Vital andHealth StatisticsCovariances forEstimated TotalsWhen ComparingBetween Years

Series 2:Data Evaluationand Methods ResearchN0,114This report presents the results of a study to measure the degree of correlationbefween yearly estimates of totals for selected characteristics from the NationalHospital Discharge Survey and from the National Health Interview Survey, Thereport also gives an idea of the magnitude of the covariances of estimatedtotals and the effect of assuming independence when making year-to-yearcomparisons of totals,

LLS, DEPARTMENTOF HEALTHANDHUMANSERVICESPublicHealthSetvlceCentersfor DiseaseControlNationalCenterfor HealthStatistics

Hyattsville,MarylandApril 1992DHHSPublicationNo, [PHS)92-1388

Copyright Information

—

All material appearng (n thle report IS (n the publfc oomaln anrt may bereproduced or copied without perm(sslon: citat!on as to source howeve,, ISappreciated.

Suggested Citation

Bean JA, Hoffman KL. Covanances for estimated totals when comParlngbetween years. National Center for Health Stabstlcs Vital Health Stat 2(1 14)1992.

Library of Congress Cataloging-in-Publication Data

Bean, Judy A.Covanances for estimated totals when comparing between years

p. cm. – (Vital and health statistics. Series 2, Data evaluatlcm ancmethods research : no. 114) (DHHS publ!catton no (PHS) 92- 1388)

“Results of a study to measure the degree of correlation between yearlvestimates of totals for selected characteristics from the National HospitalDischarge Survey and the National Health Interwew Survey. ”

By Judy A. Bean and Ketth L. Hoffman.Includes bibliographical referencesISBN 084.6.45481. Medical Care– United States Llt\llzatIon – Statistics. 2 National

Hospital Dmcharge Survey (U.S.) – Evaluation. 3. National Health InterwewSurvey (U.S.) -- Evaluation, 4. United States –Statistics, Medical. 5 Analysls ofcovarlance. 1. Hoffman, Keith L. II National Center for Health Statistics (U.S.) IllNattonal Hospital Discharge Survey (U.S.) IV National Health Interview Survey(U.S.) V. Title. V1. Series. V1l. Series: DHHS publication no (PHS) 92--1388. Vll!.Series: DHHS publications ; no. (PHS) 92-1388.

[DNLM 1, Analysis of Variance, 2, Health Status – UmtedStates– statistics. 3. Health Surveys--United States. 4 PatientDischarge– United States – statistics. W2 A N148vb no. 114] RA409. U45 no114[RA 407.3]362.1 ‘0723 S –dc2@[362.1 ‘0973’021 ]DNLM/DLCfor l-ibra~ of Congress 91-36074

CIP

National Center for Health Statistics

Manning Feinleib, M.D., Dr. P,H., Director

Jacob J. Feldman, Ph,D,, Associafe Director for Arzafysisand Epidemiology

Gail F. Fisher, Ph. D., Associate Director for Planning andExtramural Programs

Peter L. Hurley, Associate Director for 14tal and HealthStatNics Systems

Robert A. Israel, Associate Director for InternationalStatistics

Stephen E. Nieberding, Associate Director forManagement

Charles J, Rothwell, Associate Director for DataProcessing and Services

Monroe G. Sirken, Ph.D., Associate Director for Researchand Methodology

David L, Larson, Assistant Director, Atlanta

Office of Research and Methodology

Monroe G. Sirken, Ph. D., Associate Director

Kenneth W. Harris, Special Assistant for ProgramCoordination and Statistical Standards

Lester R. Curtin, Ph. D., Chief Statistical Methods Staff

James T, Massey, Ph.D., Chiej SZwvqYDesign Stafl

Andrew A. White, Ph. D., ChieJ Statistical TechnologyStaff

Contents

Introduction, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Description ofNHDSand NHIS... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .National Hospital Discharge Survey.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .National Health Interview Survey. . . . . . . . . . . . . . . . . , , , . . . . .! . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . , . . . . . . , , ,...

Study design, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Data from NHDS., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Data from NHIS ,, .,,,0, ,., ,.,.. ,, !...,. ., ..,.., . ...,,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Variance estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,. . . .Logistics of the investigation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Verification ofthe NHDS variance estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Results, ..,, ,,, ,,,,, ,, ...,,, ,, ..,,!. . . . . . . . . . . ...!.. ,. ...,,, ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. !..,.. ,NHDS diagnoses .,, , . ,.,.0 .! . , ,.,, ., . . . . . . . . . . . . . . ! ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,NHDSdays of care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NHDS surgical procedures. ..,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NHISacute and chronic conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NHISphysician visits and short-stay hospital episodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NHISrestricted-activity days, bed days, and work-loss days . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Impact of inference. .,....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Components ofvariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Discussion ,, .,,,,. . . . . . . . . . . . . . . . . !. .,.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References , , , , ,. , . , . . . . , . ,. ,, . . , ..,. ., , , , , . . . . . . . , !. . , . . . . . . . . . , . . . . ,. . . . . . . . . . . . . , , . . . . . . ., . ! . . . . . . .

List of detailed tables, . .,.,,.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

List of text tables

A, Correlation coefficients and effect of independence assumption on variances for number of patients dischargedfrom short-stay hospitals, by selected characteristics: United States, 1982-84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B. Correlation coefficients and effect of independence assumption on variances for number of days of care forpatients discharged from short-stay hospitals, by selected characteristics: United States, 1982-84 . . . . . . . . . . . . .

C, Correlation coefficients and effect of independence assumption on variances for number of surgical proceduresfor patients discharged from short-stay hospitals, by selected characteristics: United States, 1982–84 . . . . . . . . . .

D. Correlation coefficients and effect of independence assumption on variances for number of acute and chronicconditions, by selected characteristics: United States, 1982–84. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E, Correlation coefficients and effect of independence assumption on variances for number of physician visits and.short-stay hospital episodes, by selected characteristics: United States, 1982–84 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F. Correlation coefficients and effect of independence assumption on variances for number of restricted-activitydays, bed days, and work-loss days, by selected characteristics: United States, 1982-84 . . . . . . . . . . . . . . . . . . . . . .

G. Effects of independence assumption on confidence intervals using statistics from the National HospitalDischarge Survey and the National Health Interview Suwey, by selected characteristics: 1982–84 . . . . . . . . . . . . .

H, Mean, maximum, andminimurnof percent contribution of within component of variance to total variance fornumber of patients discharged from short-stay hospitals: United States, 1982–84 . . . . . . . . . . . . . . . . . . . . . . . . . . .

J, Mean, maximum, and minimumof percent contribution of within component of variance to total variance fornumber of days of care for patients discharged from short-stay hospitals: United States, 1982-84 . . . . . . . . . . . . .

K. Mean, maximum, and minimumof percent contribution of within component of variance to total variance fornumber of surgical procedures for patients discharged from short-stay hospitals: United States, 1982–84 . . . . . .

1

222

444457

8899

101112

13

14

16

17

19

8

9

10

10

11

12

13

14

15

15...Ill

L Mean, maximum, and minimum of percent contribution of within component of variance to total variance fornumber ofacute and chronic conditions: United States, 1982–84, ,,, ,. .,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 15

M. Mean, maximum, and minimum of percent contribution of within component of variance to total variance fornumber of physician visits and short-stay hospital episodes: United States, 1982–84. . . . . . . . . . . . . . . . . . ., . . . . , 15

N. Mean, maximum, and minimum of percent contribution of within component of variance to total variance fornumber of restricted-activity days, bed days, and work-loss days: United States, 1982-84, , , . . . . , , , ., ., ., . . . , 15

Covariances forEstimated Totals WhenComparing BetweenYearsby Judy A. Bean, Ph,D,, Department ofEpidemiology and Public Health, University of Miami,and Keith L, Hoffman, M.S., Office of Research andMethodology

IntroductionThe National Center for Health Statistics (NCHS)

conducts several large-scale surveys whereby data areobtained through complex designs inciuding sampling intwo or three stages, clustering, and stratification. If thedesign is multistage the first stage consists of drawing asample of primary sampling units (PSU’S). These PSU’Scan be hospitals, counties, or other units, depending uponthe specific survey. In several surveys sponsored by NCHSthe primary sampling units employed are often sampledon more than one occasion,

Two examples are the National Hospital DischargeSurvey (NHDS) and the National Health Interview Survey(NHIS), In NHDS, the design used from 1965 to 1987 wasa two-stage highly stratified one, The PSU’S selected in thefirst stage were hospitals, and within the chosen hospitals,discharges were sampled. Although some hospitals haveclosed, new ones have been added, and a few do notparticipate, the data collected annually from 1965 to 1987came from the same hospitals originally selected. NHIS isan annual survey of households located in the 50 Statesand the District of Columbia. Each year interviewerscontact approximately 41,000 new households; however,these households are selected from the same primarysampling units, which are groups of counties and metro-politan areas, From one year to the next the householdsare chosen from adjacent segments of housing units withinPsu’s.

