Technical Appendix for 1992 COMPUTATION OF RATES AND OTHER MEASURES Population bases The population bases from which death rates shown in this report are computed are prepared by the U.S. Bureau of the Census. Rates for 1940, 1950, 1960, 1970, 1980, and 1990 are based on the population enumerated as of April 1 in the censuses for those years. Rates for all other years use the estimated midyear (July 1) population. Death rates for the United States, individual States, and metropolitan areas are based on the total resident populations of the respective areas. Except as noted, these populations exclude the Armed Forces abroad but include the Armed Forces stationed in each area. The resident populations of the birth- and death-registration States for 1900-32, and of the United States for 1900-92, are shown in table 7-1. In addition, the population including Armed Forces abroad is shown for the United States. Table F lists the sources for these populations. Population for 1992--The population of the United States estimated by age, race, and sex for 1992 is shown in table 7-2, and the population for each State by broad age groups follows in table 7-3. The 1992 estimates are comparable with those for 1991 and 1990. Population for 1990--In the 1980 and 1990 censuses, a substantial number of persons did not specify a racial group that could be classified as any of the white, black, American Indian, Eskimo, Aleut, Asian, or Pacific Islander categories on the census form (41). In 1980 the number of persons of "Other" race was 6,758,319; in 1990, it was 9,804,847. In both censuses the large majority of these persons were of Hispanic origin (based on response to a separate question on the form), and many wrote in their Hispanic origin, or Hispanic origin type (for example, Mexican and Puerto Rican) as their race. In 1980 and 1990 persons of unspecified race were allocated to one of the four tabulated racial groups (white, black, American Indian, Asian, or Pacific Islander) based on their response to the Hispanic origin question. These four race categories conform with OMB Directive 15 and are more consistent with the race categories in vital statistics. In 1980 the allocation of unspecified race was determined using cross-tabulations of age, sex, race, type of Hispanic origin, and county of residence. Persons of Hispanic origin and unspecified race were allocated to either white or black based on their Hispanic origin type. Persons of "Other" race and Mexican origin were categorically assumed to be white, while persons in other Hispanic categories were distributed to white and black pro rata within the county-age-sex group. For "Other-race- not-specified" persons who were not Hispanic, race was allocated to white, black, or Asian and Pacific Islander based on proportions gleaned from sample data. The 20-percent sample (respondents who were enumerated on the longer census form) provided a highly detailed coding of race, which allowed identification of otherwise unidentifiable responses with a specified race category. Thus, allocation proportions were established at the State level and were used to distribute the non-Hispanic persons of "Other" race in the 100-percent tabulations. In 1990 the race modification procedure was implemented using individual census records. Persons whose race could not be specified - 1 - were assigned to a racial category using a pool of "race donors" that consisted of persons of specified race who had the identical responses to the Hispanic origin question and who were within the auspices of the same census district office. As in the 1980 census, it appeared that the underlying assumption made in the 1990 census was that the Hispanic origin response was the major criterion for allocating race. Unlike those responding to the 1980 census who could be assigned only to the racial groups white or black, persons of Hispanic origin, including Mexican, responding to the 1990 census could be assigned to any racial group. Also, in the 1990 census, the non-Hispanic component of "Other" race was allocated primarily on the basis of geography (district office), rather than detailed characteristic. The means by which respondent's age was determined were fundamentally different for the two censuses; therefore, the problems that necessitated the modification were different. In 1980, respondents reported year of birth and quarter of birth (within year) on the census form. When census results were tabulated, persons born in the first quarter of the year (before April 1) had age equal to 1980 minus year of birth, while persons born in the last three quarters had age equal 1979 minus year of birth. In 1990 quarter year of birth was not reported on the census form, so direct determination of age from year of birth was not possible. In 1990 census publications, age is based on respondents' direct reports of age at last birthday. This definition proved inadequate for postcensal estimates as it was apparent that many respondents had reported their age at time of either completion of the census