# Healthy People Statistical Notes - Number 27 - CDC

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Healthy People Statistical Notes Number 27 February 2016 Measuring Progress Toward Target Attainment and the Elimination of Health Disparities in Healthy People 2020 by Makram Talih, Ph.D.; and David T. Huang, Ph.D., M.P.H., C.P.H., Office of Analysis and Epidemiology Abstract Introduction—Healthy People is “absolute value of the percent change both absolute and relative measures of an initiative of the U.S. Department from baseline” is used to measure overall disparity: a) the simple difference of Health and Human Services that movement. In addition, unlike in between the highest and lowest rates, provides science-based, 10-year national HP2010, both the extent of the movement irrespective of intermediate rates; b) the objectives for improving the health and its statistical significance (when ratio between the highest and lowest of all Americans. As in the previous measures of variability are available) rates, irrespective of intermediate rates; three decades, Healthy People 2020 are used to determine progress status in c) and a summary rate ratio between the (HP2020) has established overarching HP2020 (e.g., “improving,” “little or no best group rate and the average rate for goals and objectives, and is monitoring detectable change,” or “getting worse”). all other groups in a population domain. progress toward the attainment of its For objectives expressed in terms of Comparisons to the best group rate— targets as well as the elimination of adverse outcomes, the HP2010 “index As in HP2010, all groups composing health disparities among population of disparity” is obtained by subtracting 1 a population domain (e.g., race and groups. This Statistical Note discusses from the HP2020 summary rate ratio and ethnicity, education, or income) are the HP2020 measurement practices, multiplying by 100. compared to the group with the “best” contrasting them with those that were in (i.e., most favorable or least adverse) Conclusion—The multipronged place in Healthy People 2010 (HP2010) rate. However, HP2020 uses the ratio approach to measurement in HP2020 and highlighting their strengths and instead of the percent difference addresses some of the complex limitations. between the rates. In addition, HP2020 methodological issues and limitations Objective—This Statistical Note objectives that are expressed in terms of identified in the past decade as well as documents the HP2020 methodology favorable outcomes to be increased no elsewhere in the literature. for measuring progress toward target longer need to be re-expressed using the attainment and the elimination of health complementary adverse outcomes for disparities, with a particular focus on comparisons to the best group rate. Keywords: Healthy People objectives • methodological considerations for the measurement • population subgroups • Measures of overall health disparity— interpretation of findings. health equity In addition to detailed comparisons to Progress toward target attainment— the best group rate, HP2020 provides For HP2020, the “percent of targeted measures that quantify the degree of change achieved” still measures disparity overall across all groups movement of objectives that are moving composing a population domain. Unlike from their baselines toward their targets. in HP2010, where a single relative However, for objectives moving away measure, the summary index, was used, from their baselines and targets, the HP2020 uses three measures that include U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Disease Control and Prevention National Center for Health Statistics

Measurable objectives and targets Acknowledgments There are more than 1,200 objectives in HP2020 spanning 42 topic areas, including just over 1,000 that were measurable The following individuals and teams have either as of June 2015. Each measurable objective has a nationally contributed to the development of the Healthy People representative data source, baseline value, and target for 2020 (HP2020) measures presented in this report or specific improvements to be achieved by the year 2020. A provided feedback that improved the presentation: Robert few objectives have nationally representative data, yet they Francis, Jr. and the Health Promotion Statistics Branch are tracked only for informational purposes, so they do not (HPSB) programming team at NCHS; Jeffrey N. Pearcy and the HPSB research team; Carter R. Blakey, Deborah have 2020 targets. Just over 200 developmental objectives do Hoyer, and the Office of Disease Prevention and Health not have baseline data, yet they have a potential data source Promotion’s Community Strategies Division at the and are included in HP2020 to highlight their public health U.S. Department of Health and Human Services; and importance and are expected to become measurable over the Rebecca Hines, Richard J. Klein, and Diane M. Makuc course of the decade. (consultants). Prior to their potential inclusion in HP2020, objectives are drafted by subject matter experts from various federal agencies. The proposed objectives are made available for public comment and are reviewed by the Healthy People Introduction Federal Interagency Workgroup. All objectives are approved This Statistical Note describes the Healthy People 2020 by HHS before being added to the HP2020 initiative. (HP2020) methodology for measuring progress toward target Whenever possible, targets for the HP2020 objectives are attainment and the elimination of health disparities, with set using science-based methods, such as: a particular focus on methodological issues. The HP2020 ● Modeling measurement practices are contrasted with those in place for the Healthy People 2010 (HP2010) decade; see Statistical ● Projecting trends Note No. 25, Measuring Progress in Healthy People 2010 ● Knowledge of scientific findings and current interventions (1), as well as the Healthy People 2010 midcourse and final reviews (2,3). In the absence of adequate data, knowledge, or expertise, Healthy People is an initiative of the U.S. Department HP2020 targets generally are set using a projected 10% of Health and Human Services (HHS) that provides science- improvement relative to their baseline values. On a case-by based, 10-year national objectives for improving the health case basis, other target-setting methods are used as appropriate of all Americans. For three decades, Healthy People has (e.g., minimal statistical significance; total elimination; established benchmarks and monitored progress over time to maintaining baseline level; maintaining consistency with “encourage collaborations across communities and sectors, national programs, regulations, policies, or laws; or retention empower individuals toward making informed health of HP2010 targets). decisions, and measure impact of prevention activities”; see Complete information about HP2020, including the http://www.healthypeople.gov/2020/About-Healthy-People. initiative’s history, its overarching goals, and objectives, is Healthy People 2020, the fourth decade of the initiative, was available from http://www.healthypeople.gov. launched in December 2010. Population subgroups Overarching goals Measurable HP2020 objectives that are population-based The four overarching goals established for HP2020 are to: include data by demographic and socioeconomic categories, ● Attain high-quality, longer lives free of preventable where available. For example, Table 1 shows HP2020 disease, disability, injury, and premature death. demographic and socioeconomic categories used to tabulate national data from the National Health Interview Survey ● Achieve health equity, eliminate disparities, and improve (NHIS), which is the data source for over 100 measurable the health of all groups. population-based HP2020 objectives. ● Create social and physical environments that promote HP2020 strives for consistency in tracking population good health for all. groups; however, population categories may vary by data ● Promote quality of life, healthy development, and healthy source or by objective, due to survey design, data collection behaviors across all life stages. constraints, or other considerations. Therefore, HP2020 population categories used to tabulate national data from data 2 Healthy People 2020 Statistical Notes

