National Center for Health Statistics

NCHS Data Presentation Standards for 

Rates and Counts

Jennifer D. Parker

Director, Division of Research and Methodology

National Center for Health Statistics

FCSM Research and Policy Conference

October 25, 2022

Session 18: Data Linkage, Privacy, and Modernization
The National Center for Health Statistics

 Principal statistical agency for health in the United States

 1960 - National Office of Vital Statistics and the National Health Survey 

merged to form National Center for Health Statistics

 1987 - NCHS became part of the Centers for Disease Control and 

Prevention

 Remains the official Federal Health Statistics Agency and part of the 

Federal Statistical System
Suppress unreliable estimates? 

Yes, in some publications.

 Some publications do not have the format for standard errors or 

other indicators of precision alongside estimates to inform user.

• Infographics, social media, some visualizations

 Do not fully trust the data user.

• Misinterpretation of statistics can reflect badly on the agency and federal 

statistics more broadly.

 Nearly all NCHS estimates can be obtained using public use data 

sources and all can be obtained in the Research Data Center, subject 

to disclosure review.

• Users who calculate estimates may be better able to interpret the results.
Suppress estimates?

Yes, in some publications.

 Some publications do not have the format 

for standard errors or other indicators of 

precision alongside estimates to inform user.

• Infographics, social media, some 

visualizations

 Do not fully trust the data user.

• Misinterpretation of statistics can reflect 

badly on the agency and federal statistics 

more broadly.

 Nearly all NCHS estimates can be obtained 

using public use data sources and all can be 

obtained in the Research Data Center, 

subject to disclosure review.

• Users who calculate estimates may be better 

able to interpret the results.

No.

 Estimates can be informative 

even if they’re not precise.

 Data for small subgroups may 

never meet conventional 

standards of ‘good-enough’ but 

information for these groups is 

needed for decisions.

 Trust the data user.
NCHS Data Presentation Standards for Proportions 

released August 2017

 Standard

• Criteria based on minimum sample size and 

absolute and relative width of exact confidence 

interval.

• Estimated proportions with few degrees of 

freedom or with suppressed complementary 

proportions are to be evaluated individually.

 Implementation generally led to more 

estimates presented compared to prior 

presentation criteria.
Why presentation standards for rates?

 Crude, age-specific, and age-adjusted rates are widely 

disseminated by NCHS 

– Vital statistics

• Death rates

• Birth rates, fertility rates

– Health care statistics

• Visit rates

• Hospitalization rates

 Counts follow as the ‘numerator’ of the rate
What are rates?

 The working definition of a rate is the estimated number of 

events for a given time period (typically year) divided by a 

population count for the number at risk during that year 

(typically a Census mid-year population count) and often 

multiplied by a constant.

 Age-adjusted rates: linear combination of age-specific rates 

standardized to a standard US population.
Drug 

overdose 

death rates 

among those 

aged 15 and 

over, by 

selected age 

group. US 

2019-2020

Hedegaard H, Miniño AM, Spencer MR, Warner M. Drug overdose deaths in the United States, 1999–2020. NCHS Data Brief, no 428. Hyattsville, MD: NCHS. 2021.
Suggested citation Heron M. Deaths: Leading causes for 2019. National Vital Statistics Reports; vol 70 no 9. Hyattsville, MD:

National Center for Health Statistics. 2021. DOI: https://dx.doi. org/10.15620/cdc:107021
Emergency 

department 

visit rates for 

motor vehicle 

crashes, for 

total and by 

age group: US 

2017-2018

Davis D, Cairns C. Emergency department visit rates for motor vehicle crashes by selected characteristics: United States, 2017–2018. NCHS Data Brief, no 410. 

Hyattsville, MD: National Center for Health Statistics. 2021
Percentage of 

adult ED visits with 

and without 

mental health 

disorders that 

resulted in a 

hospital 

admission, by age

Santo L, Peters ZJ, DeFrances CJ. 

Emergency department visits among 

adults with mental health disorders: 

United States, 2017–2019. NCHS Data 

Brief, no 426. Hyattsville, MD: National 

Center for Health Statistics. 2021
Types of rates

 Rates with numerators subject to random variability and denominators 

assumed relatively free from variability from vital statistics, including:

– National and state death rates; age-specific deaths rates, including infant 

death rates (deaths for persons under 1 year of age); birth rates, fertility rates.

 Rates with numerators from surveys subject to sampling variability and 

denominators assumed relatively free from variability, including:

– National and some subnational health care visit rates.
Types of rates (2)

 Rates with numerators subject to sampling variability and 

denominators subject to sampling variability, including:

– Condition specific rates where population denominator is estimated 

from a survey, such as the National Health Interview Survey.
Presentation Criteria for Rates and Counts

 Minimum sample size or effective sample size

– Minimum sample size and effective sample size (when applicable) of 10 in the 

numerator (rates and counts) and in the denominator (rates only).

 Maximum relative width of confidence interval

– If the sample size criteria are met, calculate a 95% two-sided confidence interval using 

the appropriate method and obtain its relative width. 

– Appropriate confidence interval method used ensures 95% coverage.

– Estimated rates should have a relative confidence interval width of 160% or lower. 

 Minimum degrees of freedom

– When applicable, if the degrees of freedom are fewer than 8 then flag for statistical 

review.

Variability

 Numerators or denominators estimated from a survey are subject to sampling variability. 

 Even when the actual number of events in the numerator or the size of the population at 

risk in the denominator is recorded and is free from sampling variability, there is natural 

(or “stochastic”) variability in the realized values. 

– For numerators or denominators enumerated from vital statistics and free of 

sampling variability, the number of events (that is, deaths or births) will be assumed 

to arise from a Poisson distribution. 

