scholarly journals Incidence and Case Fatality at the County Level as Contributors to Geographic Disparities in Stroke Mortality

2016 ◽  
Vol 47 (2) ◽  
pp. 96-102 ◽  
Author(s):  
Darwin R. Labarthe ◽  
George Howard ◽  
Monika M. Safford ◽  
Virginia J. Howard ◽  
Suzanne E. Judd ◽  
...  
Keyword(s):  
Racial Differences ◽  
Stroke Prevention ◽  
Case Fatality ◽  
Stroke Care ◽  
The United States ◽  
Hazard Ratio ◽  
Mortality Data ◽  
Stroke Mortality ◽  
Stroke Incidence ◽  
Stroke Case

Background: Is the high stroke mortality in the Southeastern parts of the United States driven by differences in stroke incidence or case-fatality? This question remains unanswered. Differences in incidence would underscore the need for stroke prevention, while differences in case fatality would call for improved stroke care. Methods: Quartiles of US counties were defined by stroke mortality, and this gradient was related with stroke incidence and stroke case fatality in the Reasons for Geographic and Racial Differences in Stroke (REGARDS) Study, where 1,317 incident stroke events (of which 242 were fatal) occurred among 29,650 participants. Results: There was a significant (p = 0.0025) gradient of fatal stroke events in REGARDS (quartile 4 vs. quartile 1 (Q4/Q1) hazard ratio 1.95, 95% CI 1.35-2.81), demonstrating the consistency of REGARDS with national mortality data. The gradient for incident stroke (fatal + nonfatal) was also significant (p = 0.0023; Q4/Q1 hazard ratio 1.29, 95% CI 1.10-1.52). The gradient for stroke case-fatality was marginally significant (p = 0.058), though the OR for Q4/Q1 (1.71, 95% CI 1.13-2.25) was large. Conclusions: Both stroke incidence and case-fatality in REGARDS appear to be contributing, underscoring the need for strengthening both stroke prevention and acute stroke care in order to reduce the disparity.

Abstract 52: Contributors to the Rural Excess in Stroke Mortality: The REasons for Geographic and Racial Differences in Stroke (REGARDS) Study

Stroke ◽  
2017 ◽  
Vol 48 (suppl_1) ◽  
Author(s):  
George Howard ◽  
Dawn O Kleindorfer ◽  
D. L Long ◽  
Mary Cushman ◽  
Virginia J Howard ◽  
...  
Keyword(s):  
Risk Factors ◽  
Risk Factor ◽  
Racial Differences ◽  
Proportional Hazards ◽  
Case Fatality ◽  
Stroke Mortality ◽  
Rural Regions ◽  
Stroke Incidence ◽  
Regards Study ◽  
The Impact

Introduction: One NIH goal is to investigate the US nationwide rural-urban health disparities; however, few studies provide data to help understand the 30% higher rural stroke mortality. It is unknown if the higher stroke mortality is attributable to a higher incidence of stroke, or to a higher case fatality, in rural regions. Further, the role of risk factors or SES status in higher incidence or case-fatality is unknown. Methods: REGARDS participants stroke-free at baseline (n = 25,090) were stratified by Rural-Urban Commuting Area strata: urban, large rural city/town, or small rural town or isolated region. Participants were followed for incident stroke, and case fatality was defined as death within 30-days of a stroke. Difference in incident stroke was assessed using proportional hazards analysis, and case-fatality by logistic regression, each considered after adjustment for demographic factors, further adjustment for risk factors, and further adjustment for SES. Results: Over an average follow-up of 8.2 years, 1,060 incident strokes occurred, of which 160 died within 30 days. Risk of incident stroke increased with rurality (p = 0.016), with a hazard 1.21-times (95% CI: 1.00 - 1.46) higher in large rural cities/towns, and 1.24-times (95% CI: 1.00 - 1.54) higher in small rural towns or isolated regions (see table). Adjustment for risk factors and SES attenuated the estimated risk by 50%, and the association became non-significant. There was no evidence of a higher case-fatality from stroke in rural regions (p > 0.46). Discussion: The higher stroke mortality in rural regions appears to be attributable to higher stroke incidence, and not to higher case-fatality. Higher stroke incidence in rural regions is partially attributable to a worse risk factor profile and lower SES. Efforts to reduce rural disparity in stroke mortality should focus on preventive strategies, especially those relevant to risk factor development and control, and/or mitigating the impact of lower SES.