Table 1. Main population categories for HP2020 objectives from the National Health Interview Survey Population categories Population categories Total Family income (percent of poverty threshold) Less than 100% Sex 100%–199% Female 200%–399% Male 400%–599% Race and ethnicity 600% and above American Indian or Alaska Native only Family type Asian only Single Native Hawaiian or Other Pacific Islander only Single parent with children Black or African American only Married couple or partners White only Two parent family with children Two or more races Other Hispanic or Latino Not Hispanic or Latino Country of birth Black or African American only, not Hispanic or Latino United States White only, not Hispanic or Latino Outside United States Age group (years) Disability status Under 18 Persons with activity limitations 0–4 Persons without activity limitations 5–11 12–17 Geographic location 18–44 Metropolitan 18–24 Nonmetropolitan 25–44 Health insurance status (persons under age 65) 45–64 Insured 45–54 Private 55–64 Public 65 and over Uninsured 65–74 75–84 Marital status (persons aged 18 and over) 85 and over Married Cohabiting partner Educational attainment (persons aged 25 and over) Divorced or separated Less than high school Widowed High school Never married Some college Associate’s degree NOTE: Additional population categories may be added as needed. Four-year college degree SOURCE: CDC/NCHS, HP2020 database. Advanced degree sources other than NHIS may differ from those listed in options are new for HP2020 (e.g., country of birth, family Table 1. type, and marital status). HP2020 population categories differ from those used in Several population categories may be limited to persons HP2010: of a specific age group (e.g., educational attainment, marital status, veteran status, and health insurance status). The age ● Education and income. Both education and income are groups that apply to these categories are specific to each included in HP2020 data tables when they are available. objective and may vary by data source. Caution must be In HP2010 data tables, only one of these variables used when comparing data for population categories that use typically was reported, even if the data source provided different age limits or when comparing to the total population. both. In addition, both education and income have a more granular disaggregation in HP2020 than that used in Data may be either unavailable or not collected for HP2010. population categories not shown in the HP2020 data tables. However, if the data for a population subgroup have been ● New category options in HP2020. A number of options collected and analyzed but do not meet the criteria for have been added to data tables in HP2020. Whereas some statistical reliability, data quality, or confidentiality, the data of these options were included in HP2010 when data were are suppressed and marked accordingly in the data tables. available (e.g., age, disability status, health insurance status, geographic location, and sexual orientation), other Detailed information about data suppression as well as additional considerations related to the demographic and Healthy People 2020 Statistical Notes 3

socioeconomic categories used in HP2020 are forthcoming need to make up the deficit from baseline in addition to the from: http://www.cdc.gov/nchs/healthy_people/hp2020/ desired targeted change once the baseline value is regained. hp2020_data_issues.htm. In HP2010, the amount and statistical significance of the “percent of targeted change achieved” were not considered in determining an objective’s progress status. For HP2020, Multipronged Measure of Progress both the extent of the movement and its statistical significance Toward HP2020 Targets (when measures of variability are available) are used to determine an objective’s progress status. Thus, in addition For HP2010 objectives that had at least two data points, to HP2020 objectives where the values at baseline and most the “percent of targeted change achieved” was used to recent data points are equal, those objectives with available quantify progress toward target attainment, unless the target standard errors for which movement was not statistically had been met or exceeded at baseline. The formula for the significant, and those with no available standard errors for “percent of targeted change achieved” was as follows: which movement was less than 10%, are all qualified as having demonstrated “little or no detectable” change. Percent of Most recent value – Baseline value targeted change = × 100. achieved HP2010 target – Baseline value Classification of objective progress status in HP2020 The “percent of targeted change achieved” expressed the difference between the baseline and the most recent value as a HP2020 objectives are classified according to the status percent of the targeted change between the baseline and the of their progress toward their targets or away from their HP2010 target. The “percent of targeted change achieved” baselines, as shown in Table 2. was used to compare how much of the targeted change was achieved for an objective relative to other HP2010 objectives. Determination of objective progress status For more information about the measurement of progress in HP2020 toward target attainment in HP2010, see Appendix I. As learned in the Healthy People 2010 Final Review (3), Objectives that met or exceeded their targets there are various limitations to using the “percent of targeted ● When the desired direction is increase, an objective has change achieved” as the sole measure of progress toward met or exceeded its target at the most recent data point if target attainment, some of which are listed here: most recent value ≥ HP2020 target. ● The “percent of targeted change achieved” is calculated ● When the desired direction is decrease, an objective has using only the target, baseline, and most recent data met or exceeded its target at the most recent data point if points. Fluctuations during the intervening years are not most recent value ≤ HP2020 target. considered. HP2020 objectives that met or exceeded their targets at ● The number of years between the baseline and most the most recent data point are designated by a TARGET MET recent data points might vary between objectives progress status indicator. Even though statistical significance, (e.g., data systems may have different data collection when measures of variability are available, is not factored into frequencies). the determination of the TARGET MET status, the movement ● Two objectives may be identical in their “percent of is still evaluated for statistical significance; see Table 3 for an targeted change achieved,” even though they differ in the example. amount of both the targeted and realized change from baseline. Objectives moving toward their targets ● Objectives moving away from their targets and those whose targets are exceeded at the baseline yield a Direction negative “percent of targeted change achieved” value, and ● When the desired direction is increase, an objective is these negative values are difficult to interpret. moving toward its target at the most recent data point if For HP2020, the “percent of targeted change achieved” baseline value < most recent value < HP2020 target. still quantifies progress for objectives that are moving toward ● When the desired direction is decrease, an objective is their targets. However, for objectives moving away from moving toward its target at the most recent data point if their baselines and targets, the “absolute value of the percent baseline value > most recent value > HP2020 target. change from baseline” is used to measure movement. An objective that moves away from its baseline and target would 4 Healthy People 2020 Statistical Notes