– For a denominator that is enumerated from a decennial Census or 

postcensal/intercensal population estimate there may be some natural variability in 

the realized value, however such random variation will be considered negligible and 

will not be considered in calculations.
Presentation Criteria – Confidence Intervals for Rates 

without sampling variability (1)

 Numerator subject to random variation and denominator assumed free from 

variability

– Calculate gamma interval* where the lower limit is the 0.025 quantile of the 

standard gamma with α=x and β=1, where x=number of vital events, and the 

upper limit is the 0.975 quantile of the standard gamma with α=x+1 and β=1. 

– For age-specific and crude rates, this confidence interval is considered exact.

– The adjustment used by Fay-Feuer should be applied for age-adjusted vital rates.

* In Excel, the function GAMMA.INV (probability, alpha, beta), with beta set to 1, returns the quantile of the 

standard gamma distribution for a given probability between 0 and 1. For 95% confidence limits, the probability 

associated with the lower limit is 0.05/2 = 0.025, and with the upper limit 1 - (0.05/2) = 0.975. 
Presentation Criteria – Confidence Intervals for Rates 

without sampling variability (2)

 Numerator and denominator subject to random variation 

(infant mortality rates)

– Calculate a Student’s t confidence interval for the logarithm of the rate 

and transform to get CI for the rate.

( ) /2, df 2 exp ln v

r t

r

α

      ±

   

2

1 1 x

v

y xy

  

= +       

The rate r = x/y, x is number of infant deaths, y is number of live births, v is the 

variance of r. df=min(x,y)-1
Presentation Criteria – Confidence Intervals for Rates 

with sampling variability (1)

 Numerator from survey (e.g., National Health Care Survey) with sampling 

variability, and denominator assumed free from variability

– Calculate a Student's t confidence interval for the logarithm of the rate 

and transform to get CI for the rate.

( )

2

/2, 2

1 exp ln x

df

s

x t

y x

α

      ±

   

The rate r = x/y, x is the estimated number of events, y is the population count assumed 

free of variation, and sx

2 is the standard error of x. df=min(nx, nx_eff)-1
Presentation Criteria – Confidence Intervals for Rates 

with sampling variability (2)

 Numerator subject to random variation and denominator 

subject to sampling variability

– Calculate a Student's t interval for the logarithm of the rate. 

Parameters for intervals for age-adjusted intervals can be formed using 

weighted combination of age-specific intervals.

The rate r = x/y and sy is the standard error of y. v is the variance of the rate. df=min(x, n y ,nyeff)-1

NOTE: When the denominator is based on the ACS or CPS and subject to sampling variability, the CI uses 

GVF parameters provided by Census

( ) /2, df 2 exp ln v

r t

r

α

   

  ±

   

2 2

2

1 y x s

v

y xy

   

= +        
Presentation Criteria – Confidence Intervals for Rates 

with sampling variability (3)

 Numerator and denominator both subject to sampling 

variability

– Calculate a Student’s t confidence interval for the logarithm of the rate

– The interval accounts for the sampling variability of the denominator

2 2

/2, 2 2 exp ln x ydf

x s s

t

y xy

α

          ± +

     

The rate r = x/y, x and y are survey estimates of outcomes and population. sx and 

sy are the standard errors of x and y. Df=min(nx, nx_eff, ny, ny_eff)-1
Evaluations for Vital Statistics

 Distributional assumptions: comparison of ‘exact’ gamma interval width 

thresholds, relative standard errors (RSE), and counts

 Age-adjusted death rates: simulation-based comparison of AndersonRosenberg method, used at NCHS and in CDC WONDER, with approaches 

by Fay/Feuer and Tiwari et al, used in U.S. Cancer registries.

 Simulation to examine proposed and previous standards for county-level 

data by race/Hispanic origin and cause of death

 Simulations evaluating log Student’s t interval for non-constant 

denominator, including correlation assumptions for numerator and 

denominator
Evaluations for National Health Care Surveys

 Simulations based on NAMCS data structure

– Evaluation of confidence intervals when the denominator is constant

– Evaluation of confidence intervals by nominal and effective sample 

sizes and survey years when the denominator is constant

– Evaluation of the design effect using row proportions and using totals 

or counts when the denominator is constant

– Evaluation of rates and age-adjusted rates when both the numerator 

and the denominator are non-constant
Next Steps

 Reports

– The National Center for Health Statistics Data Presentation 

Standards for Rates and Counts

– Evaluation of the National Center for Health Statistics Data 

Presentation Standard for Rates from Vital Statistics and 

Sample Surveys

 Implementation with NCHS Data Systems with 2023 data

 Web page with worked examples
Data Presentation Standards Workgroup

• Amy Branum

• Barnali Das

• Danielle Davis

• Brady Hamilton

• Katherine Irimata

• Ken Kochanek

• Don Malec (retired)

• Frances McCarty (SIS, Virginia Tech)

• Jennifer Parker

• Alex Strashny

• Makram Talih (SIS)

• Guangyu Zhang
Jennifer Parker 

jdparker@cdc.gov

Questions?
Presentation Criteria – Confidence Intervals for Rates 

with sampling variability (4)

 Denominators subject to sampling variability from American Community 

Survey

– Calculate a Student’s t interval for the logarithm of the rates with variance 

estimated using generalized variance function (GVF) with parameters supplied 

by Census. Parameters for age-adjusted intervals can be formed using 

weighted combinations of age-specific estimates.

Rate r =x/y. x is number of vital events; y is population estimate. v is the variance of r. 

Parameters for GVF, a and b, provided by Census. df=min(x,y)-1

( ) /2, df 2 exp ln v

r t

r

α

      ±

   

2

2

1 1 and x bv b v fa f a

yx y rx y

      

= + + =+ +              