Monomial patterns in the sequence Akb

AbstractWe consider the pattern of zero and nonzero elements in the sequence Akb, where A is an n × n nonnegative matrix and b is an n × 1 nonnegative column vector. We establish a tight bound of k < n for the first occurrence of a given monomial pattern, and we give a graph theoretic characterization of triples (A, b, i) such that there exists a k, k ⩾ n, for which Akb is an i-monomial. The appearance of monomial patterns with a single nonzero entry is linked to controllability of discrete n-dimensional linear dynamic systems with positivity constraints on the state and control

Projected Impact of Salt Restriction on Prevention of Cardiovascular Disease in China: A Modeling Study

Objectives To estimate the effects of achieving China’s national goals for dietary salt (NaCl) reduction or implementing culturally-tailored dietary salt restriction strategies on cardiovascular disease (CVD) prevention. Methods The CVD Policy Model was used to project blood pressure lowering and subsequent downstream prevented CVD that could be achieved by population-wide salt restriction in China. Outcomes were annual CVD events prevented, relative reductions in rates of CVD incidence and mortality, quality-adjusted life-years (QALYs) gained, and CVD treatment costs saved. Results Reducing mean dietary salt intake to 9.0 g/day gradually over 10 years could prevent approximately 197 000 incident annual CVD events [95% uncertainty interval (UI): 173 000–219 000], reduce annual CVD mortality by approximately 2.5% (2.2–2.8%), gain 303 000 annual QALYs (278 000–329 000), and save approximately 1.4 billion international dollars (Int$) in annual CVD costs (Int$; 1.2–1.6 billion). Reducing mean salt intake to 6.0 g/day could approximately double these benefits. Implementing cooking salt-restriction spoons could prevent 183 000 fewer incident CVD cases (153 000–215 000) and avoid Int$1.4 billion in CVD treatment costs annually (1.2–1.7 billion). Implementing a cooking salt substitute strategy could lead to approximately three times the health benefits of the salt-restriction spoon program. More than three-quarters of benefits from any dietary salt reduction strategy would be realized in hypertensive adults. Conclusion China could derive substantial health gains from implementation of population-wide dietary salt reduction policies. Most health benefits from any dietary salt reduction program would be realized in adults with hypertension

Health Benefits of Reducing Sugar-Sweetened Beverage Intake in High Risk Populations of California: Results from the Cardiovascular Disease (CVD) Policy Model

Background Consumption of sugar-sweetened beverage (SSB) has risen over the past two decades, with over 10 million Californians drinking one or more SSB per day. High SSB intake is associated with risk of type 2 diabetes, obesity, hypertension, and coronary heart disease (CHD). Reduction of SSB intake and the potential impact on health outcomes in California and among racial, ethnic, and low-income sub-groups has not been quantified. Methods We projected the impact of reduced SSB consumption on health outcomes among all Californians and California subpopulations from 2013 to 2022. We used the CVD Policy Model – CA, an established computer simulation of diabetes and heart disease adapted to California. We modeled a reduction in SSB intake by 10–20% as has been projected to result from proposed penny-per-ounce excise tax on SSB and modeled varying effects of this reduction on health parameters including body mass index, blood pressure, and diabetes risk. We projected avoided cases of diabetes and CHD, and associated health care cost savings in 2012 US dollars. Results Over the next decade, a 10–20% SSB consumption reduction is projected to result in a 1.8–3.4% decline in the new cases of diabetes and an additional drop of 0.5–1% in incident CHD cases and 0.5–0.9% in total myocardial infarctions. The greatest reductions are expected in African Americans, Mexican Americans, and those with limited income regardless of race and ethnicity. This reduction in SSB consumption is projected to yield $320–620 million in medical cost savings associated with diabetes cases averted and an additional savings of$14–27 million in diabetes-related CHD costs avoided. Conclusions A reduction of SSB consumption could yield substantial population health benefits and cost savings for California. In particular, racial, ethnic, and low-income subgroups of California could reap the greatest health benefits

Projected Impact of Mexico’s Sugar-Sweetened Beverage Tax Policy on Diabetes and Cardiovascular Disease: A Modeling Study

