1

VARIANCE ESTIMATION FOR PERSON DATA USING THE

NHIS PUBLIC USE PERSON DATA TAPE, 1995

January 21,1998 

(See Notes at end of this document for application to the Year 2000 Objectives data file.) 

Introduction: The data collected in the NHIS are obtained through a complex sample design involving

stratification, clustering, and multistage sampling, and the final weights are subject to several

adjustments. Any variance estimation methodology must involve numerous simplifying assumptions

about the design and weighting. We provide some oversimplified conceptual NHIS design structures

that should allow users of this Public Use Data Set to compute reasonably accurate standard errors. 

There are several available software packages for analyzing complex samples. A comparison is

beyond the scope of this document, but an Internet web page Summary of Survey Analysis Software

currently located at http://www.fas.harvard.edu/~stats/survey-soft/survey-soft.html provides

references and discussion. At NCHS the software package SUDAAN has been used to produce ®

standard errors. In this document SAS and SUDAAN computer code is provided, but without ® ®

guarantees of any kind. The computer code and methods are subject to change without notification

to the user. The entire risk as to the results and performance is assumed by the user. NCHS

recommends that any analysis of NHIS data be done under the supervision of a statistician who

understands the implications of complex-sample design surveys.

Conceptual NHIS design for 1995 The U.S. Bureau of the Census partitions the state counties or

equivalents along with metropolitan areas into a universe of about 1900 Primary Sampling Units

(PSUs) (note, PSUs may be combined counties) to provide the primary sampling areas for its many

national surveys. For the NHIS these universe PSUs are partitioned into geographical strata at the

state level. Some of the larger universe PSUs are self-representing (SR) , i.e, they are in the NHIS

with certainty. The other PSUs are called non-self-representing (NSR) or non-certainty PSUs. Within

each state the NSR PSUs are partitioned into strata based upon similarity of PSU characteristics. 

Within each NSR stratum 2 PSUs are selected using Durbin’s probability proportional to size (PPS)

sampling method using the population as a measure of size. (In some smaller states only 1 PSU is

drawn PPS). The SR PSUs are equivalent to strata, but historically they have been referred to as

PSUs. (PPS and Durbin sampling are discussed in Chapter 9A of Cochran (1977)).

Within a sampled NSR or SR PSU the geography is partitioned into smaller geographical clusters

which are used to form the universe of secondary sampling units (SSUs). These SSUs are then

partitioned into density strata based upon black and Hispanic population concentration as determined

by the 1990 Decennial Census. An additional strata for new construction since the last Decennial

Census is also created. Within each density stratum SSUs are sampled at different rates to meet

different design objectives. Within each sample SSU, all households containing black or Hispanic

persons are sampled, while all other households are subsampled. Supplemental NHIS surveys may

require additional sampling at SSU, household, or family levels. 

The fundamental sampling weights are created such that under ideal sampling conditions, unbiased

estimators for each level of sampling are available. In practice, however, the final sampling weights

are adjusted for non-response, and ratio adjusted. Furthermore, in 1995 a government shutdown

resulted in three lost weeks of sample which resulted in further weighting adjustments. The most

important adjustment is a quarterly post-stratification to 90 age/sex/race/ethnicity Census control 

totals.

For variance estimation purposes, NCHS treats the NHIS as a two-stage sample. The PSU

probabilities of selection are known, and the SSUs are treated as sampled with replacement within

PSU density strata. Sampling weights are adjusted by postratification. With these assumptions the

SUDAAN software is used to compute variances. Much of the design information, state, density

strata, and Durbin probabilities can be used to identify the smaller geographical areas. NCHS forbids

the disclosure of information which may compromise the confidentiality promised to survey

respondents, so some design information is not provided with the Public Use Data. While all design
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information is not available to the public, variance estimation methods exist which provide similar

results to the NCHS internally used methodology. Two methods are described below.

Design Information Available on the NHIS Public Use Databases.

The following variables are used to produce code for variance estimation. Field locations below are

from the PERSON level database, but may change on other databases; the user should check the

file documentation. 

Variable Tape

Name Location Field Label

STRAT_V 337-340 'STRATA FOR VARIANCE ESTIMATION'

PSU_V 341 'PSU FOR VARIANCE ESTIMATION’

SUB_V 342-343 'SUBSTRATUM FOR VARIANCE ESTIMATION'

SSU 344-350 ‘SECONDARY SAMPLING UNIT’

 

PANEL 352 ‘PANEL 4'

TYPE_PSU 351 'TYPE OF PSU' 

 

WTF 219-227 'FINAL BASIC WEIGHT' 

Two methods of variance estimation are provided.