Extent of movement toward target where SEt is the standard error at time t and SEb is the standard error at baseline. For HP2020 objectives that had not already met or exceeded their targets at baseline, the “percent of targeted Step 3. The RSE for the denominator, SDT , is calculated change achieved” measures the extent of movement toward as: the target. It is given by: SEb RSESDT = , Percent of Most recent value – Baseline value | RT – Rb | targeted change = × 100. achieved HP2020 target – Baseline value because the target RT does not contribute to the variability of the targeted change; it is constant. Statistical significance for objectives moving Step 4. An approximate RSE for the PQ is computed toward, or meeting or exceeding their targets using a first-order Taylor series linearization of the variance of In HP2010, statistical significance of the “percent the ratio of two random variables, with numerator and of targeted change achieved” was not evaluated when denominator RSEs, above: measures of variability were available. Instead, the statistical 2 2 significance of the simple difference “most recent value RSEPQ = RSESD t + RSESD T . – baseline value” was assessed to determine whether the change from baseline to the most recent value was statistically significant, irrespective of the target. Table 2. Classification of HP2020 objectives, by progress status In HP2020, statistical significance of the “percent Objective status Short explanation of targeted change achieved” is evaluated using Taylor TARGET MET Target met or exceeded linearization when measures of variability are available. A one-sided 0.05-level test is used. IMPROVING Movement is toward the target and is either: – Statistically significant when measures of When measures of variability are available, the variability are available. IMPROVING status indicator is designated for a statistically – OR – Ten percent or more of the targeted change when measures of variability are unavailable. significant “percent of targeted change achieved,” regardless of the amount of the change, whereas the LITTLE OR NO LITTLE OR NO Objective demonstrates little or no detectable DETECTABLE CHANGE status indicator is designated for a DETECTABLE CHANGE change, because either: – Movement toward the target is not statistically “percent of targeted change achieved” that is not statistically significant when measures of variability are significant, regardless of the amount of the change. available. – OR – Movement is toward the target but the Several steps are required to evaluate statistical objective has achieved less than 10% of the significance: targeted change when measures of variability are unavailable. Step 1. The “percent of targeted change achieved” (or – OR – Movement away from the baseline and “progress quotient,” PQ) is based on the ratio of the simple target is not statistically significant when measures difference SDt = Rt – Rb between the rate Rt at time t and the of variability are available. rate Rb at baseline and the targeted change SDT = RT – Rb – OR – Movement is away from the baseline and between the target rate RT and the rate Rb at baseline: target but the objective has moved less than 10% relative to its baseline when measures of variability SDt are unavailable. PQ = × 100. – OR – No change between baseline and most SDT recent data point. Because the “percent of targeted change achieved” is used GETTING WORSE Movement is away from the baseline and target and is either: only for HP2020 objectives that are moving toward, or – Statistically significant when measures of meeting or exceeding their targets, PQ ≥ 0. variability are available. – OR – Ten percent or more relative to the baseline Step 2. The relative standard error (RSE) of the above when measures of variability are unavailable. ratio is computed based on the RSE of the numerator and the denominator. The RSE for the numerator, SDt , is calculated BASELINE ONLY Baseline data only; progress cannot be assessed. as: INFORMATIONAL Objective is informational (does not have a target). SE2t + SE2b DEVELOPMENTAL Objective is developmental (does not have baseline RSESDt = , data). | Rt – Rb | SOURCE: CDC/NCHS, HP2020 database. Healthy People 2020 Statistical Notes 5

This approximation assumes the simple difference SDt is significant, regardless of the value; for an example, see Table independent of the targeted change SDT . 3. Step 5. An approximate standard error SEPQ for the PQ is When measures of variability are available, statistical given by SEPQ = RSEPQ × PQ. significance of the “absolute value of the percent change from baseline” is evaluated using Taylor linearization. A one-sided Step 6. Statistical significance of the PQ is assessed 0.05-level test is used. Several steps are required to evaluate using the statistic z = PQ/SEPQ. Because PQ ≥ 0, statistical statistical significance: significance is based on a one-sided test, which, assuming normality, compares the value of z to 1.64485 for a 0.05-level Step 1. The absolute value of the percent change from test. baseline (PC) is based on the ratio of the simple difference SDt = Rt – Rb between the rate Rt at time t and the rate Rb at When measures of variability are unavailable, the baseline and the rate Rb: IMPROVING status indicator is designated for objectives that are moving toward their targets and for which the “percent – SDt of targeted change achieved” is 10% or more. Objectives for × 100, when desired direction is increase, Rb but Rt < RT and Rt < Rb which the “percent of targeted change achieved” is 100% or PC = . + SDt more have met or exceeded their targets and are designated as × 100, when desired direction is decrease, TARGET MET. Rb but Rt > RT and Rt > Rb Objectives moving away from their baselines and By construction, PC ≥ 0. targets Step 2. The RSE of the PC is computed based on the RSE of the numerator and the denominator in the ratio. The RSE Direction for the numerator, SDt , is calculated as: ● When the desired direction is increase, an objective is moving away from its baseline and target at the most SE2t + SEb2 recent data point if most recent value < HP2020 target RSESDt = | Rt – Rb | and most recent value < baseline value. ● When the desired direction is decrease, an objective is where SEt is the standard error at time t and SEb is the moving away from its baseline and target at the most standard error at baseline. recent data point if most recent value > HP2020 target Step 3. The RSE for the denominator, Rb, is calculated as: and most recent value > baseline value. SEb Extent of movement away from baseline RSERb = . | Rb | Movement away from baseline is quantified using: Step 4. An approximate RSE for the PC is computed Most recent – Baseline Absolute value of value value using first-order Taylor series linearization, assuming the percent change = × 100. simple difference SDt is independent of the baseline rate Rb: from baseline Baseline value 2 RSEPC = RSESD t + RSER2b . A percent change from baseline of 10% or more in absolute value means that the objective is at least 10% in Step 5. An approximate standard error SEPC for the PC is deficit relative to its baseline. Such an objective would need to given by SEPC = RSEPC × PC. make up the deficit from baseline in addition to the desired targeted change once the baseline value is regained. Step 6. Statistical significance of the PC is assessed using the statistic z = PC/SEPC. Because the “absolute value of the Statistical significance for objectives moving percent change from baseline” is used only for objectives that away from their baselines and targets are moving away from their baselines and targets, significance is based on assuming normality and comparing z to 1.64485 When measures of variability are available, the for a one-sided 0.05-level test. GETTING WORSE status indicator is designated for a statistically significant “absolute value of percent change from When measures of variability are unavailable, the baseline,” regardless of the value, whereas the LITTLE OR GETTING WORSE status indicator is designated for HP2020 NO DETECTABLE CHANGE status indicator is designated objectives that are moving away from their baselines and for a percent change from baseline that is not statistically 6 Healthy People 2020 Statistical Notes