When sampling inquiries are conducted at successiveintervals of time on a continuing basis and covering thesame universe, such as in NHDS and NHIS, three dif-ferent types of parameters for totals may be estimated.These estimators are the change in a total from one timeperiod to the next, the average total for all the timeperiods, and the average total for each time period. Thebest design is not the same for these estimators anddepends upon the correlation of the estimators from onetime period to another. This report focuses only on theeffect of the correlation on estimated changes betweentime periods.

This procedure of gathering data in a survey from thesame basic units from one year to the next means that theestimates produced each year are not independent. This

lack of independence is an important feature that, for avariety of reasons, is often ignored by analysts,

Statistics produced from NHDS and NHIS are pub-lished annually in reports prepared by NCHS, In theappendix to reports presenting the NHIS statistics, thereader can find relative variances curves from which vari-ances can be calculated. If the reader wishes to computethe variance of a difference between two yearly estimates,a formula is provided. This variance formula is the sum ofthe variances of the two estimates. In using this formulaone is assuming that the covariance between the twoestimates is negligible. Similarly, the variances of NHDSestimates are given in reports, but nothing is explicitlystated about the covariances of estimated totals whencomparing between years. This report is intended to giveNCHS users an idea of the magnitude of the covariancesof estimated totals and the effect of assuming independ-ence when making year-to-year comparisons of totals.

To determine the degree of correlation between theestimates of totals, an empirical investigation was con-ducted using data from two NCHS multistage, complexsurveys, NHDS and NHIS.

The main objective of this investigation was tomeasure the degree of correlation between yearly esti-mates of totals for selected characteristics produced fromthe National Hospital Discharge Survey and the NationalHealth Interview Survey. To achieve this overall objectivethe specific aims were to:

●

●

●

●

Determine a method for applying the balanced re-peated replication (BRR) technique to the NHDSdesign.Estimate variances and covariances of totals for se-lected variables from NHDS and NHIS using theBRR method.Compute the variances of the year-to-year differencesfor totals using the BRR technique.Calculate the year-to-year correlations between thestatistics using the BRR variances and covariances,

This report shows the results of the study. Specifically,correlations of estimated totals for selected variables anda measure of the effect of independence are examined.

1

Description of NHDSand NHIS

In order to understand the methods and results of thisstudy it is crucial that a person have an understanding ofthe sample designs for the two surveys. The two designsare briefly described here.

National Hospital DischargeSurvey

This survey is a source of data on the short-stayhospital experience of the civilian noninstitutionalizedpopulation. The data are obtained through a probabilitysample of all discharges, both alive and deceased, fromshort-stay non-Federal hospitals. Estimates producedfrom the survey include the number, rate, and averagelength of stay of patients discharged from short-stay hos-pitals by selected patient and hospital characteristics.

The NHDS sample plan for 1965-87 was a two-stagestratified design, Each hospital with 1,000 or more beds inthe universe of short-stay hospitals was considered to be astratum; the other hospitals, called noncertainty hospitals,were stratified by bed size and geographic region. Thenoncertainty hospitals were classified into 24 size-by-region primary strata. If a stratum contains only onehospital, that hospital came into the sample with a proba-bility of one. Controlled-selection techniques were em-ployed to choose hospitals within each of the 24 size-by-region classes (1), Primarily because of cost, the samplehospitals were allocated to a series of subsamples, re-ferred to as panels, and the subsamples were implementedin the field over time,

The second stage of selection consisted of samplingdischarges from within each of the hospitals. The dailylisting of discharges was the sampling frame, The within-hospital sampling ratio for choosing the discharges variedinversely with the probability of selection of the hospital,

In 1988 the sampling plan changed from a two-stagedesign to a three-stage design. The first stage is geographicarea, with hospitals selected from sampled areas in thesecond stage. Discharges are then sampled from theselected hospitals. A more indepth description is given byShimizu (2).

After the abstracted data are extensively edited, anestimating procedure is used to produce nationalestimates from the survey. The procedure has threecomponents: Inflation by reciprocals of the probabilities of

sample selection, adjustment for nonresponse, and ratioadjustment.

National Health Interview Survey

This survey is designed to produce national estimatesfor the civilian noninstitutionalized population residing inthe United States, Members of the Armed Forces are notincluded in the target population. Each year data arecollected on personal and demographic characteristics,illnesses, injuries, impairments, chronic conditions, andother health topics. Estimates produced from this surveyinclude morbidity rates and measures of utilization ofhealth services.

The sampling design produces a weekly national prob-ability sample of households that are representative of thetarget population, The weekly sampling permits continu-ous measurement of characteristics and, through consoli-dation of data over time, detailed analysis of rare health-related items.

The first stage in the design used from 1973 to 1984consisted of drawing a sample of 376 primary samplingunits (PSU’S) from approximately 1,900 geographicallydesigned PSU’S. (A PSU is either a county or a group ofcontiguous counties, metropolitan areas, or minor civildivisions.) Then the housing units within each sample PSUwere geographically clustered into segments, and eachyear a cluster of four expected households was selected,Prior to 1985, the annual NHIS sample consisted ofapproximately 41,000 eligible occupied households, whichyielded a sample of about 106,000 individuals (3).

For several reasons a redesign of NHIS was imple-mented in 1985, Besides reducing the number of PSU’Sfrom 376 to 198 and increasing the number of interviewedhouseholds to 49,000, four other significant changes weremade. Instead of using a list sampling frame, an areasampling frame was employed. The number of PSU’Sselected in certain strata was changed from one to two.Furthermore, national subsamples of PSU’S were created,The fourth change was to oversimple the black population(4).

In order to produce estimates the basic data areextensively manipulated. The four steps are: Inflation bythe reciprocals of the probability of selection, householdnonresponse adjustment, first-stage ratio adjustment, and

2

poststratification by age, sex, and race. Statistical theory ried out for this reason. These adjustments also bring theindicates that a ratio estimator for a statistic generally has sample data into close conformity with U.S. Bureau of thesmaller variance than an inflation estimator has. The Census population totals.first-stage ratio adjustment and poststratification are car-

Study design

Data from NHDS

Data collected on sampled discharges of inpatientsfrom short-stay hospitals during the years 1982, 1983, and1984 were used in the study. The original frame of thesurvey consisted of the hospitals listed in the 1963 Na-tional Master Facility Invento~. To reflect the universe ofshort-stay hospitals for a given year, hospitals that havecome into existence since 1965 were also sampled, Thesedischarges represent three years of data collection inNHDS, which has been conducted since 1965. Data usedin the study were on diagnostic and surgical proceduresfor 1982, 1983, and 1984. There was one record for eachdischarge. The variables chosen for this investigation werea subset of the variables NCHS employed for computingvariances for NHDS statistics.

Data from NHIS

As described previously, NHIS uses an annual proba-bility sample of households throughout the 50 States andthe District of Columbia. Data collected each year areavailable on five different types of record formats, In thisstudy, tapes for the years 1982, 1983, and 1984 containinga record per individual or a record per condition wereused, The 60 statistics examined in this study were used ingenerating the relative variance curves formed in NCHSCurrent Estimates Series 10 reports,

Variance estimator

The variances of NHDS sample statistics are calcu-lated directly using the estimating equations discussed bySimmons and Schnack (1), In NHIS the balanced re-peated replication (BRR) procedure for general varianceestimation is employed. Further discussion of the vari-ances calculated for the survey estimates is presented inan appendix to NCHS Current Estimates Series 10 re-ports, which give NHIS estimates, and in Series 13 reportson NHDS estimates. For ease of computation the BRRmethod was used to estimate variances and covariances inthis study for both data sets.