Background: Rates of diabetes in Mexico are among the highest worldwide. In 2014, Mexico instituted a nationwide tax on sugar-sweetened beverages (SSBs) in order to reduce the high level of SSB consumption, a preventable cause of diabetes and cardiovascular disease (CVD). We used an established computer simulation model of CVD and country-specific data on demographics, epidemiology, SSB consumption, and short-term changes in consumption following the SSB tax in order to project potential long-range health and economic impacts of SSB taxation in Mexico. Methods and Findings: We used the Cardiovascular Disease Policy Model–Mexico, a state transition model of Mexican adults aged 35–94 y, to project the potential future effects of reduced SSB intake on diabetes incidence, CVD events, direct diabetes healthcare costs, and mortality over 10 y. Model inputs included short-term changes in SSB consumption in response to taxation (price elasticity) and data from government and market research surveys and public healthcare institutions. Two main scenarios were modeled: a 10% reduction in SSB consumption (corresponding to the reduction observed after tax implementation) and a 20% reduction in SSB consumption (possible with increases in taxation levels and/or additional measures to curb consumption). Given uncertainty about the degree to which Mexicans will replace calories from SSBs with calories from other sources, we evaluated a range of values for calorie compensation. We projected that a 10% reduction in SSB consumption with 39% calorie compensation among Mexican adults would result in about 189,300 (95% uncertainty interval [UI] 155,400–218,100) fewer incident type 2 diabetes cases, 20,400 fewer incident strokes and myocardial infarctions, and 18,900 fewer deaths occurring from 2013 to 2022. This scenario predicts that the SSB tax could save Mexico 983 million international dollars (95% UI $769 million–$1,173 million). The largest relative and absolute reductions in diabetes and CVD events occurred in the youngest age group modeled (35–44 y). This study’s strengths include the use of an established mathematical model of CVD and use of contemporary Mexican vital statistics, data from health surveys, healthcare costs, and SSB price elasticity estimates as well as probabilistic and deterministic sensitivity analyses to account for uncertainty. The limitations of the study include reliance on US-based studies for certain inputs where Mexico-specific data were lacking (specifically the associations between risk factors and CVD outcomes [from the Framingham Heart Study] and SSB calorie compensation assumptions), limited data on healthcare costs other than those related to diabetes, and lack of information on long-term SSB price elasticity that is specific to geographic and economic subgroups. Conclusions: Mexico’s high diabetes prevalence represents a public health crisis. While the long-term impact of Mexico’s SSB tax is not yet known, these projections, based on observed consumption reductions, suggest that Mexico’s SSB tax may substantially decrease morbidity and mortality from diabetes and CVD while reducing healthcare costs

Projected impact of a reduction in sugar-sweetened beverage consumption on diabetes and cardiovascular disease in Argentina: a modeling study

The study finds that even with conservative assumptions, a relatively small reduction in sugar-sweetened beverages (SSB) consumption could lead to a substantial decrease in diabetes incidence, cardiovascular events, and mortality in Argentina. The largest reductions in diabetes and cardiovascular events were observed in the youngest age group modeled (35–44 years) for both men and women. These results support the implementation of policies to reduce SSB consumption, such as a soda tax. Use of taxation as a health policy tool would have the additional advantage of providing a new source of public funds to support healthy lifestyles

Comparative Cost-Effectiveness of Hypertension Treatment in Non-Hispanic Blacks and Whites According to 2014 Guidelines: A Modeling Study

BACKGROUND: We compared the cost-effectiveness of hypertension treatment in non-Hispanic blacks and non-Hispanic whites according to 2014 US hypertension treatment guidelines. METHODS: The cardiovascular disease (CVD) policy model simulated CVD events, quality-adjusted life years (QALYs), and treatment costs in 35- to 74-year-old adults with untreated hypertension. CVD incidence, mortality, and risk factor levels were obtained from cohort studies, hospital registries, vital statistics, and national surveys. Stage 1 hypertension was defined as blood pressure 140-149/90-99mm Hg; stage 2 hypertension as ≥150/100mm Hg. Probabilistic input distribution sampling informed 95% uncertainty intervals (UIs). Incremental cost-effectiveness ratios (ICERs) < $50,000/QALY gained were considered cost-effective. RESULTS: Treating 0.7 million hypertensive non-Hispanic black adults would prevent about 8,000 CVD events annually; treating 3.4 million non-Hispanic whites would prevent about 35,000 events. Overall 2014 guideline implementation would be cost saving in both groups compared with no treatment. For stage 1 hypertension but without diabetes or chronic kidney disease, cost savings extended to non-Hispanic black males ages 35-44 but not same-aged non-Hispanic white males (ICER$57,000/QALY; 95% UI $15,000-$100,000) and cost-effectiveness extended to non-Hispanic black females ages 35-44 (ICER $46,000/QALY;$17,000-$76,000) but not same-aged non-Hispanic white females (ICER$181,000/QALY; $111,000-$235,000). CONCLUSIONS: Compared with non-Hispanic whites, cost-effectiveness of implementing hypertension guidelines would extend to a larger proportion of non-Hispanic black hypertensive patients