targets and for which the “absolute value of the percent Remark. The “percent of targeted change achieved” for change from baseline” is 10% or more. HP2020 objectives that are moving toward their targets and the “absolute value of percent change from baseline” for those Objectives for which progress toward target moving away from their baselines and targets are calculated attainment cannot be assessed from the “display” values of the estimates at the baseline and most recent time points—in particular, unless otherwise Progress toward target attainment cannot be assessed specified, rates and percentages are rounded to one decimal when only baseline data are available, the target was met at place before being displayed in HP2020 data tables, whereas baseline, or the objective’s desired direction is to “maintain standard errors are displayed using three decimal places when the baseline.” In addition, progress toward target attainment measures of variability are available. This is consistent with is not assessed when an objective is informational and does HP2010, where “display” values also were used in progress not have a target (e.g., PH-7.3, Increase the proportion of calculations (3). population-based HP2020 objectives for which national data are available by socioeconomic status). Considerations Illustration of HP2020 classification of objective In addition to the aforementioned limitations to using status the “percent of targeted change achieved,” HP2020 progress measures are subject to the following considerations. HP2020 contains 42 topic areas with over 1,200 ● As in HP2010, the “percent of targeted change achieved” objectives. A smaller set of HP2020 objectives, called the Leading Health Indicators, was selected at the launch of is calculated using only the target, baseline, and most HP2020 to communicate high-priority health issues; see recent data points. Similarly, the “absolute value of http://www.healthypeople.gov/2020/Leading-Health-Indicators. the percent change from baseline” is calculated using Table 3 illustrates the HP2020 classification of objective status only the baseline and most recent data points. As in using five of these HP2020 Leading Health Indicators. HP2010, to facilitate comparisons between objectives, any underlying trends and fluctuations that occur during Table 3. Objective status classification for selected HP2020 Leading Health Indicators Movement Baseline Most recent away from Movement estimate estimate Movement baseline and statistically Objective status Objective description (year) (year) Target toward target1 target2 significant3 TARGET MET TU-11.1 Children exposed to secondhand 52.2 41.3 47.0 209.6 ... Yes smoke (percent among nonsmokers aged (2005–2008) (2009–2012) 3–11) IMPROVING C-16 Adults receiving colorectal cancer 52.1 58.2 70.5 33.2 ... Yes screening based on most recent guidelines (2008) (2013) (age-adjusted percent among adults aged 50–75) LITTLE OR NO AHS-1.1 Persons with medical insurance 83.2 83.3 100 0.6 ... No DETECTABLE (percent among persons under age 65) (2008) (2013) CHANGE LITTLE OR NO D-5.1 Persons with diagnosed diabetes 17.9 21.0 16.1 ... 17.3 No DETECTABLE whose A1c value is greater than 9 percent (2005–2008) (2009–2012) CHANGE (age-adjusted percent among adults aged 18 and over) GETTING WORSE MHMD-1 Suicide (age-adjusted rate per 11.3 12.6 10.2 ... 11.5 Yes 100,000 population) (2007) (2013) … Category not applicable. 1Quantified using the “percent of targeted change achieved.” 2Quantified using the “absolute value of the percent change from baseline.” 3When measures of variability are available, statistical significance is based on a one-sided 0.05-level test for either the “percent of targeted change achieved” or the “absolute value of the percent change from baseline.” DATA SOURCES: AHS-1.1 CDC/NCHS, National Health Interview Survey. C-16 CDC/NCHS, National Health Interview Survey. D-5.1 CDC/NCHS, National Health and Nutrition Examination Survey. MHMD-1 CDC/NCHS, National Vital Statistics System-Mortality. TU-11.1 CDC/NCHS, National Health and Nutrition Examination Survey. Healthy People 2020 Statistical Notes 7

the intervening years are not considered—because the important technical and conceptual considerations in the number and spacing of data points between the baseline measurement and tracking of health disparities (3–7). Some and most recent data points vary between objectives. of the considerations that were particularly relevant to the HP2010 health disparities measures and that have provided ● As in HP2010, two objectives that are moving toward the impetus for developing the HP2020 health disparities their targets may be identical in the “percent of targeted measures are outlined below. change achieved” even though they differ in the amount of the absolute change from baseline. Similarly, two ● The percent difference (PD) relative to the best group objectives that are moving away from their baselines may rate was measured only for adverse outcomes in HP2010; be identical in the “absolute value of the percent change see Appendix II. Those dichotomous objectives that had from baseline” even though they differ in the amount of been expressed in terms of favorable outcomes were the absolute change from baseline. re-expressed using the complementary adverse outcome for the purpose of computing the PD relative to the best ● The two measures of progress in HP2020—“percent of group rate. targeted change achieved” for objectives moving toward their targets and “absolute value of percent change ● Because the best group rate is theoretically achievable from baseline” for objectives moving away from their by other groups associated with a given population baselines—are not comparable because they use different characteristic, the PD relative to the best group rate can measurement standards—targeted change versus baseline highlight an opportunity for improvement (7). However: value. For example: o In HP2010, concerns about the stability of the best o Objective MHMD-1 is getting worse, having increased group rate, and, therefore, the reliability of disparities by 1.3 percentage points from its baseline—a percent findings based on the percent differences from the best change from baseline of 11.5% in magnitude group rate, led to imposing a standard of reliability (Table 3). on its selection. When estimates of variability were o available, the RSE of the rate identified as the best C-16 is improving, having increased by 6.1 percentage group rate was required to be less than 10%; if it was points from its baseline—realizing 33.2% of the not, then the next best rate with RSE < 10% was used targeted 18.4 percentage point change from baseline. as the reference for evaluating disparities. As a result, o If, instead, C-16 had achieved just 11.5% of its the percent differences that were presented in Healthy targeted change from baseline, then it would have People 2010 Final Review tended to be smaller than if increased by only 2.1 percentage points. Thus, even this reliability standard had not been applied (3). though the “percent of targeted change achieved” for o The PD expresses disparity for the comparison group C-16 would be equal to the “absolute value of the as a percent difference relative to the best group rate. percent change from baseline” for MHMD-1, 11.5%, However, to highlight opportunities for improvement, the amount of the absolute change from baseline for lack of parity with the best group rate is more readily C-16 would be over 1.5 times that for MHMD-1 (2.1 expressed using the percent difference relative to versus 1.3 percentage points). the comparison group itself. For example, in 2008, approximately 28% of the American Indian or Alaska Native population under age 65 did not have health Measures of Health Disparities in insurance, compared with 12% of the non-Hispanic HP2020 white population under age 65 (best group rate; HP2010 objective 1-1). Thus, relative to the best group This section describes the measurement of health rate, PD = 133%. However, to express the amount disparities and changes in disparities over time in HP2020. by which the uninsurance rate among the American Detailed information on evaluating the statistical significance Indian or Alaska Native population under age 65 of the HP2020 health disparities measures when measures of would need to be reduced in 2008 to achieve parity variability are available is provided. The HP2020 disparities with the best group rate, the percent difference relative measures are also related to the corresponding HP2010 to the comparison group would be useful: 57%. measures, which are described in Appendix II. ● In part for simplicity, but also in part due to the 10% reliability standard imposed on the best group rate, the Motivation for adopting revised health standard error SEPD for the PD was not used in HP2010 disparities measures in HP2020 for assessing the statistical significance of the percent difference, PD. Instead, the simple difference, SD, was As is recognized in the Healthy People 2010 Final tested for significance, and the PD was flagged whenever Review and established elsewhere in the literature, there are the SD was statistically significant at the 0.05 level (1). 8 Healthy People 2020 Statistical Notes