The basic premise of BRR is that the variability of astatistic based on the entire sample data set can beestimated by the variability of that statistic based onsubsamples that reproduce the complex design of the total

4

‘sample. Several investigators – McCarthy (5,6), Kish andFrankel (7,8), Frankel (9), Koch and Lemeshow (10), andBean (11) – have studied this procedure extensively. Thebasic technique is described below.

Consider a finite population of N primary units classi-fied into L strata, each containing N,, units (h = 1,2, ..,,L), with

L

N = ~N~

/%=1

The sample design is a stratified simple random samplewith two units chosen from each stratum with replace-—ment, An unbiased estimator of the population mean Y is

where

Wh=.

y–,,=

The usual

weight for stratum h (h. = 1, 2, , . .. L)N,JNthe sample mean for stratum h

estimator of the variance of ~ is

h=l

where ,s~ is the sample variance for stratum h,One general method for estimating variances is ran-

dom groups, but for this situation there are only twoindependent random groups, An alternative approach isto use half-samples comprised of one unit from eachstratum. This results in half-samples that have overlappingunits, which means that they are correlated. This estima-tor can be expressed as

K

v~ (y-) = ~(y – y)?lri=l

where

K=2L

L

~i = ~wh(8hli Y /21 + s/12jY /72)h=]

rl if unit (h.,1) is selected for the ith half-sample,

%2 = 1- 5/,li

There are 2L possible half-samples. For this case of alinear statistic, V~ (~) = V(Y). When L is large thecomputation of 2 L half-samples is not feasible, McCarthy(5) derived a method for choosing a subset of the half-samples in a specific fashion so that V’ (Y) is reproduced.The set of replicates generated is said to be orthogonallybalanced.

The subsets of replicates are formed by deleting oneunit in each stratum, The set of A half-samples is definedby an A x L matrix with elements ail,, where

{

+ 1 if unit 1 in the hth stratum is in the ithhalf-sample where i = 1, 2, , . .. A,

fli,,=-1 if unit 2 in the hth stratum is in the ith half-

sample,

This set of A replicates satisfies the property

A

z aih aill’ . 0i=i

forallh

Step 3: Nonresponse problem

One program in SAS was written to perform all theremaining tasks, but these various tasks will be explainedin steps, In NHDS not all of the sampled noncertaintyhospitals in the size-by-region classes responded for allthree years – 1982, 1983, and 1984. The hospitals notresponding for all three years were dropped from the datafile used in estimating the variances and covariances.Because the number of hospitals not responding for allthree years was small –making up less than 5 percent ofthe total – this nonresponse is not thought to invalidatethe results. NHIS does not have this type of nonresponse,because a household is included in only one year ofsampling,

Step 4: Noncertainty strata

As discussed earlier in the section “Varianceestimator,” research indicates that having two units perstratum is the most efficient design in terms of BRRvariance estimator stability, However, if the NHDS non-certainty hospitals were simply paired, the number ofpseudostrata would be more than 200, which means thatan extremely large orthogonal matrix would be requiredfor variance estimation, To avoid the probIem of con-structing a large orthogonal matrix, a pseudostratum wasdefined to be four hospitals, The pseudostrata formedwere independent of the sampled hospitals.

After the original sample of hospitals was selected,other short-stay hospitals came into existence, The NHDSsurvey design was altered so that a sample of thesenoncertainty hospitals was chosen; these sample units aredesignated as panel B, The original noncertainty hospitalssampled belong to panels 1–6, The hospitals in panels 1–6were placed into one group and collapsed into strata.However, because weighting is different within panel B,the hospitals within it were collapsed to form strata,

Again a function of the statistical package SAS wasused to form the strata and pairs within them. Thehospitals within panel B were sorted by region, bed size,and hospital. This was done so that hospitals with similarcharacteristics, especially size, were paired together. Eachgroup of four was considered a stratum. Because therewere only three hospitals for the last stratum, the recordsfor the final hospital were duplicated. This procedure wasalso followed for the hospitals in panels 1-6. However, thelast pseudostratum had only two hospitals, which meantthat the records for two hospitals were duplicated,

Prior research into the behavior of BRR estimatorsindicates that if the number of units sampled from astratum is even, pairs within the stratum should be formedrandomly (8,13). Because each NHDS pseudostratum con-tained four noncertainty hospitals, random pairs wereformed.

As stated above, the pairing used by NCHS to”pro-duce BRR variances for NHIS statistics was employed inthis study, Because there were noncertainty PSU’S, pseu-dostrata were formed. .

The creation of pseudostrata raises questions con-cerning the bias introduced in the estimates of variancesthrough this procedure. Stanek (21) investigated the effecton variance estimates of pairing strata into pseudostrata.The findings indicate that, as the pairing became hetero-geneous, the bias of the BRR variance estimator in-creased. In addition, subjective pairing was studied usingdata from the National Health Examination Survey (an-other NCHS survey). The results show that the BRRestimates of variance of mean weights and heights ofchildren were not highly dependent on the arrangement ofpseudostrata,

For NHDS noncertainty hospitals, the pairing for thisinvestigation was done by combining adjacent geographic-size classes, The pairing utilized in NHIS is subjective,Although no estimates of bias were made, the varianceestimates for NHDS estimates should be only slightlyoverestimated.

Step 5: Estimation of variances,correlation coefficients, and effect ofindependence assumption

The next step was to generate an estimate of thestatistic utilizing the entire sample. SAS data statementswere employed to write a program to construct a 120 x111 orthogonal matrix consisting of 120 half-samples and111 pseudostrata for NHDS. For NHIS, a 160 x 149matrix was constructed.

The final component was calculation of the half-samples of the statistic. There were 120 half-sample esti-mates in NHDS and 160 in NHIS. This step wasaccomplished by taking advantage of SAS features. Oneexample is the use of a pointer to read both of the recordsin a stratum at one time. This process also allows thelocation in the data file where the program is reading to bemaintained.

The theory of BRR indicates that data from a half-sample should be subjected to the same estimation proce-dure as data from the total sample are. This would mean,for example, recomputing the first-stage ratio adjustmentand poststratification for each half-sample for NHISdata – a task that would require considerable work, Inves-tigations by Simmons and Baird (22) and Kish andFrankel (7,8) found that the adjustment factors based onthe parent sample can be applied without seriously biasingthe estimate. Other studies (11,23) indicate that theseadjustment factors should be calculated for each specifichalf-sample, For this study, the decision was made to usethe factors based on all the survey data.

After the half-sample estimates were produced, thevariance was calculated. This procedure was repeated foreach of the 38 diagnostic and days-of-care statistics andeach of the 23 surgical statistics from NHDS and for eachof the 60 statistics from NHIS.

The basic program was modified to yield covariancesbetween the estimates across years. The BRR formula forthe covariances computed is

6

A

c~.(Yw.Y83)= ~ (y’sz,j– Y“82) ~’~~,~– y“83)/!i=l

where

.4 = the number of half-sample estimates producedy‘s,2,j= the estimate of Y82utilizing half of the total

sampleY“s2 = the estimate of Y82based on the entire sample

y ‘ ~3,iand y “~~are defined similarIy

In addition to the variances and covariances, thevariance estimates of the year-to-year differences weredirectly computed, For example, the estimator for theyears 1982 and 1983 is

A

v, (Ysz - ‘S3) = ~ [(Y’82,i - J“S3,i) - (Y “82 – Y “S3)]2/-4i=[

All the output from the programs was passed to a SASdata file so that additional statistics could be computed.

●

I

I

●

Two other statistics were also calculated,

Correlation coefficients for the estimates – Correlationcoefficients were calculated for the estimates of 1982and 1983 and for the estimates of 19S3 and 1984. Theformula is:

6 = Cvr (yS2yL13)/ tivr 0’82) v, (Y83)

Effect of independence assumption –To determine theeffect that making the assumption of no correlationhas on the variance of the difference between twovariables, the ratio

E = [Vr (Yl) + v, (yz)]/vr (Y1 – Y2)

was computed for all the statistics,

Verification of the NHDS varianceestimator

Table 1 gives the number of patients discharged,standard error, and standard error of the differences for1982, 19S3, and 1984 from NHDS. (The variables in thetables are shown in the order of magnitude of the numberof patients with the characteristic discharged in 1982.)Examination of the relative standard errors (RSE’S) forseveral characteristics indicates that the BRR estimatesare reasonable, (The standard error divided by the esti-mate = RSE.) For example, consider these relativestandard errors:

Females:RSE = (635/21,554) x 100 = 2,9 percent

Persons 15-44 years:RSE = (520/14,515) x 100 = 3.6 percent

Atherosclerotic heart disease;RSE = (25/465) x 100 = 5.4 percent

Malignant neoplasm of lung, male:RSE = (11/188) x 100 = 5,9 percent

As the size of the statistic decreases, the RSE increases.