form or interview by an enumerator that could occur several months after the April 1 reference data. As a result, age was biased upward. For most respondents, modification was based on a respecification of age, by year of birth, with allocation to first quarter (persons aged 1990 minus year of birth) and last three quarters (aged 1989 minus year of birth) based on a historical series of registered births by month. This process partially restored the 1980 logic for assignment of age. It was not considered necessary to correct for age overstatement and heaping in 1990, because the availability of age and year of birth on the census form had provided for the elimination of spurious year-of-birth reports in the census data before modification occurred. Population estimates for 1981-89--Death rates in this volume for 1981-89 are based on revised populations that are consistent with the 1990 census level (41). They are, therefore, not comparable with death rates published in Vital Statistics of the United States for 1981-89, and in other NCHS publications for those years. The 1990 census counted approximately 1.5 million fewer persons than had been estimated earlier for April 1, 1990. Populations for 1980--The population of the United States by age, race, and sex, and the population for each State are shown in tables 7-2 and 7-3 of Vital Statistics of the United States, 1980. The figures by race have been modified as described. Population estimates for 1971-79--Death rates in this volume for 1971-79 used revised population estimates that are consistent with the 1980 census levels. The 1980 census enumerated approximately 5.5 million more persons than had been estimated for April 1, 1980 (42). These revised estimates for the United States by age, race, and sex are published by the U.S. Bureau of the Census in Current Population Reports, Series P-25, Number 917. Unpublished revised estimates for - 2 - States were obtained from the U.S. Bureau of the Census. For Puerto Rico, the Virgin Islands, and Guam, revised estimates are published in Current Population Reports, Series P-25, Number 919. Population estimates for 1961-69--Death rates in this volume for 1961-69 are based on revised estimates of the population and thus may differ slightly from rates published before 1976. The rates shown in tables 1-1 and 1-2, the life table values in table 6-5, and the population estimates in table 7-1 for each year during 1961-69 have been revised to reflect modified population bases as published in the U.S. Bureau of the Census, Current Population Reports, Series P-25, Number 519. The data shown in table 1-10 for 1961-69 have not been revised. Rates and ratios based on live births--Infant and maternal mortality rates and fetal death and perinatal mortality ratios are computed on the basis of the number of live births. Fetal death and perinatal mortality rates are computed on the basis of the number of live births and fetal deaths. Counts of live births are published annually in Vital Statistics of the United States, Volume I, Natality. New Jersey--As previously indicated, data by race are not available for New Jersey for 1962 and 1963. Therefore, for 1962 and 1963 NCHS estimated a population by age, race, and sex that excluded New Jersey for rates shown by race. The methodology used to estimate the revised population excluding New Jersey is discussed in the Technical Appendixes of the 1962 and 1963 volumes. Net census undercount Errors can be introduced into the annual rates as a result of underenumeration of deaths and the misreporting of demographic characteristics. Errors in rates can also result from enumeration errors in the latest decennial census. This is because annual population estimates for the postcensal interval, which are used in the denominator for calculating death rates, are computed using the decennial census count as a base (41). Net census undercount results from the miscounting and misreporting of demographic characteristics such as age. Age-specific death rates are affected by the net census undercount and the misreporting of age on the death certificate (43). To the extent that the net undercount is substantial and that it varies among subgroups and geographic areas, it may have important consequences for vital statistics measures. Because death rates based on a population adjusted for net census undercount may be more accurate than rates based on an unadjusted population, the possible impact of net census undercount on death rates must be considered. This can be done on a national basis using results of studies conducted by the U.S. Bureau of the Census on the completeness of coverage of the U.S. population (including underenumeration and misstatement of age, race, and sex). Such studies were conducted in the last five decennial censuses--1950, 1960, 1970, 1980, and 1990. From this work have come estimates of the national population that were not counted by age, race, and sex (44-47). The reports for 1990 (unpublished data from the U.S. Bureau of the Census) include estimates of net