● Measures of health disparities reflect implicit value standard error of the natural logarithm of the RRg is evaluated judgments and trade-offs, particularly in the choice of the using the formula: reference for evaluating disparities, whether to measure 2 2 disparities using the absolute or the relative scale, and SEB SEg whether to weight population groups equally or according SEln(RRg) = + . RB Rg to their size. These as well as other conceptual issues in the measurement of health disparities are discussed elsewhere; see (4,6,7). One-sided significance test for RRg ● Testing RRg = 1 versus RRg > 1 is equivalent to testing Because findings of health disparities in HP2010, especially when using the relative scale, could be affected by ln(RRg) = 0 versus ln(RRg) > 0. whether an objective was expressed in terms of the favorable health outcome or its adverse complementary outcome (3,4), ● The statistic for testing ln(RRg) = 0 versus ln(RRg) > 0 is HP2020 set out to construct measures of health disparities given by: that explicitly accounted for an objective’s directionality. In addition, to account for some of the conceptual issues around z = ln(RRg)/SEln(RRg). absolute versus relative disparities, HP2020 uses a suite of measures that includes both absolute and relative measures of ● The rate ratio RRg is statistically significant at the 0.05 overall disparity. The HP2020 approach to measuring health level if z > 1.64485. disparities using a suite of measures is consistent with current practices; for example, it is consistent with the National One-sided confidence interval for RRg Cancer Institute’s health disparities calculator (8,9). ● The upper limit (UL) is computed via the inverse transformation as follows: Comparisons to the best group rate in HP2020 UL = exp{ln(RRg) + 1.64485 × SEln(RRg)}. ● A 95% confidence interval for RRg has lower limit = HP2020 rate ratio (RRg) 1.000 and upper limit = UL. Definition Relation to percent difference from best group Let RB denote the best group rate and Rg denote any other rate group’s rate. The rate ratio Rg /RB (a common relative measure in the epidemiologic literature) for comparing Rg to RB can be The percent difference was used for comparisons to the modified to yield the following pairwise measure, which will best group rate in HP2010; see Appendix II. be referred to as the HP2020 rate ratio and denoted as RRg: Objectives expressed in terms of adverse outcomes RB Rg RRg = max , . For objectives expressed in terms of adverse outcomes to Rg RB be reduced, the HP2020 rate ratio RRg is given by RRg = Rg /RB. The HP2010 percent difference PDg relative to Note that regardless of whether the objective is expressed the best group rate is seen as: as a favorable outcome to be increased—in which case RRg = RB /Rg—or as an adverse outcome to be decreased—for PDg = (RRg – 1) × 100. which RRg = Rg /RB— the HP2020 rate ratio RRg is constructed such that RRg ≥ 1. Thus, the HP2010 percent difference PDg is obtained by subtracting 1 from the HP2020 rate ratio RRg and multiplying Statistical significance by 100 when objectives are expressed in terms of adverse outcomes. When measures of variability are available, statistical significance is based on assuming normality and comparing Objectives expressed in terms of favorable outcomes the test statistic to 1.64485 for a one-sided 0.05-level test. Because the distribution of the rate ratio is typically skewed to For objectives expressed in terms of favorable outcomes the right, the natural logarithm transformation is applied first, to be increased, the rate ratio RRg is given by RRg = RB /Rg. as described below. In HP2010, the percent difference PDg was calculated using the complementary adverse outcome, with rates ŘB and Řg. When RB and Rg have standard errors SEB and SEg , For example, the AHS-1.1 objective shown in Table 4 has respectively, and are assumed independent, an approximate the lowest uninsurance rate ŘB = 5.2% (100 – 94.8), realized Healthy People 2020 Statistical Notes 9