Charts providing general relative standard errors for awide variety of estimates are available in the publicationsconcerning the utilization of short-stay hospitals – for ex-ample, (24), Comparing the RSE’S produced by the BRRmethod with the values of RSES from the figures in thepublications shows that the BRR estimates are larger. Theratios of the BRR estimate of RSE divided by the valuederived from the figures are: Females – 1,16; persons15-44 years– 1.44; atherosclerotic heart disease – 1.35;and malignant neoplasm of lung, male – 1.18. Note thatthe denominators were obtained from the figures byrounding the estimates. Because empirical evidence(8,9,11) shows that in general the BRR method overesti-mates the variance, this is the result one would expect.The standard errors are consistent across the years.

Associated with each diagnosis is a days-of-care esti-mate. These values are examined next. The estimates fordays of care are presented in table 2. Most of the patternsfound in table 1 are seen again in table 2. The BRRrelative standard errors are usually larger than the valuesobtained from the chart of general RSE’S for NHDSestimates shown in NCHS publications.

The estimates for the surgical procedures and theirstandard errors are presented in table 3. The size of theestimates varies from 33,519,000 to 55,000 for 1982 data.The estimates for many variables increase from 1982 to1983 but decrease in 1984. The RSE’S for four variables in1982 are:

All procedures:Total:

RSE = (1,186/33,519) x 100 = 3.5 percentPersons 15-44 years:

RSE = (647/14,281) x 100 = 4.5 percentBilateral occlusion of fallopian tube, 15-44 years:

RSE = (54/558) x 100 = 9.7 percentHysterectomy, 65 years and over:-

RSE = (4/55) x 100 = 7.9 percent

To compare these RSE’S with the ones obtained fromthe published NCHS charts, the ratio of the BRR RSEdivided by the published RSE was calculated. The ratiosare: All procedures, total —1.09; all procedures, persons15-44 years – 1.12; bilateral occlusion of fallopian tube,15-44 years – 1.61; and hysterectomy, 65 years andover —0.88. Again the BRR estimates are generally larger,but in some cases the two RSE’S are essentially the same.

These comparisons indicate that, in general, the BRRestimate of variance is larger than the estimate producedby the design variance formula. Based on BRR researchfindings, this overestimation is to be expected. Althoughno one has compared BRR estimates of covariance withexact covariances, it is reasonable (using the results fromvariance comparisons) to assume that covariances are alsooverestimated, However, assuming that the magnitude ofthe overestimation is the same for variances and covari-ances, the correlation coefficients calculated will be ap-proximately the same as those calculated using the correctdesign formulas,

7

NHDS diagnoses

The correlation coefficients in table A for the numberof discharges for the 1982 and 1983 statistics range from0.96 for two statistics – the number of discharges formental disorders for persons ages 15-44 years and thenumber of discharges for persons under 15 years ofage – to a low of 0.45 for the number of discharges formalignant neoplasm of the lung among males, (The vari-ables in the tables are shown in the order of the magni-tude of the estimates in 1982.) Of the 19 variables, only 7have values below the value of 0.80 and none has anegative value, The average value of the correlations is0,80. No clear pattern related to the magnitude of theestimate was observed. If the statistic has an estimate ofmore than 800,000, the correlation is always larger than0.88. The other statistics have smaller correlations, withone exception: The variable congenital anomaly for per-sons under 15 years of age, which has the smallest esti-mate, has a correlation of 0.95 for 1982–83. The threemalignant neoplasm diagnoses and inguinal hernia formales have the smallest correlations, ranging from 0.45 to0.58.

For the correlations for 1983 and 1984 (table A), thevalues vary from a high of 0.98 to a low of 0.41, with anaverage of 0.81. Again the statistics with estimates larger

than 800,000 have the higher correlations; they are allbigger than 0.93. The rest of the variables – with the oneexception, congenital anomaly for persons under 15 yearsof age —range from 0.41 to 0.83. The estimated number ofdischarges for the age group under 15 years has a correla-tion of 0,98, whereas malignant neoplasm of the lungamong males has the value of 0.41. Although 11 of the 19variables have larger correlation coefficients for 1983-84than for 1982–83, generally the correlations do not ditiergreatly from one year to the next.

Table A also shows the ratios (E = independenceeffect) showing the effect on the variances when theassumption is made that the correlation between esti-mated totals across years is zero. (The formula for E ispresented earlier in the section “Logistics of theinvestigation.”) For 1982 and 1983 the ratios range from aminimum of 1.8 to a maximum of 22.4. For example, forpersons ages 15-44 years with mental disorders, the vari-ance of the difference (assuming the correlation is zero) is22,4 times larger than the variance taking into consider-ation the correlation. The values for 1983 and 1984 rangefrom 1.7 to 40.4. The mean value is 9,6 for 1982-83 and13.3 for 1983-84.

These statistics indicate that making the assumptionthat the correlation is zero results in the variance of thedifference for diagnoses always being an overestimate,

Table A, Correlation coefficients and effect of independence assumption on variances for number of patients discharged from short-stayhospitals, by selected characteristics: United States, 1982-84

Corre/.efim coerVcient Independence effect (E)

Characteristic 7982-83 1983-84 1982-83 1983-84

Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.91 0.9615-44 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10.80.92

28.2

Male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.96 12.2

0.9122.4

0.9565yeara and over . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.20.91

19,90.95

45-64 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10.2

0.8818.5

0.95Females with deliveries . . . . . . . . . . . . . . . . . . . . . . . . . .

8.60.95

18.9

Under 15years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.96 18.7

0.9624.3

Mental disorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.98 19.1

0.9540.4

Mental disorders, 15-44 years.... . . . . . . . . . . . . . . . . . .0.94 19.0

0.9616.7

Acute myocardial infarction . . . . . . . . . . . . . . . . . . . . . . . .0.93 22.4

0.7214.5

0.75Cataract, ...,.,.......,.,,,.. . . . . . . . . . . . . . . .

3.50.89

4.00.77

Atherosclerotic heart disease...,,.. . . . . . . . . . . . . . . . .8.4

0.793.7

0.63Inguinal hernia, male . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.70.56

5.1

Cataract, 65 years And over..... . . . . . . . . . . . . . . . . . .0.57 2.4

0.882.3

Malignant neoplasm of lung . . . . . . . . . . . . . . . . . . . . . . .0.76 7.3

0.493.6

Malignant neoplasm of breast, female . . . . . . . . . . . . . . . , .0.61 1.9

0.522.5

Malignant neoplasm of lung, male . . . . . . . . . . . . . . . ., . .0.49 2.1

0.452.0

Fracture of neck of femur, 65 years and ovar. . . . . . . . . . . . .0.41 1.8

0.671.7

Congenital anomaly, under 15 years . . . . . . . . . . . . . . . . .0.60 2.9

0.952.5

0.96 15.5 21.4

SOURCE Nalional Center for Health Statistic. National Hospital Oischarge Survey, 1982-84.