Method 1 - 187 Strata containing 2 PSUs per stratum sampled with replacement

Here, the NHIS universe has been partitioned into 187 strata. Most of the original NHIS strata and

PSUs retain their original sampling structure with two PSUs being sampled per stratum, but a few

strata have been collapsed, and in the largest self-representing strata, two pseudo-PSUs have been

created. All PSUs are treated as sampled with replacement within their respective strata. This

method will provide somewhat conservative standard errors, and the standard error estimator 

itself has less stability than the standard error estimator described by Method 2 below. Method 1

should be applicable to many complex survey sample design computer programs which require

exactly 2 sampled PSUs per stratum. This method is robust when analyzing subsetted data (See

the section “Subsetted Data Analysis” below).

Coding required (SAS code provided): ®

STRATUM = STRAT_V ;

PSU = PANEL ;

IF (PSU_V = 5 ) THEN PSU = INT( ( PANEL + 1) /2 ) ; 

IF( PSU_V = 8 ) THEN STRATUM = 553 ;

IF( (TYPE_PSU = 1) AND (PSU_V IN (2,4) ) ) THEN STRATUM = (STRAT_V -1 ) ;

 

IF( ( STRAT_V = 921) AND (PSU_V = 3) ) THEN STRATUM = 901 ;

As a check the user should observe 374 PSUs when using the full database.
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For the above simplification of the NHIS sample design structure, the following SUDAAN design ®

statements may be used. (Note, the input file must first be sorted by STRATUM and PSU 

variables.)

 PROC ... DESIGN = WR;

 NEST STRATUM PSU ;

 WEIGHT WTF ;

See the Section “Worked SUDAAN Examples” below for further discussion.

Method 2 - Multiple PSUs per Stratum design sampled with replacement

This method provides for more statistically efficient variance estimation than Method 1, since it

makes better use of the sampling design information. Its application is limited to software that can

handle multiple PSUs per stratum, e.g., SUDAAN. For this method the original certainty PSUs are

partitioned by aggregations of the original race-ethnic density strata used in sampling. The first

randomly sampled unit is actually the SSU variable which is now treated as the PSU variable. 

(Note, a certainty PSU unit contributes nothing to the variance at the PSU sampling level.) Noncertainty-strata PSUs are treated as being sampled with replacement within their respective strata. 

Except for a few special cases, the non-certainty PSUs have exactly the same structure in both

Methods 1 and 2. 

Coding required, ( SAS code provided ): ®

IF TYPE_PSU = 1 THEN DO ; /* certainty strata PSUs */

 STRATUM = STRAT_V*1000 + SUB_V ;

 PSU = SSU ;

 END ;

 

 ELSE DO ; /* non-certainty PSU */ ;

 

 STRATUM = STRAT_V ;

 PSU = PSU_V ;

 END ;

As a check, the user should observe the following counts:

Certainty Strata PSUs 4079

Non-certainty Strata PSUs 259

Total PSUs 4338

For the Method 2 design structure, the following SUDAAN design statements may be used. (Note, ®

the input file must first be sorted by STRATUM and PSU variables.)

 PROC ... DESIGN = WR;

 NEST STRATUM PSU ;

 WEIGHT WTF ;

See the Section “Worked SUDAAN Examples” for further discussion.
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;CAUTION. Method 2 should only be used on a full sample person data base. Using this method

with subsetted data may lead to incorrectly computed standard errors. ( See the section 

“Subsetted Data Analysis” below). If using a subsetted data set, the user should check the degree

of agreement of the certainty and non-certainty counts with the values presented above.