Abstract 84: Where Should Interventions be Focused to Reduce the Black-white Disparity in Stroke Mortality? Insights From the Reasons For Geographic And Racial Differences In Stroke (REGARDS) Study

Stroke ◽  
2015 ◽  
Vol 46 (suppl_1) ◽  
Author(s):  
George Howard ◽  
Claudia S Moy ◽  
Virginia J Howard ◽  
Leslie A McClure ◽  
Dawn O Kleindorfer ◽  
...  
Keyword(s):  
Primary Prevention ◽  
Racial Differences ◽  
Proportional Hazards ◽  
Case Fatality ◽  
Major Contributor ◽  
Stroke Mortality ◽  
Stroke Event ◽  
Stroke Incidence ◽  
Fatal Stroke ◽  
Initial Event

Introduction: The study of racial disparities in stroke mortality should guide interventions to reduce these disparities. A higher mortality in blacks than whites could result from a higher incidence of stroke in blacks, a higher case-fatality of stroke in blacks, or both. Interventions focusing on primary prevention are needed if incidence is a major contributor to disparities, while interventions addressing treatment are a priority if case-fatality is a major contributor. Hypothesis: Higher stroke mortality in REGARDS will be attributable to higher incidence, higher case fatality, or both. Methods: 29,681 black and white participants aged 45+ were followed for stroke over 7 years. Fatal stroke (stroke mortality) was defined as a stroke event with death within 30-days, incident stroke included all stroke events (regardless of death), and case-fatality as the proportion of stroke events with death within 30-days. Black-white differences in stroke mortality and stroke incidence were assessed using proportional hazards models, and case-fatality using logistic regression (with adjustment for age and sex). Results: There were 954 incident events with 242 deaths within 30-days. We showed higher stroke mortality in blacks, with a black-white disparity in fatal stroke at young ages (at age 45, HR = 4.35; 95% CI: 1.94-9.76), but a declining magnitude of the disparity at older ages (at age 85, HR = 0.87; 95% CI: 0.56 - 1.35). The pattern was similar for incident stroke, although the magnitude of the black-white disparity was smaller (at age 45: HR = 2.40; 95% CI: 1.72 - 3.33; at age 85: HR = 0.95; 95% CI: 0.76 - 1.19). There was no evidence of a black-white disparity in case-fatality rate (OR = 1.26; 95% CI: 0.93 - 1.71). Conclusion: In a nationwide cohort, we found that the black-white disparity in stroke mortality was primarily attributable to a racial disparity in stroke incidence, not case fatality. Thus, interventions designed to reduce the black-white disparity in stroke mortality require a primary prevention focus aimed at reducing the disparity in stroke incidence. While effective interventions to improve stroke outcomes are needed, these data suggest that improving treatment after the initial event will not reduce black-white disparities in stroke mortality.

Abstract WP158: Case Fatality and Risk Factor Trend Contributions to Stroke Mortality in Non-Hispanic Blacks and Non-Hispanic Whites, 1999-2012

Stroke ◽  
2016 ◽  
Vol 47 (suppl_1) ◽  
Author(s):  
Joanne Penko ◽  
Andrew E Moran ◽  
Antoinette Mason ◽  
Pamela G Coxson ◽  
Mark J Pletcher ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Risk Factor ◽  
Racial Differences ◽  
Density Lipoprotein ◽  
Case Fatality ◽  
Stroke Mortality ◽  
Mortality Trends ◽  
Stroke Risk Factor ◽  
Stroke Incidence ◽  
Policy Model