8

The price of the assumption is a variance that is at leastdouble the true one, Using the overestimated variance willhave an impact on trends of the year-to-year differencesand on hypothesis testing done on these statistics, Exami-nation of the ratios reveals that for all statistics with anestimate larger than 800,000, the effect is huge, rangingfrom 8.6 to 22.4 for 1982-83 and from 16.7 to 40.4 for1983-84,

NHDS days of care

The correlation coefficients for NHDS days-of-carestatistics are displayed in table B, The total number ofdays of care among persons under 15 years has the largestcorrelation, 0.94, for 1982-83 and again, 0.96, for 1983–84.The number of days of care for malignant neoplasm of thelung among males has the lowest correlation for 1982-83,0,34, and again for 1983–84, 0.29. All the correlations werepositive. The ranges of the correlation coefficients are 0.94to 0.34 for 1982-83 and 0,96 to 0.29 for 1983-84. Themeans are 0,74 and 0,73, respectively, The pattern bymagnitude of the estimate is similar to that seen fornumber of discharges, For statistics with an estimatelarger than 10 million, the correlations are above 0.84.Most of the other statistics have correlations ranging from(.),29 to 0.82, Exceptions are a correlation of 0.85 forcataract procedures for 1982–83 and a correlation of 0.93for congenital anomaly among children under 15 years for1982-S3,

Examination of tables A and B reveals that thecorrelations are always smaller for days of care than fornumber of discharges. One possible explanation is theintroduction of the concept of diagnosis-related groups(DRG’s) in hospitals, DRG’s were put into use during theyears 19S2 and 19S3. The use of DRG’s would affect thenumber of days of care more than the number of dis-charges for these selected 19 variables,

Because the correlations are all positive and most aregreater than 0.8, making the assumption of independenceresults in relatively large overestimates of the variance ofthe difference. The ratio for days-of-care statistics reachesa high of 26.3 for persons under 15 years for 1983–S4 anda low of 1.4 for malignant neoplasm of the lung amongmales for 19S3–84, The value of 26.3 means that when theassumption of independence is made, the variance used is26 times larger than a more accurate estimate of variance.The averages across the statistics are 6.4 for 19S2–83 andS.4 for 1983-84. In general, as the correlation coefficientapproaches one, the effect of the independence assump-tion increases,

NHDS surgical procedures

The impression obtained from studying the correla-tion coefficients in table C is that these surgical statisticsare as highly correlated from year to year as the number ofdischarge statistics are. For 19S2–83, the correlation coef-ficients vary from a high of 0.93 for females ages 15-44with bilateral occlusion of fallopian tube to a low of 0.43for females ages 65 and over with a hysterectomy, Thecorrelation coefficients for 1983-S4 range from 0.96 for allprocedures among females to 0.20 for females ages 65 andover with a hysterectomy. The average values are 0.S0 forboth time periods. In general, the statistics with largerestimates have larger correlations. The statistics with thethree smallest estimates have the smallest correlations,ranging from 0.20 for 19S3–S4 to 0.55 for 1982–S3.

Table C gives the effect of the independence assump-tion (E) for the surgical procedures, The ratios range from1.8 to 14.2 in 1982-83 and from 1.3 to 23.4 in 1983–84. Thestatistic for hysterectomy among females 65 years and overhas the smallest ratio for both sets of values. The averageratio is 6.7 for 19S2–S3 and 10.1 for 19S3–S4. The varianceassuming the correlation is zero is two times larger thanthe true variance when the correlation is about 0.43.

Table B. Correlation coefficients and effect of independence assumption on variances for number of days of care for patients dischargedfrom short.stay hospitals, by selected characteristics: United States, 1982-84

Correkrtiorr coefficient Independence effect &)

Characteristic 1982-83 1983-84 1982-83 1983-84

Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.85 0.93 8.8 13.0

Male, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.88 0.91 8.3 11.065years and over..........,.. . . . . . . . . . . . . . . . . 0.87 0.91 7.7 11.115-44 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.81 0.92 8.2 12.045-64 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.84 0.89 8.3Mental disorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.80.92 0.93 12.1 14,4

Under 15 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.94 0.96 12.4 28.3Fema18s wlthdeliverles ...,,...,.. . . . . . . . . . . . . . . . 0.90 0.95 9.8 18.7Mental disorders, 15-44 years . . . . . . . . . . . . . . . . . . . . . . 0.92 0.93 11.3 14.5Acutamyocardlal infarction .,....,, . . . . . . . . . . . . . . 053 0.63 2.2 2.7Atherosclerotic heart disease. , . . . . . . . , . . . . . . . . 0.69 0.79 3.1Fracture of neck of femur, 85 yeara and over. . . . . . . . . .

4.10.53 0.41 2.1

Malignant neoplasm of lung . . . . . . . . . . . . . . . . . . . . . . .1.7

0.44 0.46 1.6 1.9

Malignant neoplasm of breast, female . . . . . . . . . . . . . . 0.47 0.32 1.9 1.5Mallgnant neoplasm of lung, male . . . . . . . . . . . . . . . . . . . 0.34 0.29 1.5 1.4Inguinal hernia, male . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.40 0.32 1.8Cataract, ,,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.50.85 0.74 6.6

Cataract, 65 years And over . . . . . . . . . . . . . . . . . . . . . . .3.1

0.82 0.70 5.5Congenital anomaly, under 15 years. . . . . . . . . . . . . . . . . .

2,80.93 0.89 13.1 9.1

SOURCE:National Center for Health Statistics. National Hospital D]scharge Swvey, 19S2-84.

9

Table C. Correlation coefficients and effect of independence assumption on variances for number of surgical procedures for patientsdischarged from short-stay hospitals, by seiected characteristics: United States, 1982-84

Corfe/at/on coeff7cier7t Independence effect (E)

Characteristic 1982-83 1983-84 1982-83 1983-84

All procedures:Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.89 0.95Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.40.90

20.60.96

15-44years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9.2

0.9123.4

0.95Male. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.60.66

18.00.92

65years Andover . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.1

0.6612.7

0.9345–64years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.50,67

14.50.93

Under 15years. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.9313,6

0.94 1;:Circumcision, under15years .,. . . . . . . . . . . . . . . . . . . . 0.85

15.90.91

Cesarean section:6.5 10.5

Alleges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.91 0.9415-44years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.70.91

15.20.94

Hysterectomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.6

0.8815.2

0.92Bilateral occlusion of fallopian tube, 15-44 years . . . . . . . . . .

8,50.93

13.10.93

Exfracfion oflens, 65yearsandover. ., ., . . . . . . . . . . . . .14.2

0.8613.4

Cardiaccatheterization . . . . . . . . . . . . . . . . . . . . . . . . . .0.79 6.8

0.904.5

0.92Prostatectomy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8.90.68

10.70.71

Tonsillectomy, under15years. . . . . . . . . . . . . . . . . . . . . .3.2

0.743.4

0.75Prostatectomy, 65yearsandover. . . . . . . . . . . . . . . . . . .

3.80.64

3.90.67

Hysterectomy,45-84years . . . . . . . . . . . . . . . . . . . . . . . .2.8

0.633.0

0.65Dk’ectheartrevascularization.. . . . . . . . . . . . . . . . . . . . . .

3.00.84

2.70.85

Myringotomy, under15years . . . . . . . . . . . . . . . . . . . . . .6.4

0.826.6

0.83Arthroplasfy and replacement of hip:

4.6 5.5

65years Andover, . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.53 0.47Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.0 1.80.55 0.43

Hysterectomy,65years andover . . . . . . . . . . . . . . . . . . . .2.1

0.431.7

0.20 1.6 1,3

SOURCE: National Center for Health Statistics. National Hospital Discharge Swvey, 1982-84.

NHIS acute and chronic conditions

Table Dshowsthe correlations andtheeffect of theindependence assumptionson the variances for 1982–83and 1983.–84. (The statistics, standard errors, and standarderrors of differences are presented in table 4.) Thecorre-Iation coefficients for1982and 1983 range from avalue of–0,12for acute conditions among females ages 6–16yearsto a value of 0.20 for chronic conditions among black

persons ages 35-44 years. The correlations are mostly inthe range of the vah.re ofzero; of the 20 variables, 6 arenegative. The mean is 0.02, which is not different fromzero, The correlations for the three statistics with anestimate greater than 100,000 are0,08for total number ofacute conditions in the population, 0.02 for total numberof chronic conditions in the population, and–0,09 for thenumber of chronic conditions among females. Unlike the

Table D. Correlation coefficients and effect of independence assumption on variances for number of acute andchronlc conditions, byselected characteristics: United States, 1982-84

Correlation coefficient hdependence effect (E)

Characteristic 1982-63 1983-84 1982-83 1983-84

Acute conditions

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

White, 25-34 years...,,....,,.. . . . . . . . . . . . . . . . .Female, 6-16years, ,, . .,.,,.... . . . . . . . . . . . . . . .Male, 6–16years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .White, 55–64 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Married, 45-54 years. . . . . . . . . . . . . . . . . . . . . . . . . . . .Female, 55-64years . . . . . . . . . . . . . . . . . . . . . . . . . . . .75yearsand over....,.. . . . . . . . . . . . . . . . . . . . . . .Separated, 17-24years . . . . . . . . . . . . . . . . . . . . . . . . . .Black, 65-74years . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.06-0,11-0.12

0.140.010.030.000,08

-0.030.10

0.120.070.09

-0.15-0.07-0.08

0.050.130.00

-0.01

1.10,90.91.01.01.01.01.11.01.1

1.11.11.10.90.90.91.01.11.01.0

Chronic conditions

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.02 0.35Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.0-0.09

1.50.39

25-34years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.9

-0,101.6

Married, 25-34years . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.20 0.9

0.061.2

White, 45–54years, . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.21 1.1

0.02 -0,14Male, 6-16years .,, . . . . . . . . . . . . . . . . . . . . . . . . . . .