Health Benefits of Reducing Sugar-Sweetened Beverage Intake in High Risk Populations of California: Results from the Cardiovascular Disease (CVD) Policy Model

BACKGROUND: Consumption of sugar-sweetened beverage (SSB) has risen over the past two decades, with over 10 million Californians drinking one or more SSB per day. High SSB intake is associated with risk of type 2 diabetes, obesity, hypertension, and coronary heart disease (CHD). Reduction of SSB intake and the potential impact on health outcomes in California and among racial, ethnic, and low-income sub-groups has not been quantified. METHODS: We projected the impact of reduced SSB consumption on health outcomes among all Californians and California subpopulations from 2013 to 2022. We used the CVD Policy Model – CA, an established computer simulation of diabetes and heart disease adapted to California. We modeled a reduction in SSB intake by 10–20% as has been projected to result from proposed penny-per-ounce excise tax on SSB and modeled varying effects of this reduction on health parameters including body mass index, blood pressure, and diabetes risk. We projected avoided cases of diabetes and CHD, and associated health care cost savings in 2012 US dollars. RESULTS: Over the next decade, a 10–20% SSB consumption reduction is projected to result in a 1.8–3.4% decline in the new cases of diabetes and an additional drop of 0.5–1% in incident CHD cases and 0.5–0.9% in total myocardial infarctions. The greatest reductions are expected in African Americans, Mexican Americans, and those with limited income regardless of race and ethnicity. This reduction in SSB consumption is projected to yield $320–620 million in medical cost savings associated with diabetes cases averted and an additional savings of$14–27 million in diabetes-related CHD costs avoided. CONCLUSIONS: A reduction of SSB consumption could yield substantial population health benefits and cost savings for California. In particular, racial, ethnic, and low-income subgroups of California could reap the greatest health benefits

Cost-Effectiveness of Hypertension Therapy According to 2014 Guidelines

BACKGROUND: On the basis of the 2014 guidelines for hypertension therapy in the United States, many eligible adults remain untreated. We projected the cost-effectiveness of treating hypertension in U.S. adults according to the 2014 guidelines. METHODS: We used the Cardiovascular Disease Policy Model to simulate drug-treatment and monitoring costs, costs averted for the treatment of cardiovascular disease, and quality-adjusted life-years (QALYs) gained by treating previously untreated adults between the ages of 35 and 74 years from 2014 through 2024. We assessed cost-effectiveness according to age, hypertension level, and the presence or absence of chronic kidney disease or diabetes. RESULTS: The full implementation of the new hypertension guidelines would result in approximately 56,000 fewer cardiovascular events and 13,000 fewer deaths from cardiovascular causes annually, which would result in overall cost savings. The projections showed that the treatment of patients with existing cardiovascular disease or stage 2 hypertension would save lives and costs for men between the ages of 35 and 74 years and for women between the ages of 45 and 74 years. The treatment of men or women with existing cardiovascular disease or men with stage 2 hypertension but without cardiovascular disease would remain cost-saving even if strategies to increase medication adherence doubled treatment costs. The treatment of stage 1 hypertension was cost-effective (defined as <$50,000 per QALY) for all men and for women between the ages of 45 and 74 years, whereas treating women between the ages of 35 and 44 years with stage 1 hypertension but without cardiovascular disease had intermediate or low cost-effectiveness. CONCLUSIONS: The implementation of the 2014 hypertension guidelines for U.S. adults between the ages of 35 and 74 years could potentially prevent about 56,000 cardiovascular events and 13,000 deaths annually, while saving costs. Controlling hypertension in all patients with cardiovascular disease or stage 2 hypertension could be effective and cost-saving. (Funded by the National Heart, Lung, and Blood Institute and others.