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(Stroke. 1996;27:1055-1059.)
© 1996 American Heart Association, Inc.

Articles

Comparison of Additive and Multiplicative Models of Regional Variation in the Decline of Stroke Mortality in the United States

Douglas J. Lanska, MD, MS Patrick M. Peterson, PhD

From the Departments of Neurology, Preventive Medicine and Environmental Health, and Statistics, and the Sanders Brown Center on Aging, University of Kentucky Medical Center, Lexington, and the Neurology Service, Veterans Affairs Medical Center, Lexington, Ky.

Correspondence to Douglas J. Lanska, MD, Department of Neurology, Rm L412, Kentucky Clinic, University of Kentucky, Lexington, KY 40536-0284.

	Abstract

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Background and Purpose Although previous studies have shown that geographic variation in the decline of stroke mortality rates may be an important contributor to the changing geographic distribution of stroke mortality in the United States, some concern has been raised that this phenomenon may be model dependent. This study examines the geographic variation in the decline of stroke mortality rates in the United States with the use of both additive and multiplicative models.

Methods National Center for Health Statistics and Bureau of the Census data were used to assess regional-level temporal trends of underlying-cause stroke mortality rates in the United States for 1979 through 1989. Both additive and multiplicative models were fit to the data.

Results Underlying-cause stroke mortality rates have declined fairly steadily in all regions of the United States and for all race-sex groups, although there was significant regional variation in the rate of decline during the period 1979 through 1989. The South, which initially had the highest rates, had the most rapid decline for all race-sex groups when either additive or multiplicative models were used.

Conclusions From 1979 through 1989 there was significant geographic variation in the rate of decline of stroke mortality rates, with the most rapid rates of decline in the South. As a result, there has been a decrease in interregional variation in stroke mortality rates.

Key Words: cerebrovascular disorders • epidemiology • mortality • risk factors

	Introduction

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Since at least 1940 there has been a consistent pattern of marked geographic variation in stroke mortality rates within the United States.^{1 2 3 4} Very high rates are reported in the southeast, particularly along the coastal plain, whereas very low rates are reported in the Mountain census division.^{1 2 3 4} These general patterns of geographic variation have been observed for both sexes and for whites and nonwhites, although stroke rates have been consistently declining in all geographic areas of the continental United States over this interval.¹

Recently, there has been some indication that the dense concentration of excess stroke mortality in the southeastern United States is dissipating.^{1 5 6 7} With the overall decline in stroke mortality rates, there has been a convergence (decrease in variability) of age-adjusted state stroke mortality rates overall and within the various race-sex groups.^{1 6 7} In addition, at the level of state economic areas, the dense concentration of excess stroke mortality along the South Atlantic coastal plain has dissipated considerably since the early 1960s.^{5 6}

Although geographic variation in the decline of stroke mortality rates may be an important contributor to the changing geographic distribution of stroke mortality in the United States,⁷ some concern has been raised that this phenomenon may be model dependent.⁸ The present study evaluates the geographic variation in the decline of regional stroke mortality rates with the use of both additive and multiplicative models.

	Methods

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Data on deaths with cerebrovascular disease listed as an underlying or contributing cause of death were obtained from public-use, multiple-cause-of-death, machine-readable, United States mortality data files created by the National Center for Health Statistics.^{9 10 11} Data were analyzed for the period 1979 through 1989 for the contiguous United States. Variables used included the following: age, race, sex, region of residence at death, underlying cause of death, and contributing causes of death. Stroke deaths were defined as those coded to rubrics 430 through 438, with the use of either the International Classification of Diseases Adapted for Use in the United States, 8th Revision (ICDA-8), for 1970 through 1978,¹² or the International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9-CM), for 1979 to 1989.¹³

Population data tabulated by state, race, sex, and age were obtained from published data of the US Bureau of the Census for 1970, based on the population enumerated as of April 1. The racial classification used for data collected in the 1980 and 1990 censuses, however, differs from the racial classification used for vital statistics data and for data from previous censuses. To maintain comparability with the racial designations used in the vital statistics mortality data, we used Census Bureau modified-race estimates of the 1980 and 1990 US population by age, race, and sex.^{14 15 16 17 18 19}

Since the Census Bureau has no state- or regional-level intercensal estimates based on age, sex, and race (personal communication, US Bureau of the Census, 1996), population data for intercensal years were estimated by linear interpolation from decennial census data for each population group. Most of the fluctuation in intercensal estimates is due to changes in births and labor-force migration. For the population older than age 55, ie, the population most susceptible to stroke, significant deviations of age-, race-, sex-, and region-specific intercensal population estimates from the actual (unmeasured) values are unlikely (personal communication, US Bureau of the Census, 1996).