Introduction: Stroke death rates have declined nationally, but less in men and non-Hispanic Blacks. We quantified case-fatality and risk factor trend contributions to non-Hispanic Black and non-Hispanic White 1999-2012 stroke mortality trends. Methods: The CVD Policy Model is a computer simulation of heart disease and stroke incidence, prevalence, and mortality in US adults ≥ 35 years old. We modeled mean systolic blood pressure (SBP), low-density lipoprotein (LDL), and body mass index (BMI), prevalence of diabetes and smoking, and case fatality for 1999-2002, 2003-06, and 2007-12 by sex and race (NHANES; NHDS) to predict stroke mortality trends and these predictions were compared with observed data (CDC Wonder; ICD-10 I60-69). We then simulated the effects of isolated risk factors on stroke mortality in younger (age 35-64 years) and older (age 65-84 years) men and women. Results: Model predictions mirrored observed trends for stroke mortality in Whites (men: predicted -27.0% v. observed -29.2%; women: -34.8% v. -33.3%) and Blacks (men: -23.8% v. -22.2%; women: -31.0% v. -30.0%). Case fatality was the main contributor to the observed decrease in stroke mortality (approximately -25%) but did not explain differences between race groups. Combined risk factor trends contributed to decreased mortality in women (-12.8% in Whites; -8.7% in Blacks), but not men. Decreased mean SBP contributed in all women (-10.7% to -12.6%, depending on age/race) and older men (-4.0%), but not young men. Increased diabetes prevalence offset improvements in stroke mortality in older White men (+2.5%), younger Blacks (men: +4.0, women: +1.5%) and, to a larger degree, older Blacks (men: +9.9%, women: +5.6% ). Conclusions: Reduced case fatality was the strongest driver of decreased stroke mortality from 1999-2012 overall, while risk factor trends explained gender and race differences. Targeting high blood pressure in young adult men and preventing diabetes at all ages could further decrease stroke mortality and reduce racial differences. Blacks would benefit most from more aggressive stroke risk factor control.

Abstract 20: Patterns of Stroke Center Certification and the Impact on Stroke Mortality in Counties of New York State

Stroke ◽  
2021 ◽  
Vol 52 (Suppl_1) ◽  
Author(s):  
Emily Chapman ◽  
Kurt A Yaeger ◽  
J D Mocco
Keyword(s):  
New York ◽  
Socioeconomic Status ◽  
Household Income ◽  
New York State ◽  
Stroke Care ◽  
Stroke Mortality ◽  
Median Household Income ◽  
Stroke Incidence ◽  
York State ◽  
The Relationship

Introduction: To establish a statewide stroke system in March 2019, New York State (NYS) created the Stroke Designation Program. Stroke centers (SCs) must be certified by a state-approved certifying organization (CO), which is tasked with initial designation and ongoing re-certification. Previous research has found an association at the national level between socioeconomic status and access to higher levels of acute stroke care. Objective: This study characterizes the relationship between socioeconomic status of NYS populations and stroke care level access by comparing median household income and wealth in counties with and without certified SCs. Methods: Population and median household income from the U.S. Census (2010), stroke epidemiological data from the Center for Disease Control, and Area Deprivation Index (ADI) data (ranked within NYS) from the Neighborhood Atlas, a project that quantifies disadvantage by census tract, were collected and averaged for each county. Income has been used to assess local wealth and ADI to analyze community health risks. Certification data were mined from quality check databases for The Joint Commission and Det Norske Veritas, the most commonly used COs. Student’s t-tests compared income and ADI in counties with at least one certified SC to those without. Linear regression characterized the relationship between income and ADI with number of certified SCs, stroke incidence and stroke mortality. Results: All 62 counties in NYS were investigated to yield 40 certified SCs. Counties with at least one certified SC had a significantly higher income ($68,183.63 vs. $57,155.12; p=0.03) and lower ADI (5.90 vs. 7.37; p=0.004) compared to counties with no certified SC. Higher income (p<0.001) and lower ADI (p<0.001) were also associated with more certified SCs. Counties with fewer certified SCs had significantly higher stroke mortality (p<0.001) despite having similar stroke incidence. Conclusion: Socioeconomic heterogeneity in NYS counties is correlated to differential access to certified SCs and quality stroke care, as fewer centers are found in lower-income and disadvantaged communities. Although populations with less access experience stroke at similar rates, this study finds higher death rates in these counties.

Abstract 88: Social Inequalities in Stroke Mortality, Incidence and Case-fatality in Europe.