underenumeration and overenumeration for age, sex, and racial subgroups of the national population - 3 - modified for race consistency with previous population counts as described in the section "Population Bases." These studies indicate that, although coverage was improved over previous censuses, there was differential coverage among the population subgroups; that is, some age, race, and sex groups were more completely counted than others. Because estimates of net census undercount are not available by age, race, and sex for individual States and counties, it is not feasible to adjust for net census undercount when presenting rates in routine tabulations. Nevertheless, it is important to be aware that net census undercounts can affect levels of observed vital rates. Age, race, and sex--If adjustments were made for net census undercount, the size of denominators of the death rates generally would increase and the rates, therefore, would decrease. The adjusted rates for 1992 can be computed by multiplying the reported rates by ratios of the census-level resident population to the resident population adjusted for the estimated net census undercount (table 7-4). A ratio of less than 1.0 indicates a net census undercount and, when applied, results in a corresponding decrease in the death rate. A ratio greater than 1.0--indicates a net census overcount--when multiplied by the reported rate results in an increase in the death rate. Coverage ratios for all ages show that, in general, females were more completely enumerated than males and the white population more completely enumerated than the black population in the 1990 Census of Population. Underenumeration varied by age group for the total population, with the greatest differences found for persons aged 85 years and over. All other age groups were overcounted or undercounted by less than 4.0 percent. Among the age-sex-race groups, underenumeration was highest (13.3 percent) for black males aged 25-34 years. In contrast, white females in this age group were underenumerated by 2.5 percent. If vital statistics measures were calculated with adjustments for net census undercounts for each population subgroup, the resulting rates would be differentially reduced from their original levels; that is, rates for those groups with the greatest estimated undercounts would show the greatest relative reductions due to these adjustments. Similar effects would be evident in the opposite direction for groups with overcounts. Consequently, the ratio of mortality between the rates for males and females and between the rates for the white population and the black population usually would be reduced. Similarly, the differences between the death rates among subgroups of the population by cause of death would be affected by adjustments for net census undercounts. For example, in 1990 for the age group 35-39 years, the ratio of the unadjusted death rate for Homicide and legal intervention for black males to that for white males is 7.54, whereas the ratio of the death rates adjusted for net census undercount is 6.92. For Ischemic heart disease for males aged 40-44 years, the ratio of the death rate for the black population to that for the white population is 1.38 using the unadjusted rates, but it is 1.26 when adjusted for estimated underenumeration. Summary measures--The effect of net census undercount on age-adjusted death rates and life table values depends on the underenumeration of each age group and on the distribution of deaths by age. Thus, the age-adjusted death rate in 1990 for All causes would decrease from 520.2 to 512.7 per 100,000 population if the age-specific death rates were corrected for net - 4 - census undercount (table G). For Diseases of the heart, the age-adjusted death rate for white males would decrease from 202.0 to 198.2 per 100,000 population, a decline of 2.0 percent. For black males, the change from an unadjusted rate of 275.9 to an adjusted rate of 256.7 would amount to a decrease of 7.0 percent. For HIV infection, the rate for black males would decrease from 44.2 to 39.0 and for white males from 15.0 to 14.4. Table G. Age-adjusted death rates for selected causes, by race and sex, unadjusted and adjusted for estimated net census undercount: United States, 1990 [Based on age-specific death rates per 100,000 population in specified group. Age-adjusted death rates per 100,000 U.S. standard million population. Numbers after causes of death are category numbers of the Ninth Revision, International Classification of Diseases, 1975. For explanation of asterisks, see "Cause of Death."] Malignant neoplasms Human including neoplasms immunodeficiency of lymphatic and Race, sex, and adjustment All virus infection hematopoietic for net census undercount causes (*042-*044) tissues (140-208) All Races, Both Sexes Unadjusted 520.2 9.8 135.0 Adjusted 512.7 9.6 133.3 Male Unadjusted 680.2 17.7 166.3 Adjusted 664.3 17.0 162.4 Female Unadjusted 390.6 2.1 112.7 Adjusted 387.9 2.1 112.6 White, Both Sexes Unadjusted 492.8 8.0 131.5 Adjusted 485.9 7.8 