;CAUTION

 A typically used rule-of-thumb for degrees of freedom to associate with a standard error is the

quantity (number of PSUs - number of strata). This rule assumes that the PSUs are somewhat

comparable in size. For Method 2 this rule may be grossly inaccurate since the concept of PSU is

quite different for certainty and non-certainty strata. Certainty strata PSUs of Method 2 have small

weighted values relative to those of non-certainty PSUs. The rule-of-thumb degrees of freedom 

for Method 1 is 187, and Method 2 should have a “true” degrees of freedom exceeding that of

Method 1. However, for practical purposes, any degrees of freedom exceeding 120 can be treated

as infinite, i.e., one uses a normal Z-statistic instead of a t-statistic for testing. Note, that a onetailed critical t at 120 degrees of freedom is 1.98 while at an infinite degrees of freedom (i.e., a 0.025

z-value) is 1.96. If a variable of interest covers most of the NHIS PSUs, the limiting value would

probably be adequate for analysis. The user should consult a mathematical statistician for

discussion of degrees of freedom.

SUBSETTED DATA ANALYSES

 Frequently, studies of NHIS variables are restricted to select subdomains, e.g., persons aged 65

and older. To save on storage the user may delete all records outside of the domain of interest. 

This procedure of keeping only select records is called subsetting the data. With a subsetted data

set one can produce correct point estimates, e.g., the subdomain means, but standard errors may

be computed incorrectly when using a compromised design structure. For example, if a stratum of

Method 2 contains 10 PSUs and 5 are lost because of subsetting, a SUDAAN run on the subsetted

data will use an incorrect formula to compute stratum contributions to the variance. If the full 

data are run, SUDAAN correctly handles the 5 empty PSUs. Note, that SUDAAN has a SUBPOPN

option that allows the targeting of a subdomain from a full design data base. ( See the SUDAAN

manual for details ). 

Subsetting methods with SUDAAN

Strategy 1. Use Method 1 above with the MISSUNIT option on the NEST statement -

 NEST STRATUM PSU/ MISSUNIT ;

If a WR design has exactly 2 PSUs per stratum and some PSUs are removed from the database

then the SUDAAN MISSUNIT option performs a fix-up which produces a standard error identical to

that achieved when using a full data set and SUBPOPN statement. Note, other output like design

effects, degrees of freedom, standardization may be computed differently. The user is responsible

for checking that subsetted input leads to correct results.

Strategy 2. Use Method 1 or 2 above on a “fixed-up” subsetted data set. Basically, one needs to

add some dummy records containing full design information to the subsetted data set. To do this

follow these instructions: 

1. Create a 2-variable file containing STRATUM and PSU for each record of the full person file

 ( 100,000+ records )

2. Sort this file by STRATUM and PSU within STRATUM. 

3. Keep only 1 record for each PSU 

 add WTF = 10 as a very small weight -10

 add variable DUMMY = 0 to designate dummy record

 

 A file, called DESIGN containing 4 variables with 

 374 records ( Method 1 used) or with

 4338 records (Method 2 used) is created
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4. Append DESIGN to the original subsetted database, called DATASET, to form a new set, called

DATANEW.

 

 Define DUMMY = 1 on the DATASET component. 

 

 On the DESIGN component records define all variables other than STRATUM, PSU, WTF,

DUMMY as missing “.” . 

5. Sort DATANEW by STRATUM PSU

6. In SUDAAN use a "SUBPOPN DUMMY = 1;” line to direct SUDAAN to restrict estimation to the

subdomain of interest.

With the above fix-up SUDAAN will correctly handle empty PSUs when computing the standard

errors. SUDAAN output that needs the entire full sample database for correct computation, e.g,

design effects, may or may not be appropriate. See the SUDAAN manual for computational forms

or consult with a mathematical statistician for correct interpretation.

Other notes on Subsetting data: 

If a subsetted database under Method 2 has only a few missing PSUs , the subsetted database can

probably be run with SUDAAN without being fixed up. For example, a subsetting by SEX will most

likely result in all PSUs still being in sample, but black males aged 65 and older would result in the

loss of many PSUs. The impact of running SUDAAN on uncorrected subsetted data varies. 

Frequently, subsetted runs produce results consistent with those run on a full data set, but

sometimes they do not. 

Subsetting by aggregates of Strata does not need a fix-up.

The condition, doctor visit, and hospital record databases are actually subsetted files. To use with

SUDAAN properly, the information should be linked back to the appropriate person on the person

file. Some statistics, based upon aggregation of records, may be computed directly from this file

along with the fix-up. Consult with a statistician for appropriate SUDAAN usage.
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 WORKED SUDAAN EXAMPLES

In the following runs the variables used are 

LDR = proportion of persons without a doctor visit in the last 2 years

TDV_R = mean number of annual doctor visits (based upon 2 week recall) 

HLT_FP = proportion of persons with self-reported fair or poor health status ( omitting missing) 

AGE2: 1 =aged less than 18 

2 =aged 18 to 44

3 = aged 45 to 64

4 = aged 65 and older 

 The following SUDAAN code was executed for both Method 1 and Method 2:

; Caution The output presented below is based upon a preliminary NHIS Public Use database.