by persons aged 25 to under 65 with an advanced degree, pairwise absolute differences between population subgroups whereas the uninsurance rate for those with less than a will tend to 0. high school education, say, is Řg = 43.3% (100 – 56.7). The Additionally, the maximal rate ratio is useful for HP2010 percent difference PDg is given by: comparing objectives that are measured on different scales. Řg – ŘB Even though their simplicity is appealing, the maximal PDg = × 100. ŘB rate difference and maximal rate ratio are not designed to summarize “typical” or average disparities well, because they Because the difference Řg – ŘB between the adverse rates is do not take into account any of the intermediate rates (10). the same as the difference RB – Rg between the favorable rates, Instead, the HP2020 summary rate ratio, introduced below, it follows that the HP2010 percent difference PDg can be extends the HP2010 index of disparity (4,5) and focuses on a expressed as: ratio between the best group rate and the average for all other groups, resulting in a more conservative measure of overall RB 1 PDg = × 1– × 100. health disparity. ŘB RRg Maximal rate difference (RDmax) Thus, the mathematical relationship between the HP2010 percent difference PDg and the HP2020 rate ratio RRg is Definition nonlinear when objectives are expressed in terms of favorable outcomes to be increased. Let RB denote the best group rate and RW denote the worst group rate. The maximal rate difference (RDmax) is an absolute measure of health disparities that compares the highest and HP2020 measures of overall health lowest group rates in the population for a given characteristic. disparity RDmax is calculated as follows: In addition to the detailed comparisons to the best group RDmax = max{RB – RW, RW – RB}. rate that the HP2020 rate ratio RRg facilitates, HP2020 provides measures that quantify the degree of disparity overall Irrespective of whether an objective is expressed in terms across all groups composing a population domain (e.g., race of a favorable outcome to be increased—in which case and ethnicity, education, or income). Unlike in HP2010, where RRmax = RB – RW—or an adverse outcome to be decreased— a single relative measure, the summary index, was used (see from where RRmax = RW – RB—the maximal rate difference Appendix II), HP2020 uses three measures that include both RDmax remains nonnegative. absolute and relative measures of overall disparity: ● The maximal rate difference, defined as the simple Statistical significance difference between the highest and lowest rates, When RB and RW have associated standard errors SEB and irrespective of intermediate rates. SEW, respectively, the standard error of RDmax is approximated ● The maximal rate ratio, defined as the ratio between the using the following formula, which assumes the two rates are highest and lowest rates, irrespective of intermediate independent: rates. SERDmax = SEB2 + SEW2 . ● The summary rate ratio, defined using a ratio between the best group rate and the average rate for all other groups One-sided significance test for RDmax in a population domain—as seen below, for objectives expressed in terms of adverse outcomes, the HP2010 ● The statistic for testing RDmax = 0 versus RDmax > 0 is summary index is obtained by subtracting 1 from the given by: HP2020 summary rate ratio and multiplying by 100. z = RDmax /SERDmax The maximal rate difference is useful for tracking changes over time. Tracking the maximal rate difference ● The maximal rate difference RDmax is statistically over time allows the analyst to determine whether, overall, significant at the 0.05 level if z > 1.64485. the absolute difference between the highest and lowest rates is decreasing. While this does not capture whether the One-sided confidence interval for RDmax population health outcome overall is improving, it does allow the analyst to evaluate overall progress toward eliminating ● The UL is computed as follows: disparities, because as the absolute difference between UL = RDmax + 1.64485 × SERDmax . the highest and lowest rates decreases toward 0, all of the 10 Healthy People 2020 Statistical Notes

● A 95% confidence interval for RDmax has lower limit = HP2020 summary rate ratio (RRave) 0.000 and upper limit = UL. Definition Maximal rate ratio (RRmax) Given that there are K – 1 groups other than the one identified as having the best group rate, compute their average Definition rate RA by using the following summation formula: Using the same notation as above, the maximal rate ratio R1+ R2 + ... + RK – 1 is defined as: RA = . K_1 RB RW RRmax = max , . Continuing with the same notation as previously described, RW RB the HP2020 summary rate ratio is defined as: As with the HP2020 rate ratio RRg, note that, regardless RB RA of whether the objective is in terms of a favorable outcome to RRave = max , . RA RB be increased or in terms of an adverse outcome to be reduced, RRmax ≥ 1. As with the HP2020 rate ratio RRg and the maximal rate ratio RRmax, irrespective of the objective’s directionality, the Statistical significance HP2020 summary rate ratio RRave is such that RRave ≥ 1. As with the HP2020 rate ratio RRg , when measures of variability are available, the natural logarithm transformation Statistical significance is applied. Using the same notation as above and, again, In HP2010, the statistical significance of the HP2010 assuming the two rates are independent, an approximate summary index of disparity was assessed using resampling standard error of the natural logarithm of RRmax is given by: techniques because it was not directly available. In HP2020, when measures of variability are available, the evaluation 2 2 of statistical significance and confidence intervals for the SEB SEW SEln(RRmax) = + . HP2020 summary rate ratio RRave proceeds instead according RB RW to the following analytic steps: One-sided significance test for RRmax Step 1. Assuming the group rates are independent and that K ≥ 3, the standard error SEA of RA is evaluated using ● Testing RRmax = 1 versus RRmax > 1 is equivalent to the following summation formula, which yields an unbiased testing estimate of SEA: ln(RRmax) = 0 versus ln(RRmax) > 0. SE12 + SE22 + … + SEK2 – 1 SEA = , ● The statistic for testing ln(RRmax) = 0 versus ln(RRmax) > K–2 0 is given by: Step 2. Once RA and SEA are obtained, determining z = ln(RRmax)/SE ln(RRmax) . statistical significance of the summary rate ratio RRave proceeds as before. The standard error of the natural logarithm ● The maximal rate ratio RRmax is statistically significant at of RRave is approximately: the 0.05 level if z > 1.64485. 2 2 SEB SEA One-sided confidence interval for RRmax SEln(RRave) = + . RB RA ● As before, the UL is computed via the inverse transformation, as follows: One-sided significance test for RRave UL = exp{ln(RRmax) + 1.64485 × SE ln(RRmax)}. ● Testing RRave = 1 versus RRave > 1 is equivalent to ● A 95% confidence interval for RRmax has lower limit = testing 1.000 and upper limit = UL. ln(RRave) = 0 versus ln(RRave) > 0. ● The statistic for testing ln(RRave) = 0 versus ln(RRave) > 0 is computed: z = ln(RRave)/SE ln(RRave). Healthy People 2020 Statistical Notes 11