1,00.12

;::-0.01

Female, 45-54years . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1

0.041.0

-0.08lrtcome less than $5,000, 17-24years. . . . . . . . , . . . . . . .

1.0-0.03

0.9

Black, 35-44years . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0.01 1.0

0.201.0

[ncomeiessthan $5,000, 65-74years. . . . , . . , . . . . . . . .0.11 1.2

0,061.1

-0.03 1.1 1.0

SOURCE:N@tionalCentarforHealthStatlstica.NationalHealthlntewiewSuwey,1982-a4,

10

statistics for NHDS, the statistics with the largest esti-mates do not have the largest correlations, nor do thestatistics with the smallest estimates have the smallestcorrelations,

The values for 1983 and 1984 also are in the vicinity ofzero, with the smallest value being –0,15 for acute condi-tions among males 6-16 years; the largest correlation is0,39 for chronic conditions among females. For 1983-84the average correlation is 0.06. The correlations for thetwo years do not show extreme variation with two excep-tions. For example, the correlation for acute conditions forthe total population is 0.08 for 1982-83 and is 0.12 for1983-84.

Because the correlation coefficients are all in theneighborhood of the value of zero, the effect of theindependence assumption is not great, The ratio measur-ing the independence effect for 1982-83 varies from a lowof 0,9 for acute conditions among females ages 6–16 to ahigh of 1,2 for chronic conditions among black personsages 35-44. For 1983-84 the ratio goes from a high of 1.6for chronic conditions among females to a low of 0.9 foracute conditions among males ages 6–16 and three otherstatistics, The average ratio is 1.0 for 1982–83 and 1.1 for1983-84, The conclusion one would make from theseratios is that when one compares estimates between yearsby assuming that the statistics are independent, the vari-ance estimate is not an overestimation,

NHIS physician visits andshort-stay hospital episodes

The statistics, standard errors, and standard errors ofdifferences for the three years are displayed in table 5.Examination of the correlations for 1982-83 displayed in

table E shows that they vary from a low of –0.16 forshort-stay hospital episodes among divorced individuals toa maximum value of 0.39 for short-stay hospital episodesamong white persons. In this set of variables, no very clearpattern is seen between the size of the estimate and thesize of the correlation. Two of the 20 variables have anegative correlation. The average value of the correlationsfor these 20 variables for 1982-83 is 0,15.

Of the 20 correlations for 1983-84, 7 are negative; thenegative values range from –0.01 for physician visitsamong black persons and physician visits among divorcedpersons to -0,33 for short-stay hospital episodes amongblack persons ages 45–54. The range for the positivevalues is from a low of 0.06 for physician visits amongmales to a high of 0.36 for short-stay hospital episodesamong white persons. The mean is 0.10 for 1983–84;therefore, the averages of the correlations for number ofphysician visits and short-stay hospital episodes are biggerthan the means for the number of acute and chronicconditions. Although the correlations for these statisticsare slightly larger, they are still relatively low correlationcoefficients.

The last two columns in table E give the effect ofindependence assumption for the year-to-year differences.Only 2 of the 20 values for 1982–83 and 7 of the 20 valuesfor 1983-84 are less than one. As an example of the effectof assuming independence, consider the correlations forthe statistic short-stay hospital episodes among whitepersons –0.39 for 1982-83 and 0.36 for 1983-84. Althoughthe correlations are not large, the effect on theindependence assumption approach is a ratio of slightlymore than 1Vi for each time period. Thus, by making theassumption that the variables are independent, the vari-ance is lY2 times larger than the true variance. Theaverage ratios are 1.2 for 1982–83 and 1.2 for 1983–84.

Table E, Correlation coefficients and effect of independence assumption on variances for number of physician visits and short-stayhospital episodes, by selected characteristics: United States, 1982-84

Correlation coefficient Independence effect (E)

Characteristic 1982-83 1983-84 1982-83 1983-84

Physician visitsTotal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.30 0.28 1.4 1.4Male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.10 0.06 1.1 1.1Black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.14 -0.01 1.2 1.0White, 17-24 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.13 0.34 1.1 1.5Whlte,55-64 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.18 0.29 1.2 1.4Under 6years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.12 0.09 1.1Married, 36-44 yeara. . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.11 -0.08 1.1 :::Divorced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.02 -0.01 1.0Female, 86-74 years . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.00.05 -0.09 1.1 0.9

Female, 75 years and over . . . . . . . . . . . . . . . . . . . . . . . . 0.37 0.11 1.6 1.1

Short-stay hospital episodes

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .White, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75years and over . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Married, 6S-e4years . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-16years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Divorced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Male, 17-24 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Black, 45-54 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.270.390.330.040.210.17

–0.01–0.160.060.10

0.290.380.100.150.24

–0.120.09

–0.070.25

-0.33

1.41.61.51.01.31.21.00.91.11.1

1.41.61.11.21.30.91.10.9

:::

SOURCE:National Center for Health Statistics. National Health Interview Survey, 1982-a4.

11

NHIS restricted-activity days, beddays, and work-loss days

The correlations for restricted-activity, bed, and work-10SSdays are similar to those seen for the other two sets ofvariables from NHIS. (See table 6 for the statistics, stand-ard errors, and standard errors of differences.) Table Freveals that the lowest correlation coefficient for 1982–83is -0,14 for restricted-activity days among black persons45–54 years and the lowest correlation coefficient for1983-84 is -0.20 for bed days among persons 6–16 years.

The highest correlation for 1982-83 is 0.39 for restricted-activity days among white persons. The maximum correla-tion seen for 1983–84 is 0.29 for restricted-activity daysamong the total population. The averages are 0.09 and0.07, which fall between the averages for the other twosets of NHIS variables.

The effect of the independence assumption asmeasured by the ratio varies from 0.9 to 1.6 for 1982-83.For 1983-84 the minimum ratio is 0.8, whereas the maxi-mum is 1,4. The means are 1.1 and 1.1.

Table F. Correlation coefficients and effect of independence assumption on variances for number of restricted-activity days, bed days,and work-loss days, by selected characteristics: United States, 1982-84

Correlation coefficient Independence effect (E)

Characteristic 1982-83 1983-84 1982-83 1983-84

Restricted-activity daysTotal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .White . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.16 0.29 1.2 1.40.39 0.28 1.6 1.4

Male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.01 0.20 1.055-64 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.04 –0.07 1,0 ;:Black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . –0.06 0.11 0.9 1,1Male, 75 years And over . . . . . . . . . . . . . . . . . . . . . . . . . . -0,07 0.17 1.0 1.2Black, 45-54 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.14 0,04 0.9 1.0

Bed days

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.13White . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.04 1,1 1.00.34 0.05 1.5 1.0

Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.20 0.06 1.2 1.1Male . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.00 0.06 1.0 1.1Male, married, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.11 -0.06 1.1 0.96–16years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.17 -0.20 1.2 0.6Female, black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.08 0.15 0.9 1.2

Work-loss days

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.05White, married . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-0.01 1.0 1.00.32 -0.05 1.5 1.0

Female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.10 0.02 1.1 1.026-34years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.04 0.02 1.0Black . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.0–0.1 1 0.07 1.0

Separated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1

0.06 0.13 1,1 1,2

SOURCE: National Centar for Health Statistics. National Health Interview Survey, 1982-S4.