Stroke ◽  
2016 ◽  
Vol 47 (suppl_1) ◽  
Author(s):  
Marco M Ferrario ◽  
Giovanni Veronesi ◽  
Kari Kuulasmaa ◽  
Martin Bobak ◽  
Lloyd E Chambless ◽  
...  
Keyword(s):  
Risk Factors ◽  
Social Inequalities ◽  
Cox Regression ◽  
Case Fatality ◽  
Stroke Mortality ◽  
Stroke Incidence ◽  
Low Education ◽  
Mortality Incidence ◽  
European Populations

Introduction and aim: There are limited comparative data on social inequalities in stroke morbidity across Europe. We aimed to assess the magnitude of educational class inequalities in stroke mortality, incidence and 1-year case-fatality in European populations. Methods: The MORGAM study comprised 45 cohorts from Finland, Denmark, Sweden, Northern Ireland, Scotland, France, Germany, Italy, Lithuania, Poland and Russia, mostly recruited in mid 1980s-early 90s. Baseline data collection and follow-up (median 12 years) for fatal and non-fatal strokes adhered to MONICA-like procedures. Stroke mortality was defined according to the underlying cause of death (ICD-IX codes 430-438 or ICD-X I60-I69). We derived 3 educational classes from population-, sex- and birth year-specific tertiles of years of schooling. We estimated the age-adjusted difference in event rates, and the age- and risk factor-adjusted hazard ratios (HRs), between the bottom and the top of the educational class distribution from sex- and population-specific Poisson and Cox regression models, respectively. The association between 1-year case-fatality and education was estimated through logistic models adjusted for risk factors. Results: Among the 91,563 CVD-free participants aged 35-74 at baseline, 1037 stroke deaths and 3902 incident strokes occurred during follow-up. Low education accounted for 26 additional stroke deaths per 100,000 person-years in men (95%CI: 9 to 42), and 19 (7 to 32) in women. In both genders, inequalities in fatal stroke rates were larger in the East EU and in the Nordic Countries populations. The age-adjusted pooled HRs of first stroke, fatal or non-fatal, for the least educated men and women were 1.52 (95%CI: 1.29-1.78) and 1.51 (1.25-1.81), respectively, consistently across populations. Adjustment for smoking, blood pressure, HDL-cholesterol and diabetes attenuated the pooled HRs to 1.34 (95%CI: 1.14-1.57) in men and 1.29 (1.07-1.55) in women. A significant association between low education and increased 1-year case-fatality was observed in Northern Sweden only. Conclusions: Social inequalities in stroke incidence are widespread in most European populations, and less than half of the gap is explained by major risk factors.

scholarly journals Stroke Incidence and Case Fatality According to Rural or Urban Residence

Stroke ◽  
2019 ◽  
Vol 50 (10) ◽  
pp. 2661-2667 ◽  
Author(s):  
Olivier Grimaud ◽  
Yacine Lachkhem ◽  
Fei Gao ◽  
Cindy Padilla ◽  
Mélanie Bertin ◽  
...  
Keyword(s):  
Rural Areas ◽  
Urban Areas ◽  
Healthcare Access ◽  
Case Fatality ◽  
The United States ◽  
Stroke Severity ◽  
Day Case ◽  
Stroke Incidence ◽  
Stroke Registry ◽  
Stroke Type

Background and Purpose— Recent findings suggest that in the United States, stroke incidence is higher in rural than in urban areas. Similar analyses in other high-income countries are scarce with conflicting results. In 2008, the Brest Stroke Registry was started in western France, an area that includes about 366 000 individuals living in various urban and rural settings. Methods— All new patients with stroke included in the Brest Stroke Registry from 2008 to 2013 were classified as residing in town centers, suburbs, isolated towns, or rural areas. Poisson regression was used to analyze stroke incidence and 30-day case fatality variations in the 4 different residence categories. Models with case fatality as outcome were adjusted for age, stroke type, and stroke severity. Results— In total, 3854 incident stroke cases (n=2039 women, 53%) were identified during the study period. Demographic and socio-economic characteristics and primary healthcare access indicators were significantly different among the 4 residence categories. Patterns of risk factors, stroke type, and severity were comparable among residence categories in both sexes. Age-standardized stroke rates varied from 2.90 per thousand (95% CI, 2.59–3.21) in suburbs to 3.35 (95% CI, 2.98–3.73) in rural areas for men, and from 2.14 (95% CI, 2.00–2.28) in town centers to 2.34 (95% CI, 2.12–2.57) in suburbs for women. Regression models suggested that among men, stroke incidence was significantly lower in suburbs than in town centers (incidence rate ratio =0.87; 95% CI, 0.77–0.99). Case fatality risk was comparable across urban categories but lower in rural patients (relative risk versus town centers: 0.76; 95% CI, 0.60–0.96). Conclusions— Stroke incidence was comparable, and the 30-day case fatality only slightly varied in the 4 residence categories despite widely different socio-demographic features covered by the Brest Stroke Registry.

