Computation of Gutman Index of Some Cactus Chains

Let G be a finite connected graph of order n. The Gutman index Gut(G) of G is defined as $\sum_{\{x,y\}\subseteq V(G)}deg(x)deg(y)d(x, y)$, where deg(x) is the degree of vertex x in G and d(x, y) is the distance between vertices x and y in G. A cactus graph is a connected graph in which no edge lies in more than one cycle. In this paper we compute the exact value of Gutman index of some cactus chains

The global, regional, and national burden of stomach cancer in 195 countries, 1990-2017 : a systematic analysis for the Global Burden of Disease study 2017

Background: Stomach cancer is a major health problem in many countries. Understanding the current burden of stomach cancer and the differential trends across various locations is essential for formulating effective preventive strategies. We report on the incidence, mortality, and disability-adjusted life-years (DALYs) due to stomach cancer in 195 countries and territories from 21 regions between 1990 and 2017. Methods: Estimates from GBD 2017 were used to analyse the incidence, mortality, and DALYs due to stomach cancer at the global, regional, and national levels. The rates were standardised to the GBD world population and reported per 100 000 population as age-standardised incidence rates, age-standardised death rates, and age-standardised DALY rates. All estimates were generated with 95% uncertainty intervals (UIs). Findings: In 2017, more than 1·22 million (95% UI 1·19–1·25) incident cases of stomach cancer occurred worldwide, and nearly 865 000 people (848 000–885 000) died of stomach cancer, contributing to 19·1 million (18·7–19·6) DALYs. The highest age-standardised incidence rates in 2017 were seen in the high-income Asia Pacific (29·5, 28·2–31·0 per 100 000 population) and east Asia (28·6, 27·3–30·0 per 100 000 population) regions, with nearly half of the global incident cases occurring in China. Compared with 1990, in 2017 more than 356 000 more incident cases of stomach cancer were estimated, leading to nearly 96 000 more deaths. Despite the increase in absolute numbers, the worldwide age-standardised rates of stomach cancer (incidence, deaths, and DALYs) have declined since 1990. The drop in the disease burden was associated with improved Socio-demographic Index. Globally, 38·2% (21·1–57·8) of the age-standardised DALYs were attributable to high-sodium diet in both sexes combined, and 24·5% (20·0–28·9) of the age-standardised DALYs were attributable to smoking in males. Interpretation: Our findings provide insight into the changing burden of stomach cancer, which is useful in planning local strategies and monitoring their progress. To this end, specific local strategies should be tailored to each country's risk factor profile. Beyond the current decline in age-standardised incidence and death rates, a decrease in the absolute number of cases and deaths will be possible if the burden in east Asia, where currently almost half of the incident cases and deaths occur, is further reduced. Funding: Bill & Melinda Gates Foundation

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

The global, regional, and national burden of stomach cancer in 195 countries, 1990-2017: a systematic analysis for the Global Burden of Disease study 2017

Etemadi A, Safiri S, Sepanlou SG, et al. The global, regional, and national burden of stomach cancer in 195 countries, 1990-2017: a systematic analysis for the Global Burden of Disease study 2017. LANCET GASTROENTEROLOGY & HEPATOLOGY. 2020;5(1):42-54.Background Stomach cancer is a major health problem in many countries. Understanding the current burden of stomach cancer and the differential trends across various locations is essential for formulating effective preventive strategies. We report on the incidence, mortality, and disability-adjusted life-years (DALYs) due to stomach cancer in 195 countries and territories from 21 regions between 1990 and 2017. Methods Estimates from GBD 2017 were used to analyse the incidence, mortality, and DALYs due to stomach cancer at the global, regional, and national levels. The rates were standardised to the GBD world population and reported per 100 000 population as age-standardised incidence rates, age-standardised death rates, and age-standardised DALY rates. All estimates were generated with 95% uncertainty intervals (UIs). Findings In 2017, more than 1.22 million (95% UI 1.19-1.25) incident cases of stomach cancer occurred worldwide, and nearly 865 000 people (848 000-885 000) died of stomach cancer, contributing to 19.1 million (18.7-19.6) DALYs. The highest age-standardised incidence rates in 2017 were seen in the high-income Asia Pacific (29.5, 28.2-31.0 per 100 000 population) and east Asia (28.6, 27.3-30.0 per 100 000 population) regions, with nearly half of the global incident cases occurring in China. Compared with 1990, in 2017 more than 356 000 more incident cases of stomach cancer were estimated, leading to nearly 96 000 more deaths. Despite the increase in absolute numbers, the worldwide age-standardised rates of stomach cancer (incidence, deaths, and DALYs) have declined since 1990. The drop in the disease burden was associated with improved Socio-demographic Index. Globally, 38.2% (21.1-57.8) of the age-standardised DALYs were attributable to high-sodium diet in both sexes combined, and 24.5% (20.0-28.9) of the age-standardised DALYs were attributable to smoking in males. Interpretation Our findings provide insight into the changing burden of stomach cancer, which is useful in planning local strategies and monitoring their progress. To this end, specific local strategies should be tailored to each country's risk factor profile. Beyond the current decline in age-standardised incidence and death rates, a decrease in the absolute number of cases and deaths will be possible if the burden in east Asia, where currently almost half of the incident cases and deaths occur, is further reduced. Copyright (C) 2019 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license