12

Impact of inference

One of the consequences when there are correlationsamong the sample units is an impact upon the inferencesanalysts draw from the findings, Kish (25) discussed themagnitude of the effect that clustering has upon theconstruction of confidence intervals. Using his strategyand this body of empirical evidence, one can see theeffects on confidence intervals of assuming the correlationis zero,

Krewski (26) and Krewski and Rao (12) showed thatunder certain conditions the quantity

d–et = /

~Y.(o

is asymptotically distributed as a standard normal randomvariable N(O,l) when L (the number of strata) goes to w.This theory was derived for linear and nonlinear statisticsand is valid for any stratified multistage design in whichthe PSU’S are selected with replacement and in whichindependent subsamples are taken for those PSU’S se-lected more than once. The PSU’S in NHDS and NHISwe not selected with replacement, and the effect of thisdifference on the result is not known.

TO observe the magnitude of the effects ofindependence upon the confidence intervals, correlations

from each of the six sets of variables for NHDS and NHISthat vary across the observed range were used, The vari-ables, correlations, and effects are displayed in table G,

The column labeled E shows the ratio of the varianceassuming the correlation is zero to the true variance,whereas the next column gives the ratio of the standarderrors. The last column shows the probabilities of exceed-ing the true population value for u = 0,05. Whena = 0.05, the coefficient 1.96 is multiplied by the standarderror. One would expect that 5 percent of the time anerror will be made. However, this percent is either higheror lower depending upon whether the true variance islarger or smaller than the variance utilized. For example,if ti is 1.3, the number of standard errors being used is1.96 x 1.3 = 2.55. Thus, 0.0120 of the time an error willbe made.

Table G indicates that when the correlations arelarge, the confidence level is zero. This means that usingthe variance estimate calculated under the assumption ofzero correlation leads to no incorrect statements. Correla-tions that are negative result in confidence levels rangingfrom 0.0524 to 0,0688, Confidence intervals constructedbased on variance estimates that ignore correlations canbe distorted. These distortions would also be present inhypothesis testing procedures.

Table G. Effects of independence assumption on confidence intervals using statistics from the National Hospital Discharge Survey andthe National Health Interview Survey, by seiected characteristics: 1982-84

Probability ofincorrect statements

Characteristic Correlation E V7 (a= 0.05)

Congenital anomaly, under 15years ... . . . . . . . . . . . . . . . . . . . . . . 0.9570 21.4 4.615-44 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.0000

Cataract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...11o.8e13 12.0 3.5 0.00000.7347 3.1 1.8

Arthroplasty and replacement of hip, 65 years and over . . . .0.0006

0.5272 2.0Chronic conditions, female, ,,, . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4 0.00520.3861 1.6 1.3 0.0120

Physlclan vlslte, under 6yeers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.1162 1.1 1.0Work-[oss days, female . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.03760.0197 1.0

Work-loss daye, total, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.0 o.047a

-0.0131 1.0Short-stay hospital episodes, marriad, 55-64 yeara . . . . . . . . . . . . . . . .

1.0 0.0524-0.1233 0.9

Short-stay hospital episodes, divorced . . . . . . . . . . . . . . . . .0.9 0.0658

-0.1628 0.9 0.9 0.0686

13

Components ofvariance

The correlations for NHIS are not as large as thosefor NHDS, In both designs the PSU’S are the same fromyear to year; it is the second stage of sampling that variesfrom one year to the next, In NHDS the same hospitalsremain in the survey and, for the specified year, dischargesare sampled. The PSU’S in NHIS are groups of countiesand metropolitan areas; the same PSU’S are used fromyear to year, but different households within the samesegments are selected. The large correlations for NHDSprobably reflect the fact that the composition of hospitalsis not likely to change when measured by discharge andsurgical procedures performed from one year to the next.These features are structured by the facilities and staff ofthe hospital, In contrast, measures of morbidity, such asacute conditions and limitation of activity, are morevariable.

If the difference in the values of correlations dependsupon the type of primary sampling units, most of thevariability in NHDS should be among hospitals, whereasfor NHIS the largest component should be the variabilityamong the households within the PSU’S. Casady (27) andBean and Schnack (28) demonstrate how to apply theBRR method to obtain estimates of the components ofvariance.

To estimate the within component of variance, de-noted as Vw, each of the PSU’S is considered to be apseudostratum. Here, the sampled elements are randomlyplaced in one of two equal-sized groups. Constructing ahalf-sample thus consists of choosing one of the twogroups of elements from each of the PSU’S. The data froma half-sample are subject to the same estimation proce-dure as the -data from the total sample, creating anotherestimate of 9. ~y means of a second orthogonal pattern, Bestimates of 0 are produced, Then an estimate of thewithin component of variance is:

B

V~(i)‘~ (ij ‘i)2/Bi=l

The BRR estimator of Vii, was applied to both theNHDS and NHIS data. Each of the sampled PSU’S in thesample was considered to be a pseudostratum. Thenwithin each of these PSU’S, either the hospitals in NHDSor the households in NHIS were randomly allocated intoone of two groups.

Instead of displaying the within and between compo-nents of variance for each of the NHDS and NHISstatistics, the mean, maximum, and minimum of thepercent contribution of the within component of varianceare presented by year in tables H–N. Tables 7-12 show thepercent contribution for each variable by year, For severalstatistics in NHIS the within component of variance esti-mate is larger than the estimate for the total variance,NCHS assumes that the between component of variance iszero in this case.

As observed in table H, the within component ofvariance for the number of diagnostic discharges contrib-utes, on the average, 13–15 percent of the total variance,Therefore, most of the variability is between rather thanwithin hospitals. For the days-of-care statistics, the meanof the within component of variance increases to 21-23percent of the total variance (table J). The maximumacross the three years is 89 percent. Similar results arefound in table K for the within component of variancepercent contribution to the total variability for the numberof surgical procedures. Here the means are 17 percent for1982, 18.5 percent for 1983, and 12 percent for 1984. Thisbody of empirical evidence suggests that, regardless of thestatistic, the between component of variance is consider-ably larger than the within component of variance.

The opposite is true for the 60 NHIS statistics. For theacute and chronic conditions, the within component ofvariance counts for at least half of the variance (table L),The maximum is 97,9 percent for the year 1984, For theother 40 statistics, the average contribution is higher than50 percent; the mean percent contribution ranges from71.6 percent to 77.8 percent (tables M and N). Thesevalues provide empirical evidence that for NHIS most ofthe variability is among the households in the second stageof sampling,

Table H. Mean, maximum, and minimum of percent contributionof within component of variance to total variance for number ofpatients discharged from short-stay hospitals: United Statesj1982-84

Summary statist;c 1982 1983 1984

Percent

Mean . . . . . . . . . . . . . . . . . . 15.5 12.6 13.1Maximum . . . . . . . . . . . . . . . . 64.3 43.1 43.9Minimum . . . . . . . . . . . . . . . . 0.8 0.5 0.6

SOURCE National Center for Health Statistics. National Hospital Discharge S!mey, 1982-84,

14

Table J. Mean, maximum, and minimum of percent contribution ofwithin component of variance to total variance for number ofdays of care for patients discharged from short-stay hospitals:United States, 1982-84

Summary statistic 1982 1983 1984

Percent

Mean . . . . . . . . . . . . . . . . . . 22.9 22.6 21.5Maximum. . . . . . . . . . . . . . . . 89.3 66.8 54.3Mlnlmum . . . . . . . . . . . . . . . . 2.7 2.3 3.0

SOURCE National Center for Health Statistics. National Hospital Discharge Survey, 1982-84.

Table K. Mean, maximum, and minimum of percent contributionof within component of variance to total variance for number ofsurgical procedures for patients discharged from short-stayhospitals: United States, 1982-84

Summary statistic 1982 1983 1984

Table M. Mean, maximum, and minimum of percent contributionof within component of variance to total variance for number ofphysician visits and short-stay hospital episodes: United States,1982-84

Summary statistic 1982 1983 1984

Percent

Mean, . . . . . . . . . . . . . . . . . 75.5 76.7 77.0Maximum. . . . . . . . . . . . . . . . 96.5 97.7 93.2Minimum . . . . . . . . . . . . . . . . 35.9 27.1 56.6

SOURCE Nat!onal Canter for Health Statistics. National Health Intarviaw Survey, 19S2-84.