129.9 Male Unadjusted 644.3 15.0 160.3 Adjusted 631.0 14.4 156.9 Female Unadjusted 369.9 1.1 111.2 Adjusted 367.0 1.0 110.8 Black, Both Sexes Unadjusted 789.2 25.7 182.0 Adjusted 760.0 23.9 177.0 Male Unadjusted 1,061.3 44.2 248.1 Adjusted 980.8 39.0 230.9 Female Unadjusted 581.6 9.9 137.2 Adjusted 579.4 9.7 138.4 - 5 - Table G (cont'd). Age-adjusted death rates for selected causes, by race and sex, unadjusted and adjusted for estimated net census undercount: United States, 1990 [Based on age-specific death rates per 100,000 population in specified group. Age-adjusted death rates per 100,000 U.S. standard million population. Numbers after causes of death are category numbers of the Ninth Revision, International Classification of Diseases, 1975. For explanation of asterisks, see "Cause of Death."] Cerbro- Homicide Race, sex, and Diabetes Diseases of vascular and legal adjustment for net mellitus heart (390-398, diseases intervention census undercount (250) 402, 404-429) (430-438) (E960-E978) All Races, Both Sexes Unadjusted 11.7 152.0 27.7 10.2 Adjusted 11.5 149.9 27.3 10.1 Male Unadjusted 12.3 206.7 30.2 16.3 Adjusted 12.1 202.1 29.6 15.9 Female Unadjusted 11.1 108.9 25.7 4.2 Adjusted 11.0 107.9 25.4 4.2 White, Both Sexes Unadjusted 10.4 146.9 25.5 5.9 Adjusted 10.2 145.0 25.2 5.7 Male Unadjusted 11.3 202.0 27.7 8.9 Adjusted 11.1 198.2 27.3 8.7 Female Unadjusted 9.5 103.1 23.8 2.8 Adjusted 9.5 102.2 23.5 2.7 Black, Both Sexes Unadjusted 24.8 213.5 48.4 39.5 Adjusted 24.1 207.2 46.9 37.4 Male Unadjusted 23.6 275.9 56.1 68.7 Adjusted 21.9 256.7 52.3 62.9 Female Unadjusted 25.4 168.1 42.7 13.0 Adjusted 25.7 168.2 42.7 12.7 If death rates by age were adjusted, the corresponding life expectancy at birth computed from these rates would change. When calculating life expectancy, the impact of an undercount or overcount is greatest at the younger ages. In general, the effect of correcting the death rates is to increase the estimate of life expectancy at birth. For example, adjustment for net census undercount would increase life expectancy in 1990 by an estimated 0.2 years, from 75.4 years to 75.6 years for the total U.S. population. - 6 - Adjustment for differential underenumeration among race-sex groups would lead to greater changes in life expectancy for some groups than for others. For males and females, increases would be 0.3 and 0.1 years, respectively; for the black population and white population, 0.6 and 0.2 years, respectively. The largest increase would be for black males, 1.2 years, followed by white males (0.3 years), black females (0.2 years), and white females (0.2 years). Age-adjusted death rates Age-adjusted death rates are used to compare relative mortality risk across groups and over time. However, they should be viewed as constructs or indexes rather than as direct or actual measures of mortality risk. Statistically, they are weighted averages of the age-specific death rates, where the weights represent the fixed population proportions by age (48). The age-adjusted death rates presented in this volume were computed by the direct method, that is, by applying age-specific death rates for a given cause of death to the U.S. standard million population (relative age distribution of 1940 enumerated population of the United States totaling 1,000,000 (26)). By using the same standard population, the rates for the total population and for each race-sex group were adjusted separately. It is important not to compare age-adjusted death rates with crude rates. The U.S. standard million population is as follows: Age Number All ages............................... 1,000,000 Under 1 year............................ 15,343 1-4 years............................... 64,718 5-14 years.............................. 170,355 15-24 years............................. 181,677 25-34 years............................. 162,066 35-44 years............................. 139,237 45-54 years............................. 117,811 55-64 years............................. 80,294 65-74 years............................. 48,426 75-84 years............................. 17,303 85 years and over....................... 2,770 Life Tables U.S. abridged life tables are constructed by reference to a standard table (49). Life tables for the decennial period 1979-81 are used as the standard life tables in constructing the 1980-92 abridged life tables. Life table values for 1981-89 appearing in this volume are based on revised intercensal estimates of the populations for those years. Therefore, these life table values may differ from life table values of those years published in previous volumes. Life tables for the decennial period 1969-71 are used as the standard life tables in constructing the 1970-79 abridged life tables. Life table values for 1970-73 were first revised in Vital Statistics of the United States, 1977; before 1977, life table values for 1970-73 - 7 - were constructed using the 1959-61 decennial life tables. In addition, life table values for 1951-59, 1961-69, and 1971-79 appearing in this volume are based on