Age-, race-, and sex-specific rates were calculated by region for deaths with stroke listed as the underlying cause of death (underlying-cause rates). The states in each region are listed in the Appendix. Annual age-adjusted stroke mortality rates (per 100 000 population) by race and race-sex groups were computed by the direct method, that is, by applying the age-specific death rates for stroke to the standard population distributed by age. The reference population used was the total US population enumerated on April 1, 1980.

Two different models were fitted to the annual age-adjusted stroke mortality rates. A linear or additive model was fit by linear regression of stroke mortality rates on calendar year, ie, rate=ßyear+.^{20 21} The average annual rate of change in regional or state age-adjusted stroke mortality rates was measured as the slope of the regression of these rates on year. An exponential decay or multiplicative model (ie, rate=e^ßyear) was fit by linear regression of ln-transformed rates on calendar year, since rate=e^ßyear is equivalent to ln(rate)=ßyear+'.^{20 21} The average annual percent change in regional age-adjusted stroke mortality rates was measured as a function of the slope of the regression of ln-transformed rates on year [average annual percent change=100(1-e^ß)]. With both models, comparison of slopes between regions was achieved by considering an expanded linear model with either the mortality rates or ln-transformed mortality rates as a function of both year and region. A significant interaction effect between year and region indicates a significant difference in absolute change or percent change across regions. Goodness of fit of the models was assessed with the use of the square of the sample correlation coefficient (r²), which may be interpreted as the proportion of total variability in the dependent or response variable that is explained by the independent or explanatory variable.²⁰

	Results

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
Underlying-cause stroke mortality rates have declined fairly steadily in all regions of the United States and for all race-sex groups (Figure). However, there has been significant regional variation in the rate of decline, with the South having consistently both the most rapid average annual declines in rates and the most rapid average annual percentage declines in rates (Figure, and Tables 1 and 2). In 1979 the South had the highest rates for all race-sex groups, but among whites there was a crossover of trend lines due to the more rapid decline in the South so that by 1989 the South no longer had the highest rates. In all of the race-sex groups there was a decrease in interregional variation in stroke mortality rates over the study period.

View larger version (25K): [in this window] [in a new window]   Figure 1. Graph of annual underlying-cause stroke mortality rates (per 100 000 population), by region and race-sex group for the United States for 1979 through 1989. As illustrated, rates declined steadily in all regions of the United States and for all race-gender groups. However, there was significant regional variation in initial rates and in the rate of decline, with the South having initially the highest rates but also the most rapid decline, so that by 1989 the South no longer had the highest rates. In all of the race-gender groups there was a decrease in interregional variation in stroke mortality rates over the study period.

View this table: [in this window] [in a new window]   Table 1. Average Annual Rate of Decline in Underlying-Cause Stroke Mortality Rates1 (Stroke Deaths/100,000 Population/Y2) Derived From Additive Models for the United States During 1979-1989, by Region and Race-Sex Group

View this table: [in this window] [in a new window]   Table 2. Average Annual Percent Decline in Underlying-Cause Stroke Mortality Rates Derived From Multiplicative Models for the United States During 1979-1989, by Region and Race-Sex Group

Both additive and multiplicative models generally fit the data extremely well (Table 3). The relationship between stroke rates and year was approximately linear within the study period; analyses of residuals in the additive models revealed no marked departures from linearity. Indeed, r² values for the additive models ranged from .927 to .975 for the various race-sex groups in the national models and from .904 to .981 for whites and .595 to .963 for blacks in the regional models. The relationship between ln-transformed stroke rates and year was also approximately linear within the study period; analyses of residuals in the multiplicative models revealed no marked departures from linearity. r² values for the multiplicative model ranged from .943 to .987 for the various race-sex groups in the national models and from .927 to .992 for whites and .581 to .971 for blacks in the regional models. The relatively poor fit for both models among blacks in the West reflects the erratic rates due to the small number of blacks in that region.