Your Public Use database may produce slightly different SUDAAN output.

 PROC DESCRIPT DATA = HIS.infile FILETYPE=SAS DESIGN = WR; 

 

 NEST STRATUM PSU ;

 WEIGHT WTF;

 

 VAR LDR TDV_R HLT_FP ;

 

 SUBGROUP SEX AGE2;

 LEVELS 2 4;

 TABLES SEX AGE2;

 PRINT NSUM WSUM MEAN SEMEAN 

 / WSUMFMT=F10.0 MEANFMT=F8.5 SEMEANFMT=F8.5 ;

 
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Method 1: partial output:

 S U D A A N

 Software for the Statistical Analysis of Correlated Data

 Copyright Research Triangle Institute April 1996

 Release 7.00

Number of observations read : 102467 Weighted count :261889548

Number of observations skipped : 0

(WEIGHT variable nonpositive)

Denominator degrees of freedom : 187

 

 

 Research Triangle Institute 

 The DESCRIPT Procedure 

 

by: Variable, SEX. 

----------------------------------------------------------------------------- 

| | | 

| Variable | | SEX 

| | | Total | 1 | 2 | 

----------------------------------------------------------------------------- 

| | | | | | 

| LDR | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 0.13797 | 0.18013 | 0.09793 | 

| | SE Mean | 0.00178 | 0.00250 | 0.00178 | 

----------------------------------------------------------------------------- 

| | | | | | 

| TDV_R | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 5.90759 | 4.90385 | 6.86089 | 

| | SE Mean | 0.09060 | 0.10039 | 0.12407 | 

----------------------------------------------------------------------------- 

| | | | | | 

| HLT_FP | Sample Size | 101277 | 48266 | 53011 | 

| | Weighted Size | 258963568 | 126221708 | 132741859 | 

| | Mean | 0.10126 | 0.09124 | 0.11079 | 

| | SE Mean | 0.00157 | 0.00188 | 0.00176 | 

----------------------------------------------------------------------------- 

 

 

by: Variable, AGE2. 

 

------------------------------------------------------------------------------------------------------- 

| | | 

| Variable | | AGE2 

| | | Total | 1 | 2 | 3 | 4 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| LDR | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 0.13797 | 0.08894 | 0.18489 | 0.14461 | 0.07606 | 

| | SE Mean | 0.00178 | 0.00269 | 0.00268 | 0.00293 | 0.00251 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| TDV_R | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 5.90759 | 4.29682 | 4.88589 | 7.08504 | 11.09843 | 

| | SE Mean | 0.09060 | 0.09797 | 0.12432 | 0.17859 | 0.30642 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| HLT_FP | Sample Size | 101277 | 29183 | 40423 | 19834 | 11837 | 

| | Weighted Size | 258963568 | 69438212 | 107054300 | 51315866 | 31155190 | 

| | Mean | 0.10126 | 0.02552 | 0.06610 | 0.16651 | 0.28344 | 

| | SE Mean | 0.00157 | 0.00129 | 0.00168 | 0.00356 | 0.00519 | 

------------------------------------------------------------------------------------------------------- 
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 S U D A A N

 Software for the Statistical Analysis of Correlated Data

 Copyright Research Triangle Institute April 1996

 Release 7.00

Number of observations read : 102467 Weighted count :261889548

Number of observations skipped : 0

(WEIGHT variable nonpositive)

Denominator degrees of freedom : 4030

 Research Triangle Institute 

 The DESCRIPT Procedure 

 

by: Variable, SEX. 

----------------------------------------------------------------------------- 

| | | 

| Variable | | SEX 

| | | Total | 1 | 2 | 

----------------------------------------------------------------------------- 

| | | | | | 

| LDR | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 0.13797 | 0.18013 | 0.09793 | 

| | SE Mean | 0.00174 | 0.00231 | 0.00184 | 

----------------------------------------------------------------------------- 

| | | | | | 

| TDV_R | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 5.90759 | 4.90385 | 6.86089 | 

| | SE Mean | 0.07704 | 0.08503 | 0.11403 | 

----------------------------------------------------------------------------- 

| | | | | | 

| HLT_FP | Sample Size | 101277 | 48266 | 53011 | 

| | Weighted Size | 258963568 | 126221708 | 132741859 | 

| | Mean | 0.10126 | 0.09124 | 0.11079 | 

| | SE Mean | 0.00152 | 0.00174 | 0.00182 | 

----------------------------------------------------------------------------- 

 

by: Variable, AGE2. 