The global, regional, and national burden of colorectal cancer and its attributable risk factors in 195 countries and territories, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017

Safiri S, Sepanlou SG, Ikuta KS, et al. The global, regional, and national burden of colorectal cancer and its attributable risk factors in 195 countries and territories, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017. LANCET GASTROENTEROLOGY & HEPATOLOGY. 2019;4(12):913-933.Background Data about the global, regional, and country-specific variations in the levels and trends of colorectal cancer are required to understand the impact of this disease and the trends in its burden to help policy makers allocate resources. Here we provide a status report on the incidence, mortality, and disability caused by colorectal cancer in 195 countries and territories between 1990 and 2017. Methods Vital registration, sample vital registration, verbal autopsy, and cancer registry data were used to generate incidence, death, and disability-adjusted life-year (DALY) estimates of colorectal cancer at the global, regional, and national levels. We also determined the association between development levels and colorectal cancer age-standardised DALY rates, and calculated DALYs attributable to risk factors that had evidence of causation with colorectal cancer. All of the estimates are reported as counts and age-standardised rates per 100 000 person-years, with some estimates also presented by sex and 5-year age groups. Findings In 2017, there were 1.8 million (95% UI 1.8-1.9) incident cases of colorectal cancer globally, with an age-standardised incidence rate of 23.2 (22.7-23.7) per 100 000 person-years that increased by 9.5% (4.5-13.5) between 1990 and 2017. Globally, colorectal cancer accounted for 896 000 (876 300-915 700) deaths in 2017, with an age-standardised death rate of 11.5 (11.3-11.8) per 100 000 person-years, which decreased between 1990 and 2017 (-13.5% [-18.4 to -10.0]). Colorectal cancer was also responsible for 19.0 million (18.5-19.5) DALYs globally in 2017, with an age-standardised rate of 235.7 (229.7-242.0) DALYs per 100 000 person-years, which decreased between 1990 and 2017 (-14.5% [-20.4 to -10.3]). Slovakia, the Netherlands, and New Zealand had the highest age-standardised incidence rates in 2017. Greenland, Hungary, and Slovakia had the highest age-standardised death rates in 2017. Numbers of incident cases and deaths were higher among males than females up to the ages of 80-84 years, with the highest rates observed in the oldest age group (>= 95 years) for both sexes in 2017. There was a non-linear association between the Socio-demographic Index and the Healthcare Access and Quality Index and age-standardised DALY rates. In 2017, the three largest contributors to DALYs at the global level, for both sexes, were diet low in calcium (20.5% [12.9-28.9]), alcohol use (15.2% [12.1-18.3]), and diet low in milk (14.3% [5.1-24.8]). Interpretation There is substantial global variation in the burden of colorectal cancer. Although the overall colorectal cancer age-standardised death rate has been decreasing at the global level, the increasing age-standardised incidence rate in most countries poses a major public health challenge across the world. The results of this study could be useful for policy makers to carry out cost-effective interventions and to reduce exposure to modifiable risk factors, particularly in countries with high incidence or increasing burden. Copyright (C) 2019 The Author(s). Published by Elsevier Ltd

Global Burden of Cardiovascular Diseases and Risks, 1990-2022

Age-standardized CVD mortality rates by regionranged from 73.6 per 100,000 in High-income Asia Pacific to432.3 per 100,000 in Eastern Europe in 2022. Global CVDmortality decreased by 34.9% from 1990 to 2022. Ischemicheart disease had the highest global age-standardized DALYsof all diseases at 2,275.9 per 100,000. Intracerebralhemorrhage and ischemic stroke were the next highest CVDcauses for age-standardized DALYs. Age-standardized CVDprevalence ranged from 5,881.0 per 100,000 in South Asia to11,342.6 per 100,000 in Central Asia. High systolic bloodpressure accounted for the largest number of attributableage-standardized CVD DALYs at 2,564.9 per 100,000globally. Of all risks, household air pollution from solid fuelshad the largest change in attributable age-standardizedDALYs from 1990 to 2022 with a 65.1% decrease

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundRegular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations.MethodsThe Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model—a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates—with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality—which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds.FindingsThe leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2–100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1–290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1–211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4–48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3–37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7–9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles.InterpretationLong-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere