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NATIONAL CENTER FOR HEALTH STATISTICS Vital and Health Statistics Series 2, Number 175 August 2017 National Center for Health Statistics Data Presentation Standards for Proportions Data Evaluation and Methods Research U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Disease Control and Prevention National Center for Health Statistics This report was revised on November 1, 2018, where on page 4, RSE(Var) was misattributed as RSE(SE). This revision had no effect on the related standard.

Copyright information All material appearing in this report is in the public domain and may be reproduced or copied without permission; citation as to source, however, is appreciated. Suggested citation Parker JD, Talih M, Malec DJ, et al. National Center for Health Statistics Data Presentation Standards for Proportions. National Center for Health Statistics. Vital Health Stat 2(175). 2017. Library of Congress Cataloging-in-Publication Data Names: National Center for Health Statistics (U.S.), issuing body. Title: National Center for Health Statistics Data Presentation Standards for Proportions. Other titles: Vital and health statistics. Series 2, Data evaluation and methods research ; no. 175. | DHHS publication ; no. (PHS) 2017-1375. 0276-4733 Description: Hyattsville, Maryland : U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Health Statistics, August 2017. | Series: Vital and health statistics. Series 2, Data evaluation and methods research ; number 175 | Series: DHHS pub ; number 2017-1375 | Includes bibliographical references and index. Identifiers: LCCN 2017033531 | ISBN 0840606826 (pbk. : alk. paper) Subjects: | MESH: National Center for Health Statistics (U.S.) | Data Accuracy | Health Surveys--standards | Data Display--standards | Research Design | Statistics as Topic | United States Classification: LCC RA409 | NLM W2 A N148vb no.175 2017 | DDC 614.4/2--dc23 LC record available at https://lccn.loc.gov/2017033531 For sale by the U.S. Government Printing Office Superintendent of Documents Mail Stop: SSOP Washington, DC 20402–9328 Printed on acid-free paper.

Vital and Health Statistics Series 2, Number 175 National Center for Health Statistics Data Presentation Standards for Proportions Data Evaluation and Methods Research U.S. DEPARTMENT OF HEALTH AND HUMAN SERVICES Centers for Disease Control and Prevention National Center for Health Statistics Hyattsville, Maryland August 2017 DHHS Publication No. 2017–1375

National Center for Health Statistics Charles J. Rothwell, M.S., M.B.A., Director Jennifer H. Madans, Ph.D., Associate Director for Science Division of Research and Methodology Charles J. Rothwell, M.S., M.B.A., Acting Director Donald J. Malec, Ph.D., Associate Director for Science Office of Analysis and Epidemiology Irma E. Arispe, Ph.D., Director Makram Talih, Ph.D., Associate Director for Science Division of Health and Nutrition Examination Surveys Kathryn S. Porter, M.D., M.S., Director Ryne Paulose-Ram, Ph.D., Associate Director for Science Division of Health Interview Statistics Marcie L. Cynamon, Director Stephen J. Blumberg, Ph.D., Associate Director for Science Division of Health Care Statistics Denys T. Lau, Ph.D., Acting Director Alexander Strashny, Ph.D., Associate Director for Science Division of Vital Statistics Delton Atkinson, M.P.H., M.P.H., P.M.P., Director Hanyu Ni, Ph.D., M.P.H., Associate Director for Science

Contents Acknowledgments iv Abstract 1 Introduction 1 NCHS Data Presentation Standards for Proportions 2 Sample Size 2 Confidence Intervals 3 Degrees of Freedom 4 Complementary Proportions 4 Discussion 5 References 6 Appendix I Figure Implementation of NCHS Data Presentation Standards for Proportions 7 Appendix II Examples of the Application of NCHS Data Presentation Standards for Proportions 8 Text Table NCHS Data Presentation Standards for Proportions 2 Appendix Tables I Percentage of children aged 8–17 years with elevated and normal or borderline blood pressure, by race and Hispanic origin: United States, 2013–2014 8 II Percentage of adults aged 60 and over who are overweight, by sex and race and Hispanic origin: United States, 2013–2014 9 III. Percentage of adults aged 18 and over with hearing difficulties, by race and Hispanic origin and family income: United States, 2013 10 IV Percentage of ambulatory care visits, by setting type according to diagnosis: United States, 2009–2010 11 V Percentage of fathers aged 15–44 with children under age 5 years who live with their children, by how often they played with their children in the last 4 weeks and father’s age: United States, 2006–2010 12 VI Proportion of triplet and higher-order multiple births, by age and race and Hispanic origin of mother for mothers aged 15–19 and 40–54: United States, 2015 14 iii

Acknowledgments The authors would like to acknowledge the contribution of Cynthia A. Reuben, NCHS Office of Analysis and Epidemiology and the contributions of the following people who participated in sessions on this topic in 2015 at the Joint Statistical Meetings and the National Center for Health Statistics (NCHS) National Conference on Health Statistics: Michael Davern, NORC at the University of Chicago; Jennifer Madans, NCHS Associate Director for Science; Virginia Lesser, Oregon State University; Ron Jarmin, U.S. Census Bureau; and Arthur Hughes, Substance Abuse and Mental Health Services Administration. This report was edited and produced by the NCHS Office of Information Services, Information Design and Publishing Staff: Jen Hurlburt edited the report, typesetting was done by Erik L. Richardson (contractor), and graphics were produced by Dorothy M. Day. iv

Abstract Background The National Center for Health National Center for Health Statistics (NCHS) disseminates information on a broad range of Statistics Data Presentation Standards for Proportions health topics through diverse publications. These publications must rely on clear and transparent presentation standards that can be broadly and efficiently applied. by the Data Suppression Workgroup: Jennifer D. Parker, Ph.D., Standards are particularly important Division of Research and Methodology; Makram Talih, Ph.D., Office for large, cross-cutting reports where estimates cannot be individually of Analysis and Epidemiology; Donald J. Malec, Ph.D., Division of evaluated and indicators of precision Research and Methodology; Vladislav Beresovsky, Ph.D., Division of cannot be included alongside the Research and Methodology; Margaret Carroll, M.S.P.H., Division of estimates. Health and Nutrition Examination Surveys; Joe Fred Gonzalez, Jr., M.S., Division of Research and Methodology; Brady E. Hamilton, Objective Ph.D., Division of Vital Statistics; Deborah D. Ingram, Ph.D., Office This report describes the NCHS Data Presentation Standards for of Analysis and Epidemiology; Kenneth Kochanek, M.A., Division of Proportions. Vital Statistics; Frances McCarty, M.Ed., Ph.D., Division of Research and Methodology; Chris Moriarity, Ph.D., Division of Health Interview Results Statistics; Iris Shimizu, Ph.D., Division of Research and Methodology; The multistep NCHS Data Alexander Strashny, Ph.D., Division of Health Care Statistics; and Presentation Standards for Brian W. Ward, Ph.D., Division of Health Care Statistics Proportions are based on a minimum denominator sample size and on the absolute and relative widths of a confidence interval calculated Introduction in part, attributed to each data system’s unique features and constraints. using the Clopper-Pearson method. Standards also change over time, due Proportions (usually multiplied by The National Center for Health to changes in the purpose and scope of 100 and expressed as percentages) Statistics (NCHS) collects, analyzes, the data’s use, the feasibility of users are the most commonly reported and disseminates information on a broad carefully reviewing published estimates, estimates in NCHS reports. range of health topics through diverse the ability to provide explanatory text publications, databases, and tables. Some discussing the precision of the published Conclusions data products present information based estimates, and advances in statistical The NCHS Data Presentation on a single data system, while others methodology. Standards for Proportions will be summarize information from many data This report describes the NCHS Data applied to all NCHS publications. systems. These reports and data products Presentation Standards for Proportions. Using these Standards, some estimates will be identified as may include estimates on a wide range Proportions (usually multiplied by 100 unreliable and suppressed and of topics or focus on a particular health and expressed as percentages) are the some estimates will be flagged for outcome. Furthermore, data products may most commonly reported estimates statistical review. For reports where include estimates based on data sources in NCHS reports. For many NCHS estimates are evaluated individually, a outside of NCHS. However, many of reports, an automated rule is needed particular proportion not meeting the these reports do not display supporting to determine whether or not estimates NCHS Data Presentation Standards information about an estimate to provide are sufficiently stable for publication. could be identified as unreliable the reader with information about the The multistep NCHS Data Presentation but not be suppressed if it can be estimate’s reliability, such as its standard Standards for Proportions are based on interpreted appropriately in the error (SE) or confidence interval (CI), a minimum denominator sample size context of subject-specific factors due to space and format constraints. As and on criteria based on the absolute and and report objectives. a result, reports must rely on clear and relative widths of a CI calculated using Keywords: confidence interval • transparent presentation criteria that can the Clopper-Pearson method (2,3). The sample size • degrees of freedom • be broadly and efficiently implemented. next section provides details about the health surveys • vital statistics Statistical standards for data Standards and their implementation. For presentation vary across agencies, all NCHS data products, the Standards data systems, and data products (1). will be applied and departures from the Differences among standards can be, Standards will be justified. A flow chart Page 1

Page 2 Series 2, No. 175 describing the Standards and examples of Table. NCHS Data Presentation Standards for Proportions their implementation are provided in the Statistic Standard appendices. Sample size Estimated proportions should be based on a minimum denominator sample size and effective denominator sample NCHS Data size (when applicable) of 30. Estimates with either a denominator sample size or an effective denominator sample size (when applicable) less than 30 should be suppressed. Presentation Standards 1 If the number of events is 0 (or its complement ), then the denominator sample size should be used to obtain confidence for Proportions intervals. If all other criteria are met for presentation, an 1 estimate based on 0 events (or its complement ) should be flagged for statistical review by the clearance official. The review could result in either the presentation or the suppression of the proportion. The Table summarizes the NCHS Confidence interval If the sample size criterion is met, calculate a 95% two-sided Data Presentation Standards for confidence interval using the Clopper-Pearson method, or the Proportions, and Appendix I shows the Korn-Graubard method for complex surveys, and obtain its width. process used to implement the Standards. Small absolute confidence interval width If the absolute confidence interval width is greater than 0.00 When applying the NCHS Data and less than or equal to 0.05, then the proportion can be Presentation Standards for Proportions, presented if the number of events is greater than 0 and the degrees of freedom criterion (below) is met. If the number of estimates identified as unreliable will 1 events is 0 (or its complement ) or the degrees of freedom be suppressed. Other estimates will criterion is not met, then the estimate should be flagged for statistical review by the clearance official. The review could be flagged for statistical review by the result in either the presentation or the suppression of the clearance official. Flagged estimates may proportion. Large absolute confidence interval width If the absolute confidence interval width is greater than or equal be suppressed or presented, depending to 0.30, then the proportion should be suppressed. on the outcome of the review. To ease Relative confidence interval width If the absolute confidence interval width is between 0.05 and production of large reports, the decision 0.30 and the relative confidence interval width is more than 130%, then the proportion should be suppressed. process for flagged estimates could Relative confidence interval width If the absolute confidence interval width is between 0.05 and be automated at the discretion of the 0.30 and the relative confidence interval width is less than clearance official, with the suppression of or equal to 130%, then the proportion can be presented if the degrees of freedom criterion below is met. If the degrees all flagged estimates. When an estimate of freedom criterion is not met, then the estimate should is flagged or suppressed, a footnote be flagged for statistical review by the clearance official. The review could result in either the presentation or the indicating the reason the estimate has suppression of the proportion. been flagg Degrees of freedom When applicable for complex surveys, if the sample size and confidence interval criteria are met for presentation and the degrees of freedom are fewer than 8, then the proportion The NCHS Data Presentation should be flagged for statistical review by the clearance Standards for Proportions will be applied official. This review may result in either the presentation or the suppression of the proportion. to all NCHS reports and data systems. Complementary proportions If all criteria are met for presenting the proportion but not for its Importantly, the Standards presented 1 complement , then the proportion should be shown. A footnote indicating that the complement of the proportion may be in this report apply to estimates that unreliable should be provided. are known to meet all confidentiality 1 The complement of a proportion p is (1 – p). The complement of the number of events in the numerator for p is the number of requirements, or in the case of vital events in the numerator for (1 – p). statistics, meet all agreements between NCHS and the states. Like other statistical agencies, NCHS may restrict America’s Children and Older Americans, Proportions are described more fully in access to certain data or estimates to and journal articles authored by NCHS the following sections. protect the confidentiality of survey staff members. For such reports, the participants (4,5). analyst(s) should provide justification Sample Size Departures from the Standards for including the estimate in the report should be justified. In reports in which to the clearance official(s) and a final The sample size (denominator) is estimates are evaluated individually, determination will be made jointly by an important indicator of an estimate’s a particular estimate not meeting the analyst(s) and clearance official(s) precision. The variance of a proportion the Standards could be identified as on a case-by-case basis. If the final is directly related to the sample size unreliable but not be suppressed if it determination is to present an estimate, and, with large samples, applying the can be interpreted appropriately in a footnote or appropriate language in the normal approximation to the binomial the context of subject-specific factors report indicating that the estimate does distribution for proportions can be useful and report objectives. Currently such not meet the NCHS Data Presentation for many analyses (6). reports include, but are not limited to, Standards should be provided. For vital statistics, the sample size Data Briefs, National Health Statistics The specific components of the for a proportion is the number of births Reports, multi-agency reports such as NCHS Data Presentation Standards for (or deaths) in the denominator. For an

Series 2, No. 175 Page 3 estimate from a complex survey, the Standard and relative CI widths for estimated effective sample size, ne, is defined as proportions are based on the 95% two- the sample size, n, divided by the design ● Estimated proportions should be based sided Clopper-Pearson CI. The Clopper- effect (7). One approach used to calculate on a minimum denominator sample Pearson CI is known to perform well for ne for estimated proportions from a size and effective denominator sample estimated proportions with few events complex sample survey is: size (when applicable) of 30. Estimates in the numerator. For complex sample with either a denominator sample size surveys, the calculation of the Clopper- or an effective denominator sample Pearson CI using the approach of Korn and size (when applicable) less than 30 Graubard incorporates information from should be suppressed. the survey design, including the effective where, in this case, the design effect is: ● If the number of numerator events sample size and, when appropriate, the is 0 (or its complement), then the degrees of freedom. Finally, the coverage denominator sample size should be of a 95% Clopper-Pearson CI is generally used to obtain confidence intervals. conservative, meaning that the Clopper- If all other criteria are met for Pearson CI includes the true proportion presentation, an estimate based on 0 more than 95% of the time. Other intervals Documentation for specific surveys events (or its complement) should be have been shown to have poorer coverage, should be consulted when calculating flagged for statistical review by the meaning that a 95% CI includes the true design effects, as approaches can differ clearance official. The review could proportion less than 95% of the time among surveys and for specific analytic result in either the presentation or the (10–12). purposes. suppression of the proportion. In particular, the commonly used If the number of numerator events Wald CI [p ± 1.96 × SE(p) for a two-sided is 0 or equal to the denominator (the Confidence Intervals 95% CI] is known to perform poorly complement of 0 events), the estimated for proportions (10–12). In addition to proportion will be 0 or 1, respectively. The NCHS Data Presentation sometimes producing negative lower As a result, the estimated variance of the Standards for Proportions are based on the bounds for small proportions or upper proportion will be 0, and the effective evaluation of absolute and relative 95% bounds greater than 1 for large proportions, sample size will be undefined. In these CI widths. CIs provide a way to assess the Wald CI does not always produce cases, the sample size should be used to an estimate’s precision, and technical adequate coverage. In other words, determine whether the minimum sample definitions are available in many standard published simulation studies demonstrate size criterion is met, and it should also statistical texts, including Bickel and that the true proportion is contained within be used for CIs and other computations Doksum (8) and Casela and Berger (9). a 95% Wald CI in less than 95% of the that include the effective sample size. More generally, under repeated sampling, if simulated CIs, with greater undercoverage Because observing no events or events a proportion and its 95% CI are estimated for smaller and larger proportions. for everyone in a category can provide from each sample, the true value of the From a calculated CI, the absolute important information (e.g., in the context proportion is expected to be contained in CI width is obtained by subtracting the of rare health outcomes or conditions), 95% of the calculated intervals. A handful value of the lower confidence limit from estimates based on 0 events (or the of methods to calculate CIs for proportions the value of the upper confidence limit. complement) that meet absolute CI and are available and the expectation of 95% The relative CI width is calculated as the degrees of freedom criteria should be coverage may not be attained for some absolute CI width divided by the proportion flagged and considered for presentation intervals or under some conditions. and multiplied by 100%. Past practice after statistical review by a clearance Methods used to calculate a CI lead to for many surveys has been to evaluate official to confirm the validity of the point undercoverage if the true proportion is relative standard errors (RSEs), which and interval estimates. contained in fewer than the expected are calculated by dividing the SE by the For complex sample surveys, due number of intervals (e.g., less than 95%). proportion and multiplying by 100%. to sampling design and variability, Conversely, methods are considered However, when dividing the SE by very there may be cases where the effective conservative if the true proportion is small proportions, the RSE can be too sample size is greater than the sample contained in more than the expected conservative, and when dividing the SE size. When the effective sample size is number of intervals. by very large proportions, the RSE can be greater than the sample size, the sample The Clopper-Pearson CI (2) [adapted too liberal. Because the relative CI width is size should be used to determine whether for complex surveys by Korn and Graubard calculated in a similar manner, this property the minimum sample size criterion is (3) when applicable] should be used to of the RSE also applies to the relative met, and it should also be used for CIs determine whether or not the CI of a CI width. The NCHS Data Presentation and other computations that include the proportion meets the presentation criteria. Standards for Proportions rely on both the effective sample size. For the purposes of setting thresholds relative and absolute CI widths to reduce for the Standards, the determinations of the impact of this property. small and large in the context of absolute

Page 4 Series 2, No. 175 For complex sample surveys, default less than or equal to 130%, Standard calculations from survey software then if the degrees of freedom may not be appropriate or feasible for criterion described in the next ● When applicable for complex all situations, including age-adjusted section is met, the proportion surveys, if the sample size and CI estimates, estimates based on multiple can be presented. If the degrees criteria are met for presentation and imputation, estimates for subgroups of freedom criterion is not met, the degrees of freedom are fewer represented in only a subset of primary then the estimate should be than 8, then the proportion should be sampling units (PSUs) (e.g., some flagged and statistically reviewed flagged for statistical review by the racial and ethnic groups and region- by the clearance official. This clearance official. This review may specific estimates), and when calculating review may result in either the result in either the presentation or the annual or survey cycle estimates using presentation or the suppression of suppression of the proportion. a multiyear or multicycle data file. In the proportion. these instances, the relevant information Complementary should be extracted and the CIs directly Degrees of Freedom Proportions calculated. For complex sample surveys, the The SE and width of the CI for the Standard precision of the estimated variance is complement of a proportion (1 – p) are approximately related to the square root the same as those for the proportion, ● If the sample size criterion is met, of the degrees of freedom. Using resulting p. As described in previous sections, calculate a 95% two-sided confidence SEs with low precision to assess estimated relative measures for the smaller interval using the Clopper-Pearson proportions may lead to poor measures proportion are much larger than for its method (2), or the Korn-Graubard of effective sample size and CI widths. larger complement. Consequently, there method (3) for complex sample Under certain conditions, the variance is a range of proportions where the CI surveys, and obtain the width of the estimate is approximately proportional to criteria will yield conflicting assessments confidence interval. a chi-squared distribution, and the RSE of reliability. For these proportions, the ○ If the absolute confidence of the variance obtained from a complex relative CI width may indicate that a interval width is greater than sample survey can be approximated as small proportion is unreliable but that its 0.00 and less than or equal to . From this complement is not. 0.05, then the proportion can be expression, estimated proportions based For a given health indicator or presented if the number of events on fewer than 8 degrees of freedom have publication, the larger proportion may is greater than 0 and the degrees an of 50% or higher. be the most salient measure, while for of freedom criterion (described As one rule of thumb, the degrees of others, the smaller proportion may be in the next section) is met. If freedom can be calculated as the number the most important. Typically, both the number of events is 0 (or of PSUs minus the number of strata. This proportions are not shown (e.g., only the complement) or the degrees calculation is used in most NCHS surveys the proportion with health insurance of freedom criterion is not met, and implemented in survey software, would be shown, not both the proportion then the estimate should be although specific calculations can vary with and the proportion without health flagged and statistically reviewed across packages. However, default insurance). Given that the complement by the clearance official. This calculations of degrees of freedom from of the presented proportion can be review may result in either the survey software may not be appropriate determined by subtraction, consideration presentation or the suppression of for subgroups represented in only a subset of the precision of the complement the proportion. of PSUs (e.g., some racial and ethnic is important. For some publications, ○ If the absolute confidence groups and region-specific estimates) and the practice has been to suppress both interval width is greater than or when calculating annual or survey cycle proportions if one of the proportions is equal to 0.30, then the proportion estimates using a multiyear or multicycle identified as unreliable. However, this should be suppressed. data file. In these instances, the relevant practice may lead to the suppression of ○ If the absolute confidence information should be extracted and the important information. interval width is between degrees of freedom directly calculated to 0.05 and 0.30 and the relative assess estimate precision. The calculation Standard confidence interval width is more of degrees of freedom as a measure of than 130%, then the proportion precision for the SE may not be applicable ● If all criteria are met for presenting should be suppressed. for all surveys (see survey-specific the proportion but not for its ○ If the absolute confidence documentation) and does not apply to complement, then the proportion interval width is between vital statistics. For additional information should be shown. A footnote 0.05 and 0.30 and the relative on degrees of freedom, see Korn and indicating that the complement of the confidence interval width is Graubard (13) and Valliant and Rust (14). proportion may be unreliable should be provided.

Series 2, No. 175 Page 5 Discussion previously, measures derived solely from the SE (e.g., Wald CI and RSE) means are also regularly reported. Death rates, for example, are calculated as the can perform poorly for proportions. number of events reported in a calendar The NCHS Data Presentation Consequently, whenever space permits, year divided by the corresponding census Standards for Proportions will be applied appropriate CIs should be provided, population estimate at the midpoint of to all NCHS publications. Using these rather than just SEs. the calendar year. The NCHS Standards Standards, some estimates will be Age-adjusted estimates are often were not developed to apply to these identified as unreliable and suppressed produced for national statistics. Age estimators. Although the principles and some estimates will be flagged for adjustment allows for a comparison considered by the workgroup for statistical review. There are two scenarios of outcomes between two groups with proportions can be considered for other where the estimates will be flagged for differing age distributions, as many health estimators, including the evaluation of statistical review by a clearance official: outcomes are highly correlated with age effective sample size and CIs to guide a) when the number of events is 0 (or its (15,16). These estimates can be handled decisions, no specific thresholds for complement, equal to the denominator); in a similar manner as unadjusted these estimators are provided by these and b) for estimates from sample surveys estimates. There may be instances in Standards. Rates calculated from vital with fewer than 8 degrees of freedom. which the age-adjusted estimates will statistics will continue to use the criterion Statistical review by a clearance official not meet the presentation criteria but the of requiring 20 or more events for of flagged estimates will consider the crude estimate would, or vice versa. In reporting. In addition to precision, there recommendation of the analyst(s) and these cases, the estimate that meets the are other statistical issues, not addressed factors such as the estimate’s sample size, presentation criteria will be shown, and here, that affect the quality of the CI, and degrees of freedom; the report’s the one that does not will be suppressed. estimates, including measurement error objectives and format (including the If CIs for age-adjusted estimates are not and survey nonresponse (17). ability to present CIs or other measures readily obtained from survey software, The NCHS Data Presentation of precision); and the other estimates in the relevant information can be extracted Standards for Proportions can be the report to determine whether to present and the CIs can be directly calculated. considered in planning analytic studies or suppress the estimate. In some large For the NCHS Data Presentation or table shells for reports. Collapsing reports, this process may be automated Standards for Proportions, there is subgroups and aggregating years leads to ease the production process, with all no minimum number of events (i.e., to estimates with less uncertainty and flagged estimates suppressed without numerator size). For the calculation of might be more appropriate for a specific review. the Clopper-Pearson CI, a minimum report than disaggregated estimates, even When the NCHS Data Presentation numerator is not needed. A numerator when minimum presentation guidelines Standards for Proportions are used for with few events may provide useful are met. Other items to be considered shorter, more focused reports, specific information for some purposes. Although may include the intended use of the estimates that do not meet the standards observing no events (or its complement, estimate, the amount and structure of may be reported after being evaluated observing events for all records in supporting information about uncertainty individually by the analyst(s) and the category) can provide important that can be conveyed, and the availability clearance official(s). Some estimates information (e.g., in the context of of corresponding estimates for other identified as unreliable based on the subgroup-specific analyses of rare [or subgroups or other time periods. Standards may be important and can be prevalent] health outcomes), an estimate interpreted appropriately in the context of measures of precision and other subject- based on 0 events (or its complement) should be flagged for statistical review References specific information. In these cases, the to confirm the validity of the point and estimate could be presented. Because interval estimates. In addition, inferences 1. Klein RJ, Proctor SE, Boudreault report objectives and subject-specific based on the normal approximation, MA, Turczyn KM. Healthy People factors vary widely, justification for including statistical comparisons of 2010 criteria for data suppression. presenting an unreliable estimate should proportions between subgroups, require Statistical Notes, no 24. Hyattsville, be provided by the analyst(s) and final a minimum number of events. Finally, MD: National Center for Health determination should be made by the some estimates based on restricted data Statistics. 2002. analyst(s) and clearance official(s) on a or vital statistics may require a minimum 2. Clopper CJ, Pearson ES. The use case-by-case basis. In all publications, number of events to decrease disclosure of confidence or fiducial limits unreliable estimates, whether presented risks, and reporting of these estimates illustrated in the case of the or suppressed, should be identified with a may be based on different criteria (e.g., binomial. Biometrika 26(4):404–13. footnote. confidentiality). 1934. Many NCHS data products include Although most estimates produced SEs so that data users can assess the in NCHS reports are proportions, other precision of the point estimates. As stated estimates, such as rates, percentiles, and

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Series 2, No. 175 Page 7 Appendix I. Figure. Implementation of NCHS Data Presentation Standards for Proportions Calculate effective sample size Is nominal or effective YES sample size < 30? NO Calculate 95% confidence interval (CI) Is absolute value YES of CI width ≥ 0.30? Suppress NO YES Is absolute value of CI width ≤ 0.05? NO Calculate relative CI width Is relative CI width YES > 130% of the proportion? NO NO NO Is number of Are degrees of Present events = 0? freedom < 8? YES Statistical YES review SOURCE: NCHS, 2017.

Page 8 Series 2, No. 175 Appendix II. Examples of the Application of NCHS Data Presentation Standards for Proportions This appendix describes National only and should not be used as the Table I shows the percentage of Center for Health Statistics (NCHS) source for subject-specific information. children aged 8–17 years with elevated data sets and provides examples of the blood pressure, a relatively rare outcome application of the NCHS Presentation National Health and for children, by race and Hispanic origin Standards using excerpts of previously using the 2013–2014 NHANES data. published tables or new tabulations. Nutrition Examination Percentage estimates for elevated blood Shown in these examples are: the Survey pressure range from 0.5% among non- sample size, the effective sample Hispanic white children to 2.5% among size (when applicable), the estimated The National Health and Nutrition Hispanic children. For illustration, the proportion, the standard error (SE) of Examination Survey (NHANES) complements of these percentages, the the proportion, the upper and lower is a program of studies designed to percentages with normal or borderline bounds of the two-sided 95% Clopper- assess the health and nutritional status elevated blood pressure, are also shown. Pearson (or Korn-Graubard when of adults and children in the United States. Currently, the survey examines ● All sample sizes and effective applicable) confidence interval (CI), the a nationally representative sample of samples sizes are 30 or higher. absolute CI width, the relative CI width, about 5,000 participants each year. These ● Absolute CI widths for elevated high and, if appropriate, the degrees of participants are located in counties across blood pressure for non-Hispanic freedom and the number of events in the the country, 15 of which are included in white and Hispanic children are less numerator. Because survey estimates the sample each year. Data are released than 5 percentage points, so these with high relative standard errors in 2-year cycles. The NHANES interview estimates can be presented if the [RSE = 100% × (SE/Estimate)] have includes demographic, socioeconomic, number of events is not 0 (or equal to been marked as potentially unreliable dietary, and health-related questions. the denominator) and there are 8 or or suppressed in previous NCHS The examination component consists more degrees of freedom. publications, the implications of the of medical, dental, and physiological ● Absolute CI widths for elevated Standards are compared with decisions measurements, as well as laboratory tests high blood pressure for non- based on the RSE > 30% criterion administered by highly trained medical Hispanic black and Asian children for survey estimates. Estimates in the personnel (18). are between 5 and 30 percentage Appendix II tables are for illustration Table I. Percentage of children aged 8–17 years with elevated and normal or borderline blood pressure, by race and Hispanic origin: United States, 2013–2014 Standard Relative Race and Hispanic origin Sample Effective Percent error of standard Lower Upper Absolute Relative Degrees of 1 2 3 3 4 5 and blood pressure size sample size estimate percent error bound bound CI width CI width freedom Non-Hispanic white, 8 elevated . . . . . . . . . . . . . . . . 460 583.0 0.5 0.29 58.0 0.1 1.6 1.6 320.0 15 Non-Hispanic white, 8 normal or borderline . . . . . . . 460 583.0 99.5 0.29 0.3 98.4 99.9 1.6 1.6 15 Non-Hispanic black, 6 elevated . . . . . . . . . . . . . . . . 447 145.3 2.0 1.17 58.5 0.3 6.4 6.1 305.0 13 Non-Hispanic black, 7 normal or borderline . . . . . . . 447 145.3 98.0 1.17 1.2 93.6 99.7 6.1 6.2 13 Non-Hispanic Asian, 6 elevated . . . . . . . . . . . . . . . . 164 124.8 0.9 0.83 92.2 0.0 5.1 5.1 566.7 13 Non-Hispanic Asian, 7 normal or borderline . . . . . . . 164 124.8 99.1 0.83 0.8 94.9 100.0 5.1 5.2 13 8 Hispanic, elevated . . . . . . . . . 589 946.8 2.5 0.51 20.4 1.4 4.1 2.7 108.0 15 Hispanic, normal or 8 borderline . . . . . . . . . . . . . . . 589 946.8 97.5 0.51 0.5 95.9 98.6 2.7 2.8 15 1 Sample size divided by the design effect. It is calculated in this table using this formula: . 2 Standard error divided by the estimated percent multiplied by 100%. 3 Lower and upper confidence bounds were computed using the Korn-Graubard method. 4 Difference between the upper and lower confidence bounds. 5 Absolute width divided by the estimated percent multiplied by 100%. 6 Relative CI width is greater than 130%. Estimate would be suppressed. 7 Estimate would have a footnote indicating its complement is suppressed. 8 Effective sample size is greater than sample size. Sample size used in CI calculations. NOTES: CI is confidence interval. Percent estimate and its lower and upper confidence bounds are equal to the proportion estimate and its lower and upper confidence bounds, respectively, multiplied by 100. Standard error of percent and absolute CI width are expressed in percentage points. Numbers in the table are subject to rounding. SOURCE: NCHS, National Health and Nutrition Examination Survey.

Series 2, No. 175 Page 9 points, so the relative CI width Table II shows the prevalence of ● The degrees of freedom for non- should be examined. overweight among adults aged 60 and Hispanic Asian men and women are ● Relative CI widths for elevated high over by sex and race and Hispanic 7, indicating that these estimates blood pressure for non-Hispanic origin using NHANES 2013–2014 data. would be flagged for statistical black and non-Hispanic Asian Prevalence estimates for these subgroups review by the clearance official. children are greater than 130%, so range from around 25% for non-Hispanic ● The RSE for all subgroups is less these estimates would be suppressed. black and Asian women to more than than 30%. Under the RSE > 30% ● The number of events is greater than 50% for Hispanic men. suppression criterion, all estimates 0 (and not equal to the denominator) would have been presented, whereas ● All sample sizes and effective and there are more than 8 degrees using the NCHS Data Presentation sample sizes are 30 or higher. of freedom for all estimates, so Standards for Proportions, the ● Absolute CI widths for men in each estimates that have met all other percentage for non-Hispanic Asian race and Hispanic-origin group and sample size and CI criteria would be women would be suppressed. for Hispanic, non-Hispanic white, presented. and non-Hispanic black women are ● If the outcome of interest is the between 5 and 30 percentage points, National Health Interview complement (normal or borderline high blood pressure), the absolute so the relative CI width would be Survey examined. CI widths are the same. However, First fielded in 1957, the main ● The relative CI widths for men in the relative CI widths for non- objective of the National Health each race and Hispanic-origin group Hispanic black and non-Hispanic Interview Survey (NHIS) is to monitor and for Hispanic, non-Hispanic Asian children are less than 130%, the health of the U.S. population through white, and non-Hispanic black so these estimates would be the collection and analysis of data on a women are all less than 130%, so presented with a note indicating broad range of health topics (19). NHIS the percentages could be presented that their complements do not meet is conducted continuously throughout the if the degrees of freedom are 8 or presentation standards. calendar year, collecting data from the greater. ● Estimates of elevated blood pressure civilian noninstitutionalized population ● The absolute CI width for non- for non-Hispanic white children would of the United States. Each year, a Hispanic Asian women is 30.6 be presented using the NCHS Data representative sample of households percentage points, indicating that Presentation Standards for Proportions across the country is selected for NHIS the percentage would be suppressed. but would have been suppressed or using a multistage cluster sample design. ● The number of events for all identified as unreliable based on the Parsons et al. (2014) contains more estimates is greater than 0 (and not RSE > 30% criterion. information on the design and estimation equal to the denominator). methods for 2006–2015 (20). Table II. Percentage of adults aged 60 and over who are overweight, by sex and race and Hispanic origin: United States, 2013–2014 Effective Standard Relative Sample sample Percent error of standard Lower Upper Absolute Relative Degrees of size1 2 3 3 4 5 Sex and race and Hispanic origin size estimate percent error bound bound CI width CI width freedom Men Hispanic . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 124.3 52.2 4.49 8.6 42.0 61.5 19.5 37.4 11 Non-Hispanic white. . . . . . . . . . . . . . . . . . . 384 246.2 38.6 3.10 8.0 32.0 47.1 15.2 39.3 15 6 Non-Hispanic black. . . . . . . . . . . . . . . . . . . 195 240.7 34.9 3.06 8.8 27.6 45.2 17.6 50.5 12 6 7 Non-Hispanic Asian . . . . . . . . . . . . . . . . . . 74 108.8 47.8 4.79 10.0 33.8 62.6 28.7 60.1 7 Women Hispanic . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 152.1 36.1 3.89 10.8 27.7 47.7 20.1 55.6 12 Non-Hispanic white. . . . . . . . . . . . . . . . . . . 466 296.8 34.3 2.76 8.0 28.4 42.3 13.8 40.4 15 6 Non-Hispanic black. . . . . . . . . . . . . . . . . . . 175 236.5 25.1 2.83 11.3 18.2 36.5 18.3 72.8 12 6 8 Non-Hispanic Asian . . . . . . . . . . . . . . . . . . 82 107.9 25.0 4.16 16.6 14.6 45.2 30.6 122.4 7 1 Sample size divided by the design effect. It is calculated in this table using this formula: . 2 Standard error divided by the estimated percent multiplied by 100%. 3 Lower and upper confidence bounds were computed using the Korn-Graubard method. 4 Difference between the upper and lower confidence bounds. 5 Absolute width divided by the estimated percent multiplied by 100%. 6 Effective sample size is greater than sample size. Sample size used for CI calculations. 7 Degrees of freedom fewer than 8. Estimate would be flagged for statistical review by the clearance official and may be presented or suppressed. 8 Absolute CI width is greater than or equal to 30. Estimate would be suppressed. NOTES: CI is confidence interval. Overweight is defined as a body mass index (BMI) of at least 25 but less than 30 kilograms per square meter. BMI is calculated as weight (kilograms) divided by height squared (meters). Percent estimate and its lower and upper confidence bounds are equal to the proportion estimate and its lower and upper confidence bounds, respectively, multiplied by 100. Standard error of percent and absolute CI width are expressed in percentage points. Numbers in the table are subject to rounding. SOURCE: NCHS, National Health and Nutrition Examination Survey.

Page 10 Series 2, No. 175 Table III illustrates the application of denominator), so percentages that anesthesiologists, and radiologists) and to the presentation standards using an meet all other sample size and CI community health centers. The sampling excerpt of data from the 2013 NHIS, criteria for presentation would be frames for physicians are constructed showing hearing difficulty among adults presented. from the master files of the American by race and Hispanic origin and family ● The RSE for several subgroups, Medical Association and the American income relative to the federal poverty including Hispanic adults with Osteopathic Association; the sampling level (FPL). Percentage estimates range incomes below the FPL, 200%–399% frames for community health centers from 0.47% among non-Hispanic black of the FPL, and 400% of the FPL or are obtained from the federal Health adults with incomes 400% of the FPL higher and non-Hispanic black adults Resources and Services Administration and higher to 3.2% among non-Hispanic with incomes 200%–399% of the and the Indian Health Service. NAMCS white adults with incomes below the FPL and 400% of the FPL or higher data were collected on approximately FPL. NHIS guidelines do not recommend is greater than 30%. Percentages for 32,000 and 31,000 visits to office- calculating degrees of freedom using these subgroups would have been based physician practices in samples variance units available on the data file suppressed or identified as unreliable of geographic primary sampling units (https://www.cdc.gov/nchs/data/ using the RSE > 30% criterion (PSUs) in 2009 and 2010, respectively. nhis/2006var.pdf). For national estimates, but would be presented using the The National Hospital Ambulatory the degrees of freedom are assumed to be NCHS Data Presentation Standards Medical Care Survey (NHAMCS) large enough for a normal approximation. for Proportions. is a nationally representative survey Table III is based on Table 49 in Health, of nonfederal general and short-stay United States, 2014 (21). National Ambulatory Medical hospitals that is conducted annually. NHAMCS uses a multistage probability ● All sample sizes and effective Care Survey and National design with samples of geographic sample sizes are 30 or higher. ● All absolute CI widths are less Hospital Ambulatory Medical PSUs, hospitals within PSUs, and than 5 percentage points, so all Care Survey patient visits within emergency and outpatient departments. NHAMCS data percentages should be presented The National Ambulatory Medical were collected on approximately 35,000 if the number of events is greater Care Survey (NAMCS) is an annual, emergency department visits in both than 0 (and not equal to the nationally representative survey 2009 and 2010 and on approximately denominator). of visits to nonfederal office-based 34,000 and 35,000 outpatient department ● The numbers of events are all physicians (excluding pathologists, visits in 2009 and 2010, respectively. greater than 0 (and not equal to the Table III. Percentage of adults aged 18 and over with hearing difficulties, by race and Hispanic origin and family income: United States, 2013 Effective Standard Relative Race and Hispanic origin and Sample sample Percent error of standard Lower Upper Absolute Relative 1 2 3 3 4 5 family income (percentage of FPL) size size estimate percent error bound bound CI width CI width Hispanic Under 100% . . . . . . . . . . . . . . . . . . . . . 1,675 559.3 1.43 0.50 35.2 0.62 2.79 2.18 152.7 100%–199% . . . . . . . . . . . . . . . . . . . . . 1,744 1,061.7 1.55 0.38 24.4 0.90 2.49 1.59 102.6 200%–399% . . . . . . . . . . . . . . . . . . . . . 1,621 586.8 1.10 0.43 39.1 0.42 2.32 1.90 172.0 400% and higher . . . . . . . . . . . . . . . . . 903 516.1 0.80 0.39 49.1 0.22 2.00 1.78 223.6 Non-Hispanic white Under 100% . . . . . . . . . . . . . . . . . . . . . 2,468 1,514.3 3.21 0.45 14.1 2.38 4.22 1.85 57.5 100%–199% . . . . . . . . . . . . . . . . . . . . . 3,650 3,167.7 2.86 0.30 10.3 2.31 3.51 1.19 41.7 200%–399% . . . . . . . . . . . . . . . . . . . . . 6,419 4,713.9 2.36 0.22 9.4 1.95 2.84 0.89 37.7 400% and higher . . . . . . . . . . . . . . . . . 8,020 4,909.4 1.78 0.19 10.5 1.43 2.19 0.76 42.7 Non-Hispanic black Under 100% . . . . . . . . . . . . . . . . . . . . . 1,470 912.8 1.36 0.38 28.2 0.72 2.35 1.63 119.6 6 100%–199% . . . . . . . . . . . . . . . . . . . . . 1,367 1,421.8 1.11 0.28 25.0 0.63 1.83 1.20 107.4 200%–399% . . . . . . . . . . . . . . . . . . . . . 1,375 1,143.7 0.71 0.25 35.0 0.31 1.38 1.08 152.2 6 400% and higher . . . . . . . . . . . . . . . . . 940 1,301.5 0.47 0.19 40.3 0.14 1.15 1.01 214.9 1 Sample size divided by the design effect. It is calculated in this table using this formula: . 2 Standard error divided by the estimated percent multiplied by 100%. 3 Lower and upper confidence bounds were computed using the Korn-Graubard method. 4 Difference between the upper and lower confidence bounds. 5 Absolute width divided by the estimated percent multiplied by 100%. 6 Effective sample size is greater than the sample size. Sample size is used in CI calculations. NOTES: FPL is federal poverty level. CI is confidence interval. Percent estimate and its lower and upper confidence bounds are equal to the proportion estimate and its lower and upper confidence bounds, respectively, multiplied by 100. Standard error of percent and absolute CI width are expressed in percentage points. This table is based on Health, United States, 2014 Table 49. Numbers in the table are subject to rounding. SOURCE: NCHS, National Health Interview Survey.