● The summary rate ratio RRave is statistically significant at summary index IDisp cannot be directly related to the HP2020 the 0.05 level if z > 1.64485. summary rate ratio RRave when objectives are expressed in terms of favorable outcomes to be increased. One-sided confidence interval for RRave ● The UL is computed via the inverse transformation: Two examples from the HP2020 health UL = exp{ln(RRave) + 1.64485 × SE ln(RRave)}. disparities tool ● A 95% confidence interval for RRave has lower limit = The following examples from the HP2020 online health 1.000 and upper limit = UL. disparities tool, released in spring 2015, serve to illustrate the HP2020 disparities measures; see http://www.healthypeople.gov. Relation to HP2010 summary index Education disparities in medical insurance for The index of disparity (IDisp) was the single summary measure of health disparities used in HP2010; see persons aged 25 to under 65, 2013 Appendix II. HP2020 AHS-1.1 objective is to increase the proportion of persons with medical insurance. Accordingly, educational Objectives expressed in terms of adverse outcomes attainment groups in Table 4 are sorted from most to least favorable outcome; here, that is the percentage of persons For objectives expressed in terms of adverse outcomes to aged 25 to under 65 in a given group with medical insurance be reduced, the HP2020 rate ratio RRg for each of the K – 1 in 2013. groups other than the “best” group is given by RRg = Rg /RB . Similarly, the HP2020 summary rate ratio RRave is given by As in HP2010, HP2020 uses the group with the RRave = RA /RB. Thus, most favorable (best) rate to highlight opportunities for improvement. Thus, all insurance rates in Table 4 are 1 ∑ K – 1R K–1 g=1 g ∑ gK =– 11RRg compared with the best group rate. For example, the ratio RRave = = 94.8/56.7 between the insurance rate for persons aged 25 RB K–1 to under 65 with an advanced degree (best group rate) and the insurance rate for those with less than a high school The HP2010 summary index IDisp is obtained by education equals 1.671 (see note, below, about rounding); it subtracting 1 from the HP2020 summary rate ratio RRave and indicates that the best group rate is 1.671 times the insurance multiplying by 100 when objectives are expressed in terms of rate among persons aged 25 to under 65 with less than a adverse outcomes. Indeed: high school education. Said another way, assuming no other changes, the increase in insurance coverage that would be ∑ Kg =– 11 PDg ∑ Kg =– 11 (RRg – 1) × 100 needed among persons aged 25 to under 65 with less than a IDisp = = = (RRave – 1) × 100. K_1 K_1 high school education to achieve parity with those with an advanced degree (best group) is 67.1% [(1.671 – 1.000) × 100]. Objectives expressed in terms of favorable outcomes Remark. All disparity calculations in Table 4 are applied For objectives expressed in terms of favorable outcomes to the unrounded values of the estimates and their standard to be increased, the HP2020 rate ratio RRg for each of the errors that are available in the HP2020 database. Thus, after K – 1 groups other than the “best” group is given by rounding to three decimals, values displayed in Table 4 for RRg = RB /Rg. Similarly, the summary rate ratio RRave is rate ratios may differ from the results of calculations that use given by RRave = RB /RA. In HP2010 the percent difference the displayed values of the estimated rates in Table 4. This PDg and summary index IDisp were calculated using the departs from HP2010, where rounded “display” values were complementary adverse outcomes, with rates ŘB and Řg. Using used in disparity calculations (3). the expression for the percent difference PDg of the adverse In particular, working with the unrounded values of the complementary outcomes derived previously, the HP2010 estimates and their standard errors (when available) allows summary index IDisp can be written as: more possibilities for breaking ties in the ranking of rates K–1 from highest to lowest. For example, if, even after comparing RB 1 1 the rates using their unrounded values, two groups are tied for IDisp = × 1– × 100 . ŘB K – 1 g = 1 RRg the highest, most favorable rate, the group with the smaller standard error is selected as the “best” rate when measures Note that the average of the reciprocals of the rate ratios of variability are available. (If measures of variability are RRg in this last expression is not equal to the reciprocal of the unavailable, then a tie in the unrounded values of two rates average or summary rate ratio RRave; thus, the HP2010 may be resolved using group size or any other characteristic; 12 Healthy People 2020 Statistical Notes

Table 4. Persons with medical insurance (percentage, aged ● 1.049 times the rate among persons aged 25 to under 65 25 to under 65) by educational attainment: United States, with a 4-year college degree 2013 ● 1.132 times the rate among those with an Associate’s Disparity degree statistically Educational attainment Percent Disparity significant ● 1.185 times the rate among those with some college education Advanced degree 94.8 × 1.000 CI 94.1/95.5 ... ● 1.258 times the rate among those with a high school SE 0.348 degree 4-year college degree 90.3 × 1.049 Yes ● 1.671 times the rate among those with less than a high CI 89.6/91.0 CI 1.000/1.059 school education SE 0.352 Associate’s degree 83.7 × 1.132 Yes HP2020 measures of overall disparity CI 82.6/84.8 CI 1.000/1.146 SE 0.560 Instead of reporting all pairwise comparisons relative Some college 80 × 1.185 Yes to the best group rate, three measures provided in Table 4 CI 79.0/81.0 CI 1.000/1.200 allow for an overall assessment of disparities by educational SE 0.525 attainment for objective AHS-1.1: High school 75.4 × 1.258 Yes ● Maximal rate difference. The absolute (or range) CI 74.4/76.3 CI 1.000/1.274 difference between the highest and lowest group rates SE 0.491 was 38.1 percentage points in 2013. Less than high school 56.7 × 1.671 Yes CI 55.0/58.4 CI 1.000/1.715 ● Maximal rate ratio. The highest group rate was 1.671 SE 0.870 Maximal rate ratio times the lowest group rate in 2013. Average group rate 77.2 × 1.227 Yes ● HP2020 summary rate ratio. In 2013, the best group rate excluding best group rate SE 0.654 CI 1.000/1.246 was 1.227 times the average rate for all other educational Summary rate ratio attainment groups (excluding the best), 77.2%. Maximal rate difference 38.1 Yes (in percentage points) ... CI 0.0/39.3 SE 0.741 Racial and ethnic disparities in infant mortality, … Category not applicable. 2011 NOTES: CI is 95% confidence interval; SE is standard error. Data are for HP2020 objective AHS-1.1: HP2020 objective MICH-1.3 is to reduce the rate of all Increase the proportion of persons with medical insurance. The calculations of the HP2020 rate ratio as well as the three HP2020 measures of overall disparity, namely the maximal rate difference, the maximal infant deaths within 1 year of a live birth. Thus, racial and rate ratio, and the HP2020 summary rate ratio, are as described previously. The statistical significance ethnic groups in Table 5 are sorted from least to most adverse of the HP2020 rate ratio and measures of overall disparity is based on one-sided significance tests at the 0.05 level of significance. Similarly, the CIs for the HP2020 rate ratio and measures of overall disparity are outcome. As before, comparisons are relative to the best group one-sided 95% CI. rate. For example, the ratio 11.5/4.4 between the infant death DATA SOURCE: CDC/NCHS, National Health Interview Survey. rate among non-Hispanic black mothers and the infant death rate for Asian or Pacific Islander mothers (best group rate) the HP2020 summary measures, described above, are not equals 2.625 (see note, above, about rounding); it indicates affected by group size). that the former is 2.625 times the best group rate. Thus, assuming no other changes, the infant death rate among non- In addition, unlike in HP2010, the identification of the Hispanic black mothers would need to be reduced by 61.9% best group rate in HP2020 does not require the 10% threshold [100 × (1 – 1/2.625)] to achieve parity with the best group for its RSE; see “Motivation for adopting revised disparities rate. measures in HP2020” and (4) for more information. In Table 5, disparities are examined using the rate ratios In Table 4, disparities are examined using the rate ratios between each of the other (more adverse) group rates and the between the best (most favorable) group rate and each of the best (least adverse) group rate. other (less favorable) group rates. Comparisons to the best group rate Comparisons to the best group rate In 2011, the best group rate by race and ethnicity for In 2013, the best group rate by educational attainment for objective MICH-1.3, 4.4 infant deaths per 1,000 live births, objective AHS-1.1 was realized by persons aged 25 to under was attained by infants born to Asian or Pacific Islander 65 with an advanced degree. The best group rate was: mothers. Healthy People 2020 Statistical Notes 13