View this table: [in this window] [in a new window]   Table 3. Comparison of Goodness of Fit (r2) for Additive and Multiplicative Models of Decline in Underlying-Cause Stroke Mortality Rates in the United States for 1979-1989

	Discussion

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 
In this study we used US mortality data spanning two decades and the four census regions. The comparability of these statistics may be affected by differences in diagnostic and death-certification practices, systems for classifying causes of death, and procedures for selecting the underlying cause of death from among all listed causes. However, analyses by the National Center for Health Statistics indicate that stroke mortality data coded in the interval covered by this report are generally comparable, even though such data were coded with two different revisions of the ICD; dual coding of mortality data for ICD transition years produced virtually identical numbers of stroke deaths when either the ICD-8A or ICD-9-CM classification system was used.²² In addition, available data do not indicate significant regional variation in either diagnostic accuracy or death-certificate reporting of stroke.^{23 24}

Although the causes of the long-standing regional variation in stroke mortality in the United States are unknown, the nonrandom distribution of stroke mortality across the United States, the large magnitude of the difference between high and low rate areas, the persistence of the pattern over more than four decades, the similarity of the distribution for different race-sex groups, and the lack of delimitation by administrative or political boundaries suggest that the pattern of excess stroke mortality is not an artifact of different diagnostic and reporting practices.^{1 2 4 7} In addition, in the 1960s, national cooperative studies confirmed the apparent large differences in stroke mortality rates among geographic areas in the United States^{23 25} ; these large variations in mortality rates could not be explained by differences in certification practices (such as choice of underlying cause of death when multiple causes contributed to death), the frequency with which clinical stroke diagnoses were listed on the certificates, differences in the accuracy of the diagnosis of stroke, or variations in the standards of medical care.^{23 24 25 26 27} Furthermore, the large regional differences in stroke mortality parallel geographic differences in stroke incidence²⁸ and in hospital utilization rates for stroke.^{2 29}

The present results demonstrate that the regional heterogeneity of temporal changes in stroke mortality rates is not simply a function of the additive models initially used to help understand and interpret the regional trends.⁷ Without recourse to any modeling whatsoever, it is evident (see the Figure) that (1) stroke mortality rates have decreased for all regions and for all race-sex groups over the study period; (2) the magnitude of interregional differences has declined; and (3) while the South initially had the highest rates, the rates dropped most quickly in the South, and for whites crossed over other trend lines so that by 1989 the South no longer had the highest rates for white males or females. Moreover, both additive and multiplicative models are consistent in (1) providing extremely good fits to the data and (2) indicating that the South had the most rapid (absolute or relative) decline in stroke mortality rates during the study period.

The results of the present study support the previous suggestion^{5 6 7} that the long-standing excess of stroke mortality in the southeastern United States is beginning to dissipate. The South experienced the greatest declines in stroke mortality over the period from 1979 through 1989. Stroke mortality rates in the South now much more closely reflect the national experience than they did in previous decades. Although areas of very high stroke mortality rates still persist,^{1 2} they are becoming fewer and more isolated,^{5 6} especially when examined on a smaller geographic scale, and the magnitudes of the differences between high-rate areas and low-rate areas have lessened dramatically.^{1 7}

The results of the present study are not accounted for by regional variation in the diffusion of CT. While the advent of CT has significantly improved the diagnosis of stroke types,^{30 31 32} in some cases affecting trend estimates for individual types of stroke,³¹ the impact of this technology on aggregate stroke mortality estimates is probably small. In most cases, clinical diagnostic errors identified by CT were in the diagnosis of the stroke type rather than in recognition of the presence or absence of cerebrovascular disease³² ; correction of these diagnostic errors by use of CT did not result in significant changes in estimates of the number of individuals with a stroke of any type. Furthermore, the regional per capita availability of this and related MRI technology^{33 34 35 36} and regional trends in the use of CT³⁷ parallel neither the regional stroke mortality rates nor the regional rate of decline in stroke mortality rates.

	Acknowledgments

 
This project was supported in part by a Clinical Investigator Development Award from the National Institutes of Health (K08-NS01549-01 to Dr Lanska), by Research Advisory Group funding from the Office of Research and Development of the Department of Veterans Affairs (to Dr Lanska), and by the philanthropic support of Jayne Bolotin (to Dr Lanska).

	Appendix 1

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View this table: [in this window] [in a new window]   Table 4. States by Census Region for the Contiguous United States

Received October 9, 1995; revision received February 27, 1996; accepted February 27, 1996.

	References

Top Abstract Introduction Methods Results Discussion Appendix 1 References

 

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