scholarly journals Racial Differences in Mechanical Thrombectomy Utilization for Ischemic Stroke in the United States

2020 ◽  
Vol 30 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Charles Esenwa ◽  
Alain Lekoubou ◽  
Kinfe G. Bishu ◽  
Kemar Small ◽  
Ava Liberman ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Racial Differences ◽  
Population Sample ◽  
Standard Of Care ◽  
Stroke Care ◽  
The United States ◽  
Vessel Occlusion ◽  
Stroke Treatment ◽  
Nationally Representative ◽  
Adjusted Model

Background: Compared with non-Hispanic Whites (NHW), racial-ethnic minorities bear a disproportionate burden of stroke and receive fewer evidence-based stroke care processes and treatments. Since 2015, me­chanical thrombectomy (MT) has become standard of care for acute ischemic stroke (AIS) patients with proximal anterior circula­tion large vessel occlusion (LVO).Objectives: Our objectives were to: assess recent trends in nationwide MT utilization among patients with AIS; determine if there were racial differences; and identify what factors were associated with such differ­ences.Methods: We performed a retrospective cohort study using nationally representative data of a non-institutionalized population sample from 2006 to 2014 obtained from the Nationwide Inpatient Sample (NIS). We identified a total of 889,309 observations of AIS, of which there were 5,256 MT observa­tions.Results: In the fully adjusted model, rate of thrombectomy utilization was significantly lower in African Americans (AA) (OR .67, CI .58-.76, P<.001) compared with NHW and Hispanics (OR .94, CI .78-1.13, P=.5).Conclusion: We found a significant dispar­ity in MT utilization for AA compared with NHW and Hispanics. More work is needed to understand the drivers of this racial disparity in stroke treatment. Ethn Dis. 2020;30(1):91-96; doi:10.18865/ed.30.1.91

scholarly journals Consistent declining trends in stroke mortality in Brazil: mission accomplished?

2016 ◽  
Vol 74 (5) ◽  
pp. 376-381 ◽  
Author(s):  
Valéria M. A. Passos ◽  
Lenice H. Ishitani ◽  
Glaura C. Franco ◽  
Gustavo C. Lana ◽  
Daisy M. X. Abreu ◽  
...  
Keyword(s):  
State Space Model ◽  
Case Fatality ◽  
Stroke Mortality ◽  
Correct Interpretation ◽  
Mortality Trends ◽  
Stroke Incidence ◽  
Space Model ◽  
Steady Decrease ◽  
Northern Regions ◽  
Mortality Estimates

ABSTRACT Stroke mortality rates are declining in Brazil, but diferences among regions need to be better investigated. The age-adjusted stroke mortality trends among adults (30-69 years-old) from Brazilian regions were studied between 1996 and 2011. Method Data were analyzed after: 1) reallocation of deaths with non-registered sex or age; 2) redistribution of garbage codes and 3) underreporting correction. A linear regression model with autoregressive errors and a state space model were fitted to the data, aiming the estimation of annual trends at every point in time. Results Although there were high values, a steady decrease of rates was observed. The decreasing trends among all regions were statistically significant, with higher values of decline among the Northeast and Northern regions, where rates were the highest. Conclusion Standardized methodology use is mandatory for correct interpretation of mortality estimates. Although declining, rates are still extremely high and efforts must be made towards prevention of stroke incidence, reduction of case-fatality rates and prevention of sequelae.

scholarly journals Electrocardiographic ST-T Abnormities Are Associated With Stroke Risk in the REGARDS Study

Stroke ◽  
2020 ◽  
Vol 51 (4) ◽  
pp. 1100-1106
Author(s):  
Mitsuaki Sawano ◽  
Ya Yuan ◽  
Shun Kohsaka ◽  
Taku Inohara ◽  
Takeki Suzuki ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Racial Differences ◽  
Stroke Risk ◽  
Proportional Hazards ◽  
The United States ◽  
Incidence Rates ◽  
Cox Proportional Hazards ◽  
Hazard Ratio ◽  
Common Finding ◽  
Increased Risk