● The rate for those born to non-Hispanic white mothers Table 5. All infant deaths (per 1,000 live births, under age 1 was 1.162 times the best group rate. year), by race and ethnicity: United States, 2011 ● The rate for those born to Hispanic or Latina mothers was Disparity 1.181 times the best group rate. Rate per 1,000 statistically Race and ethnicity live births Disparity significant ● The rate for those born to American Indian or Alaska Native mothers was 1.882 times the best group rate. Asian or Pacific Islander 4.4 ÷ 1.000 CI 4.1/4.6 ... ● The rate for those born to non-Hispanic black mothers SE 0.131 was 2.625 times the best group rate. White, not Hispanic or 5.1 ÷ 1.162 Yes Latino CI 5.0/5.2 CI 1.000/1.224 HP2020 measures of overall disparity SE 0.049 As before, three measures provided in Table 5 allow for Hispanic or Latino 5.2 ÷ 1.181 Yes an overall assessment of disparities by mother’s race and CI 5.0/5.3 CI 1.000/1.247 SE 0.075 ethnicity for objective MICH-1.3: American Indian or 8.2 ÷ 1.882 Yes ● Maximal rate difference. The absolute (or range) Alaska Native CI 7.4/9.0 CI 1.000/2.075 difference between the highest and lowest group rates SE 0.422 was 7.1 deaths per 1,000 in 2011. Black or African 11.5 ÷ 2.625 Yes ● Maximal rate ratio. The highest group rate was 2.625 American, not Hispanic CI 11.2/11.7 CI 1.000/2.768 or Latino SE 0.141 Maximal rate ratio times the lowest group rate in 2011. Average group rate 7.5 ÷ 1.712 Yes ● HP2020 summary rate ratio. In 2011, the average rate for excluding best group rate SE 0.262 CI 1.000/1.847 all other race and ethnicity groups (excluding the best), Summary rate ratio 7.5 infant deaths per 1,000 live births, was 1.712 times Maximal rate difference 7.1 Yes the best group rate. (in deaths per 1,000) ... CI 0.0/7.4 SE 0.192 Changes in health disparities over time in … Category not applicable. HP2020 NOTES: CI is 95% confidence interval; SE is standard error. Data are for HP2020 objective MICH-1.3: Reduce the rate of all infant deaths (within 1 year). Race and ethnicity is that of the mother. The calculations of the HP2020 rate ratio as well as the three HP2020 measures of overall disparity, namely In HP2020, changes in disparities over time are assessed the maximal rate difference, the maximal rate ratio, and the HP2020 summary rate ratio, are as described previously. The statistical significance of the HP2020 rate ratio and measures of overall disparity is based principally for the three measures of overall disparity on one-sided significance tests at the 0.05 level of significance. Similarly, the CIs for the HP2020 rate ratio described above, although changes in disparities for specific and measures of overall disparity are one-sided 95% CI. groups relative to the best rate also may be tracked over time DATA SOURCE: CDC/NCHS, Linked Birth/Infant Death Data Set. as long as the group with the best rate remains unchanged. As stated earlier, tracking the maximal rate difference highest rate is at least twice the lowest rate, a finding that may RDmax over time allows the analyst to evaluate overall motivate action to address disparities among the underlying progress toward eliminating disparities, because as the population groups. Highlighting such findings becomes absolute difference between the highest and lowest rates useful as the HP2020 initiative assesses progress toward its decreases toward 0, all of the pairwise absolute differences overarching goal of eliminating disparities. between population subgroups will tend to 0. Similarly, as the When measures of variability are available, the evaluation maximal rate ratio RRmax decreases toward the value 1.000, all of the statistical significance of changes in the three HP2020 of the pairwise rate ratios between population subgroups will measures of overall disparity—as well as changes in the tend toward the value 1.000. HP2020 rate ratios when the group with the best rate remains The HP2020 summary rate ratio extends the HP2010 unchanged—follows from the standard error calculations index of disparity and focuses on a ratio between the best detailed previously. The natural logarithm transformation may group rate and the average for all other population groups for be used, as appropriate, to correct for lack of normality. The a demographic or socioeconomic characteristic. The HP2020 difference between the values S1 and S2 of measure S at two summary rate ratio is more conservative than the maximal rate time points is tested using a two-sided 0.05-level test based on ratio. For example, RRave may remain less than 1.100 even the statistic if RRmax ≥ 1.100, indicating that, while the highest rate is at least 10% higher than the lowest rate, intermediate rates may S2 – S1 be at (near) parity with the best group rate. On the other hand, z= . 2 2 if the HP2020 summary rate ratio RRave ≥ 2.000, then the SE1 + SE2 14 Healthy People 2020 Statistical Notes

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