALYs) due to 369 diseases and injuries, for two sexes, and for 204 countries and territories. Input data were extracted from censuses, household surveys, civil registration and vital statistics, disease registries, health service use, air pollution monitors, satellite imaging, disease notifications, and other sources. Cause-specific death rates and cause fractions were calculated using the Cause of Death Ensemble model and spatiotemporal Gaussian process regression. Cause-specific deaths were adjusted to match the total all-cause deaths calculated as part of the GBD population, fertility, and mortality estimates. Deaths were multiplied by standard life expectancy at each age to calculate YLLs. A Bayesian meta-regression modelling tool, DisMod-MR 2.1, was used to ensure consistency between incidence, prevalence, remission, excess mortality, and cause-specific mortality for most causes. Prevalence estimates were multiplied by disability weights for mutually exclusive sequelae of diseases and injuries to calculate YLDs. We considered results in the context of the Socio-demographic Index (SDI), a composite indicator of income per capita, years of schooling, and fertility rate in females younger than 25 years. Uncertainty intervals (UIs) were generated for every metric using the 25th and 975th ordered 1000 draw values of the posterior distribution.Findings Global health has steadily improved over the past 30 years as measured by age-standardised DALY rates. After taking into account population growth and ageing, the absolute number of DALYs has remained stable. Since 2010, the pace of decline in global age-standardised DALY rates has accelerated in age groups younger than 50 years compared with the 1990-2010 time period, with the greatest annualised rate of decline occurring in the 0-9-year age group. Six infectious diseases were among the top ten causes of DALYs in children younger than 10 years in 2019: lower respiratory infections (ranked second), diarrhoeal diseases (third), malaria (fifth), meningitis (sixth), whooping cough (ninth), and sexually transmitted infections (which, in this age group, is fully accounted for by congenital syphilis; ranked tenth). In adolescents aged 10-24 years, three injury causes were among the top causes of DALYs: road injuries (ranked first), self-harm (third), and interpersonal violence (fifth). Five of the causes that were in the...

and Risk Factors Study 2019 (GBD 2019) provided systematic estimates of incidence, morbidity, and mortality to inform local and international efforts toward reducing cancer burden. OBJECTIVE To estimate cancer burden and trends globally for 204 countries and territories and by Sociodemographic Index (SDI) quintiles from 2010 to 2019. EVIDENCE REVIEWThe GBD 2019 estimation methods were used to describe cancer incidence, mortality, years lived with disability, years of life lost, and disability-adjusted life years (DALYs) in 2019 and over the past decade. Estimates are also provided by quintiles of the SDI, a composite measure of educational attainment, income per capita, and total fertility rate for those younger than 25 years. Estimates include 95% uncertainty intervals (UIs).FINDINGS In 2019, there were an estimated 23.6 million (95% UI, 22.2-24.9 million) new cancer cases (17.2 million when excluding nonmelanoma skin cancer) and 10.0 million (95% UI, 9.36-10.6 million) cancer deaths globally, with an estimated 250 million (235-264 million) DALYs due to cancer. Since 2010, these represented a 26.3% (95% UI, 20.3%-32.3%) increase in new cases, a 20.9% (95% UI, 14.2%-27.6%) increase in deaths, and a 16.0% (95% UI, 9.3%-22.8%) increase in DALYs. Among 22 groups of diseases and injuries in the GBD 2019 study, cancer was second only to cardiovascular diseases for the number of deaths, years of life lost, and DALYs globally in 2019. Cancer burden differed across SDI quintiles. The proportion of years lived with disability that contributed to DALYs increased with SDI, ranging from 1.4% (1.1%-1.8%) in the low SDI quintile to 5.7% (4.2%-7.1%) in the high SDI quintile. While the high SDI quintile had the highest number of new cases in 2019, the middle SDI quintile had the highest number of cancer deaths and DALYs. From 2010 to 2019, the largest percentage increase in the numbers of cases and deaths occurred in the low and low-middle SDI quintiles. CONCLUSIONS AND RELEVANCEThe results of this systematic analysis suggest that the global burden of cancer is substantial and growing, with burden differing by SDI. These results provide comprehensive and comparable estimates that can potentially inform efforts toward equitable cancer control around the world.

Background Prevention, control, and treatment of respiratory tract cancers are important steps towards achieving target 3.4 of the UN Sustainable Development Goals (SDGs)-a one-third reduction in premature mortality due to non-communicable diseases by 2030. We aimed to provide global, regional, and national estimates of the burden of tracheal, bronchus, and lung cancer and larynx cancer and their attributable risks from 1990 to 2019.Methods Based on the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 methodology, we evaluated the incidence, mortality, years lived with disability, years of life lost, and disability-adjusted life-years (DALYs) of respiratory tract cancers (ie, tracheal, bronchus, and lung cancer and larynx cancer). Deaths from tracheal, bronchus, and lung cancer and larynx cancer attributable to each risk factor were estimated on the basis of risk exposure, relative risks, and the theoretical minimum risk exposure level input from 204 countries and territories, stratified by sex and Socio-demographic Index (SDI). Trends were estimated from 1990 to 2019, with an emphasis on the 2010-19 period. Findings Globally, there were 2•26 million (95% uncertainty interval 2•07 to 2•45) new cases of tracheal, bronchus, and lung cancer, and 2•04 million (1•88 to 2•19) deaths and 45•9 million (42•3 to 49•3) DALYs due to tracheal, bronchus, and lung cancer in 2019. There were 209 000 (194 000 to 225 000) new cases of larynx cancer, and 123 000 (115 000 to 133 000) deaths and 3•26 million (3•03 to 3•51) DALYs due to larynx cancer globally in 2019. From 2010 to 2019, the number of new tracheal, bronchus, and lung cancer cases increased by 23•3% (12•9 to 33•6) globally and the number of larynx cancer cases increased by 24•7% (16•0 to 34•1) globally. Global age-standardised incidence rates of tracheal, bronchus, and lung cancer decreased by 7•4% (-16•8 to 1•6) and age-standardised incidence rates of larynx cancer decreased by 3•0% (-10•5 to 5•0) in males over the past decade; however, during the same period, agestandardised incidence rates in females increased by 0•9% (-8•2 to 10•2) for tracheal, bronchus, and lung cancer and decreased by 0•5% (-8•4 to 8•1) for larynx cancer. Furthermore, although age-standardised incidence and death rates declined in both sexes combined from 2010 to 2019 at the global level for tracheal, bronchus, lung and larynx cancers, some locations had rising rates, particularly those on the lower end of the SDI range. Smoking contributed to an estimated 64•2% (61•9-66•4) of all deaths from tracheal, bronchus, and lung cancer and 63•4% (56•3-69•3) of all deaths from larynx cancer in 2019. For males and for both sexes combined, smoking was the leading specific risk factor for age-standardised deaths from tracheal, bronchus, and lung cancer per 100 000 in all SDI quintiles and GBD regions in 2019. However, among females, household air pollution from solid fuels was the leading specific risk factor in the low SDI quintile and in three GBD regions (central, eastern, and wester...

We compute the treewidth of a family of graphs we refer to as the glued grids, consisting of the stacked prism graphs and the toroidal grids. Our main technique is constructing strict brambles of large orders. We discuss connections to divisorial graph theory coming from tropical geometry, and use our results to compute the divisorial gonality of these graphs.