Background and Purpose— In previous studies, isolated nonspecific ST-segment and T-wave abnormalities (NSSTTAs), a common finding on ECGs, were associated with greater risk for incident coronary artery disease. Their association with incident stroke remains unclear. Methods— The REGARDS (Reasons for Geographic and Racial Differences in Stroke) study is a population-based, longitudinal study of 30 239 white and black adults enrolled from 2003 to 2007 in the United States. NSSTTAs were defined from baseline ECG using the standards of Minnesota ECG Classification (Minnesota codes 4-3, 4-4, 5-3, or 5-4). Participants with prior stroke, coronary heart disease, and major and minor ECG abnormalities other than NSSTTAs were excluded from analysis. Multivariable Cox proportional hazards regression was used to examine calculate hazard ratios of incident ischemic stroke by presence of baseline NSSTTAs. Results— Among 14 077 participants, 3111 (22.1%) had NSSTTAs at baseline. With a median of 9.6 years follow-up, 106 (3.4%) with NSSTTAs had ischemic stroke compared with 258 (2.4%) without NSSTTAs. The age-adjusted incidence rates (per 1000 person-years) of stroke were 2.93 in those with NSSTTAs and 2.19 in those without them. Adjusting for baseline age, sex, race, geographic location, and education level, isolated NSSTTAs were associated with a 32% higher risk of ischemic stroke (hazard ratio, 1.32 [95% CI, 1.05–1.67]). With additional adjustment for stroke risk factors, the risk of stroke was increased 27% (hazard ratio, 1.27 [95% CI, 1.00–1.62]) and did not differ by age, race, or sex. Conclusions— Presence of NSSTTAs in persons with an otherwise normal ECG was associated with a 27% increased risk of future ischemic stroke.

scholarly journals Racial disparities in COVID-19 mortality are driven by unequal infection risks.

2020 ◽  
Author(s):  
Jon Zelner ◽  
Rob Trangucci ◽  
Ramya Naraharisetti ◽  
Alex Cao ◽  
Ryan Malosh ◽  
...  
Keyword(s):  
Racial Disparities ◽  
Data Science ◽  
Age Groups ◽  
Case Fatality ◽  
The United States ◽  
Mortality Rates ◽  
Bayesian Regression ◽  
Mortality Data ◽  
Incidence And Mortality ◽  
The U.S

Background. As of August 5, 2020, there were more than 4.8M confirmed and probable cases and 159K deaths attributable to SARS-CoV-2 in the United States, with these numbers undoubtedly reflecting a significant underestimate of the true toll. Geographic, racial-ethnic, age and socioeconomic disparities in exposure and mortality are key features of the first and second wave of the U.S. COVID-19 epidemic. Methods. We used individual-level COVID-19 incidence and mortality data from the U.S. state of Michigan to estimate age-specific incidence and mortality rates by race/ethnic group. Data were analyzed using hierarchical Bayesian regression models, and model results were validated using posterior predictive checks. Findings. In crude and age-standardized analyses we found rates of incidence and mortality more than twice as high than Whites for all groups other than Native Americans. Of these, Blacks experienced the greatest burden of confirmed and probable COVID-19 infection (Age- standardized incidence = 1,644/100,000 population) and mortality (age-standardized mortality rate 251/100,000). These rates reflect large disparities, as Blacks experienced age-standardized incidence and mortality rates 5.6 (95% CI = 5.5, 5.7) and 6.9 (6.5, 7.3) times higher than Whites, respectively. We also found that the bulk of the disparity in mortality between Blacks and Whites is driven by dramatically higher rates of COVID-19 infection across all age groups, particularly among older adults, rather than age-specific variation in case-fatality rates. Interpretation. This work suggests that well-documented racial disparities in COVID-19 mortality in hard-hit settings, such as the U.S. state of Michigan, are driven primarily by variation in household, community and workplace exposure rather than case-fatality rates. Funding. This work was supported by a COVID-PODS grant from the Michigan Institute for Data Science (MIDAS) at the University of Michigan. The funding source had no role in the preparation of this manuscript.

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