Series 2, No. 175 Page 11 More details about the designs of neoplasm of breast visits to primary so this estimate would have been NAMCS and NHAMCS are available care offices are less than 30, so these suppressed or identified as unreliable elsewhere (22,23). estimates would be suppressed. using the RSE > 30% criterion Table IV shows the percent ● Absolute CI widths for the but would be presented using distribution of ambulatory care visits percentage of malignant neoplasms the NCHS Data Standards for by setting type according to diagnosis of colon and rectum visits and the Proportions. group for two conditions: a) malignant percentage of malignant neoplasm ● The RSEs for the percentage of neoplasms of the colon and rectum and of breast visits to emergency malignant neoplasms of colon and b) malignant neoplasm of the breast. As departments are less than 5 rectum visits and the percentage these are percent distributions, the sum percentage points, so these estimates of malignant neoplasm of breast of the values across all settings is 100%, could be presented if the number of visits in medical specialty physician and the values range from less than 1% to events is not 0 (and not equal to the offices are each less than 30%, so more than 50%. As a result, if one value denominators) and the other criteria these estimates would have been is suppressed among the setting types, it for presentation are met. presented using the RSE > 30% may be inferred from those shown. These ● Absolute CI widths for the suppression criterion but would be data are an extract of a larger table found percentage of malignant neoplasms suppressed using the NCHS Data at: https://www.cdc.gov/nchs/data/ahcd/ of colon and rectum visits and the Standards for Proportions. combined_tables/2009-2010_combined_ percentage of malignant neoplasm web_table01.pdf. For this table, data for of breast visits in medical specialty National Survey of Family visits to office-based practices of physician offices are greater than 30 physicians in primary care, surgical percentage points, so these estimates Growth specialties, and medical specialties would be suppressed. The primary purpose of the National were obtained from the 2009–2010 ● Degrees of freedom are all greater Survey of Family Growth (NSFG) NAMCS, and data for visits to outpatient than 8 and the numbers of events are is to produce national estimates of: departments and emergency departments all greater than 0 (and not equal to factors affecting pregnancy, including were obtained from the 2009–2010 the denominator), so estimates that sexual activity, contraceptive use, and NHAMCS. meet all other sample size and CI infertility; medical care associated with criteria for presentation would be contraception, infertility, and childbirth; ● Design effects (not shown) for many presented. factors affecting marriage, divorce, estimates are large. Effective sample ● The RSE for the percentage of cohabitation, and family building; sizes for the percentage of malignant malignant neoplasms of colon and adoption and caring for nonbiological neoplasms of colon and rectum rectum visits made to emergency children; fathers’ involvement with their visits and percentage of malignant departments is greater than 30%, children; use of sexual and reproductive Table IV. Percentage of ambulatory care visits, by setting type according to diagnosis: United States, 2009–2010 Effective Standard Relative Sample sample Percent error of standard Lower Upper Absolute Relative Degrees of size1 2 3 3 4 5 Diagnosis and setting type size estimate percent error bound bound CI width CI width freedom Malignant neoplasms of colon and rectum 6 Primary care office . . . . . . . . . . . . . . . . . . . . 411 22.4 12.4 6.6 56.2 2.4 33.0 30.6 247.7 52 Surgical specialty office . . . . . . . . . . . . . . . . 411 68.1 17.3 4.6 26.5 9.2 28.4 19.2 110.6 52 7 Medical specialty office. . . . . . . . . . . . . . . . . 411 37.5 53.4 8.2 15.3 36.5 69.8 33.3 62.4 52 Hospital outpatient department . . . . . . . . . . 411 64.4 16.3 4.6 28.2 8.3 27.6 19.3 118.3 52 8 Hospital emergency department. . . . . . . . . . 411 416.7 0.6 0.4 64.3 0.1 1.9 1.8 311.2 52 Malignant neoplasm of breast 6 Primary care office . . . . . . . . . . . . . . . . . . . . 1,006 22.3 10.4 6.5 62.0 1.6 30.7 29.1 278.8 77 Surgical specialty office . . . . . . . . . . . . . . . . 1,006 97.8 19.4 4.0 20.6 12.1 28.6 16.5 85.3 77 7 Medical specialty office. . . . . . . . . . . . . . . . . 1,006 42.4 54.2 7.6 14.1 38.2 69.6 31.4 57.9 77 Hospital outpatient department . . . . . . . . . . 1,006 71.4 15.8 4.3 27.4 8.2 26.3 18.1 114.8 77 Hospital emergency department. . . . . . . . . . 1,006 57.7 0.2 0.1 27.4 0.0 0.8 0.7 316.8 77 1 Sample size divided by the design effect. It is calculated in this table using this formula: . 2 Standard error divided by the estimated percent multiplied by 100%. 3 Lower and upper confidence bounds were computed using the Korn-Graubard method. 4 Difference between the upper and lower confidence bounds. 5 Absolute width divided by the estimated percent multiplied by 100%. 6 Effective sample size is less than 30. Estimate would be suppressed. 7 Absolute CI width is greater than or equal to 30. Estimate would be suppressed. 8 Effective sample size is greater than sample size. Sample size used in CI calculations. NOTES: CI is confidence interval. Percent estimate and its lower and upper confidence bounds are equal to the proportion estimate and its lower and upper confidence bounds, respectively, multiplied by 100. Standard error of percent and absolute CI width are expressed in percentage points. Numbers in the table are subject to rounding. SOURCES: NCHS, National Ambulatory Medical Care Survey and National Hospital Ambulatory Medical Care Survey.

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