revised intercensal estimates of the populations for those years. As such, these life table values may differ from life table values for those years published in previous volumes. There has been an increasing interest in data on the average length of life (øe0) for single calendar years before the initiation of the annual abridged life table series for selected race-sex groups in 1945. The figures in table 6-5 for the race and sex groups for the following years were estimated to meet these needs (50). Years Race and sex groups 1900-45.................................... Total 1900-47.................................... Male 1900-47.................................... Female 1900-50.................................... White 1900-44.................................... White, male 1900-44.................................... White, female 1900-50.................................... All other 1900-44.................................... All other, male 1900-44.................................... All other, female The geographic areas covered in life tables before 1929-31 were limited to the death-registration areas. Life tables for 1900-02 and 1909-11 were constructed using mortality data from the 1900 death-registration States--10 States and the District of Columbia--and for 1919-21 from the 1920 death-registration States--34 States and the District of Columbia. The tables for 1929-31 through 1958 cover the conterminous United States. Decennial life table values for the 3-year period 1959-61 were derived from data that include Alaska and Hawaii for each year (table 6-4). Data for each year shown in table 6-5 include Alaska beginning in 1959 and Hawaii beginning in 1960. It is believed that the inclusion of these two States does not materially affect life table values. Random variation in numbers of deaths, death rates, and mortality rates and ratios Deaths and population-based rates--Except for those reported in 1972, the numbers of deaths reported for a community represent complete counts of such events. As such, they are not subject to sampling error, although they are subject to errors in the registration process. However, when the figures are used for analytical purposes, such as the comparison of rates over a period or for different areas, the number of events that actually occurred may be considered as one of a large series of possible results that could have arisen under the same circumstances (51). The probable range of values may be estimated from the actual figures according to certain statistical assumptions. - 8 - In general, distributions of vital events may be assumed to follow the binomial distribution. Estimates of standard error and tests of significance under this assumption are described in most standard statistics texts. When the number of events is large, the standard error, expressed as a percent of the number or rate, is usually small. When the number of events is small (perhaps less than 100) and the probability of such an event is small, considerable caution must be observed in interpreting the conditions described by the figures. This is particularly true for infant mortality rates, cause-specific death rates, and death rates for counties. Events of a rare nature may be assumed to follow a Poisson probability distribution. For this distribution, a simple approximation may be used to estimate a confidence interval, as follows. If N is the number of registered deaths in the population and R is the corresponding rate, the chance is 19 in 20 that 1. N - 2ûN and N + 2ûN covers the "true" number of events. 2. R - 2(R/ûN) and R + 2(R/ûN) covers the "true" rate. If the rate R1 corresponding to N1 events is compared with the rate R2 corresponding to N2 events, the difference between the two rates may be regarded as statistically significant at the 0.05 level of significance, if it exceeds 2 x [û of (R1 squared/N1 + R2 squared/N2)] For example, if the observed death rate for a community were 10.0 per 1,000 population and if this rate were based on 20 recorded deaths, the chance is 19 in 20 that the "true" death rate for that community lies between 5.5 and 14.5 per 1,000 population. If the death rate for this community of 10.0 per 1,000 population were being compared with a rate of 15.0 per 1,000 population for a second community, which is based on 25 recorded deaths, the difference between the rates for the two communities is 5.0. This difference is less than twice the standard error of the difference 2 x [û of (10.0 squared/20 + 15.0 squared/25)] of the two rates, which is computed to be 7.5. From this it is concluded that the difference between the rates for the two communities is not statistically significant at the 0.05 level of significance. Rates, proportions, and ratios--Beginning in 1989 an asterisk is shown in place of a rate based on fewer than 20 deaths. These rates have a relative standard error of 23 percent or more and therefore are considered highly variable. For age-adjusted death rates, this criterion is applied to the sum of the age-specific deaths. - 9 -