------------------------------------------------------------------------------------------------------- 

| | | 

| Variable | | AGE2 

| | | Total | 1 | 2 | 3 | 4 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| LDR | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 0.13797 | 0.08894 | 0.18489 | 0.14461 | 0.07606 | 

| | SE Mean | 0.00174 | 0.00271 | 0.00254 | 0.00303 | 0.00269 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| TDV_R | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 5.90759 | 4.29682 | 4.88589 | 7.08504 | 11.09843 | 

| | SE Mean | 0.07704 | 0.09116 | 0.11805 | 0.16109 | 0.28387 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| HLT_FP | Sample Size | 101277 | 29183 | 40423 | 19834 | 11837 | 

| | Weighted Size | 258963568 | 69438212 | 107054300 | 51315866 | 31155190 | 

| | Mean | 0.10126 | 0.02552 | 0.06610 | 0.16651 | 0.28344 | 

| | SE Mean | 0.00152 | 0.00118 | 0.00157 | 0.00351 | 0.00501 | 

------------------------------------------------------------------------------------------------------- 
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----------------------------------------------------------------------------- 

| | | 

| Variable | | SEX 

| | | Total | 1 | 2 | 

----------------------------------------------------------------------------- 

| | | | | | 

| LDR | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 0.13784 | 0.17991 | 0.09789 | 

| | SE Mean | 0.00170 | 0.00221 | 0.00182 | 

----------------------------------------------------------------------------- 

| | | | | | 

| TDV_R | Sample Size | 102467 | 48809 | 53658 | 

| | Weighted Size | 261889549 | 127570237 | 134319312 | 

| | Mean | 5.90468 | 4.89733 | 6.86141 | 

| | SE Mean | 0.07511 | 0.08320 | 0.11217 | 

----------------------------------------------------------------------------- 

| | | | | | 

| HLT_FP | Sample Size | 101277 | 48266 | 53011 | 

| | Weighted Size | 258974266 | 126232939 | 132741328 | 

| | Mean | 0.10127 | 0.09125 | 0.11080 | 

| | SE Mean | 0.00137 | 0.00159 | 0.00165 | 

----------------------------------------------------------------------------- 

 

 

Post-stratified estimates 

by: Variable, AGE2. 

------------------------------------------------------------------------------------------------------- 

| | | 

| Variable | | AGE2 

| | | Total | 1 | 2 | 3 | 4 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| LDR | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 0.13784 | 0.08845 | 0.18484 | 0.14484 | 0.07587 | 

| | SE Mean | 0.00170 | 0.00258 | 0.00248 | 0.00298 | 0.00268 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| TDV_R | Sample Size | 102467 | 29711 | 40801 | 20000 | 11955 | 

| | Weighted Size | 261889549 | 70670755 | 108040689 | 51713265 | 31464840 | 

| | Mean | 5.90468 | 4.29787 | 4.87876 | 7.08472 | 11.09687 | 

| | SE Mean | 0.07511 | 0.09066 | 0.11858 | 0.16180 | 0.27613 | 

------------------------------------------------------------------------------------------------------- 

| | | | | | | | 

| HLT_FP | Sample Size | 101277 | 29183 | 40423 | 19834 | 11837 | 

| | Weighted Size | 258974266 | 69441900 | 107059972 | 51315313 | 31157082 | 

| | Mean | 0.10127 | 0.02555 | 0.06624 | 0.16633 | 0.28322 | 

| | SE Mean | 0.00137 | 0.00116 | 0.00153 | 0.00342 | 0.00487 | 

-------------------------------------------------------------------------------------------------------
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A @

A @

Sampling techniques
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Notes for Year 2000 application

A @

 WTF 207-212 'FINAL BASIC WEIGHT' 

method 2

As a check, the user should observe the following counts:

Certainty Strata PSUs 3804

Non-certainty Strata PSUs 259

Total PSUs 4063