Table N. Mean, maximum, and minimum of percent contributionof within component of variance to total variance for number ofrestricted-activity days, beddays, and work-loss days:United States, 1982-84

Summary statistic 1982 1983 1984

Percent Percent

Mean . . . . . . . . . . . . . . . . . . 17.0 16.5 12.4Maximum. . . . . . . . . . . . . . . . 69.9 70.s 55.7Minimum . . . . . . . . . . . . . . . . 0.2 0.1 0.1

Mean . . . . . . . . . . . . . . . . . . 71.6 77.1 77,6Maximum . . . . . . . . . . . . . . . . 97.4Minimum . . . . . . . . . . . . . . . .

99.9 97.825.1 41.5 49,7

SOURCE:National Center for Health Statistics. National Hospital OischargeSurvey, 1982-84.

Table L, Mean, maximum, and minimum of percent contributionof within component of variance to total variance for number ofacute andchronlc conditions: United States, 1982-84

Summary statistic 1982 1983 1984

SOURCE: National Center for Health Statiatica. National Health lnterviaw Survey, 1982-64.

Mean . . . . . . . . . . . . . . . . . . 57.5 57.9 61.7Maximum . . . . . . . . . . . . . . . . 96.9 91.6 97.9Mlnlmum . . . . . . . . . . . . . . . . 1.9 1.6 2.3

SOURCE National Center for Health Statistics. National Health Interview Survey, 1982-84.

15

Discussion

Both NHDS and NHIS are conducted on a continuingbasis for the purpose of producing various estimates. Datafrom these surveys can be employed to estimate parame-ters for all the years combined, parameters for the currentyear, and parameters measuring change from one year tothe next, As discussed by Cochran (29), each of theseestimators requires a different design to achieve maximumprecision. Sampling theory indicates that for estimatingchange the same sampling units should be retained forboth surveys, whereas different sampling units are betterfor estimates using data from all time periods, An efficientscheme for constructing a current estimate is to retain afraction h of the sampling units from the previous surveywhile selecting 1- h fraction of new units. The optimumpercentage to retain depends upon the correlation. Mak-ing specific assumptions about the design, Cochran (29)shows that for sampling on two to four occasions, as thecorrelation increases, the optimum to retain decreases.For example, when sampling at two time periods, if thecorrelation is 0.7, the optimum to retain is 42 percent, butif the correlation increases to 0,8, the percentage shouldbe only 38 percent. For this design, the best type ofestimator is a double-sampling regression estimate.

The findings for number of discharges, days of care,and surgical procedures clearly indicate that varianceestimates based on the assumption that statistics from yearto year are independent are in error. The overestimationof variance becomes larger as the correlation nears one.These empirical results demonstrate that NHDS can beused to detect very small differences from year to year.However, with large correlations the design of 100-percentoverlap is not the most efficient for maximizing the preci-sion of yearly estimates. As Cochran (29) demonstratedfor simple random sampling and a regression estimator, ifthe correlation is 0,9 and the number of occasions is four,the percentage gain in efficiency is 59 percent when theoverlap is 50 percent; the gain in efficiency drops to40 percent when the overlap is 75 percent. Research isrequired to determine if this holds for NHDS. Because thehospitals are the same for each survey, the NHDS designis not very efficient at producing data for combining acrossthe years.

However, for reasons of economy, selecting a differentsample each year may not be feasible. A possible compro-mise that should be considered by NCHS is a designwhereby part of the sample is changed from year to year,Another consideration is using a regression-type estimator

that would take into account the estimates produced fromthe previous year.

The formula for the variances of differences given inthe appendixes to NHIS reports is based on the assump-tion that the sample for a given year, say 1982, is independ-ent of other sampIe years even though the primarysampling units are the same across the years, By assumingindependence, data are compared using the formula:

v (Yl – Y2) = v (YJ + v (YJ

The investigation of this assumption for 60 NHISstatistics indicates that the correlations range from anegative value of –0.20 to a high positive value of 0,39.The evidence here suggests that NHIS is great for addingyearly data together, but the design is not as efficient forexamining differences from one year to the next. Theresults do not provide any clear findings on how an annualpoint estimate would compare with a yearly regressionestimate.

A caveat to these conclusions is that the empiricalresults are for totals only. Correlations for means andproportions were not calculated. Parsons (30) estimatedcorrelations for selected statistics from the 1985 and 1986NHIS, For eight estimates of totals, the correlationsranged from 0.03 to 0,36, which are similar to the valuesobserved in this study. The range of correlations for 26means and proportions was from a low of -0.03 to a highof 0.38, which is similar to values observed for totals. Noresults are available for means and proportions for NHDS.A further evaluation of means and proportions for bothsurveys is warranted.

In summary, making the assumption of independencein NHDS may result in extreme overestimates of variance,at least for totals. The results clearly indicate that NHDSis ideally suited for measuring change over time, Thisfeature of the survey should be utilized more than itcurrently is. In NHIS when the assumption of independ-ence does not hold, the findings show that the varianceestimate is not an excessive overestimation. The varianceestimated was never more than 1.6 times as large as itshould be. One possible explanation is the difference inprimary sampling units. Empirical evidence suggests thatfor NHDS the within component of variance is less than26 percent of the total variance, whereas for NHIS thewithin component of variance accounts for at least half thevariability.

16

References

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Simmons WR, Baird JT. Pseudoreplication in the NCHSHealth Examination Survey. In: Goldfield ED, ed. Proceed-ings of the Social Statistics Section of the American Statis-tical Association, Pittsburgh: American StatisticalAssociation, 19-30.1968.

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18

List of detailed tables

1. Number of patients discharged from short-stay hospi-

2,

3.

~4.

5.,

6.

7,

tills, standard errors, and ;tandard errors o; diff&-ence, by selected characteristics: United States,1992-S4, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Number of days of care for patients discharged fromshort-stay hospitals, standard errors, and standarderrors of difference, by selected characteristics: UnitedStates, 19S2-S4 . . . . . . . . . . . ...

Table 1. Number of patients discharged from short-stay hospitals, standard errors, and standard errors of difference, by selectedcharacteristics: United States, 1982-84

Standard error1982 1983 1984 of dh%rerrce

Number of Number of Number of

patients Standard patients Standard patients StandardCharacteristic discharged error discharged error discharged error 1982-83 1983-84

Female . . . . . . . . . . . . . . . . . . . . . . . . . . .15–44years . . . . . . . . . . . . . . . . . . . . . . . .Male . . . . . . . . . . . . . . . . . . . . . . . . . . . .65years Andover . . . . . . . . . . . . . . . . . . . .45–64years. . . . . . . . . . . . . . . . . . . . . . . .Femaleswith deliveries.. ., . . . . . . . . . . . . .Under 15years . . . . . . . . . . . . . . . . . . . . . .Mentaldisorders . . . . . . . . . . . . . . . . . . . . .Mental disorders, 15-44years . . . . . . . . . .Acute myocardial infarction . . . . . . . . . . . .Cataract . . . . . . . . . . . . . . . . . . . . . . . . . .Atherosclerotic heart disease. . . . . . . . . . . . ,lnguinal hernia, male . . . . . . . . . . . . . . . . . .Cataract, 65yearsandover. . . . . . ., . . .Malignant neoplasmoflung. . . . . . . . . . , .Malignant neoplasm of breast, famale . . . . . . .Malignant neoplasm oflung, male. . . . . . . . .Fracture ofneckof femur, 65years and over, . .Congenital anomaly, under 15years . . . . . . . .

21,55414,51514,4289,9828,0943,6953,3921,614

892631520465417399301210168177161

6355204383162452162141037129362515301411111026

22,02714,53714,80510,7528,1003,7953,4431,627

912642562436403451320230203164178

Number in thousands

687 21,380547 13,973446 14,296362 10,801249 7,806229 3,734249 3,094108 1,63077 93430 67044 48728 32517 37836 38417 32512 22511 20511 19834 164

6955304393752552242331057429312118262113141131

284216186150119737534222220171517161112

1;

184161140121626554372821281616231713141010

SOURCE:National Center for Health Statiatica. National Hospital Oiacharga Survey, 1982-64,

Table 2. Number of days of care for patients discharged from short-stay hospitals, standard errors, and standard errors of difference, byseiected characteristics: United States, 1982-84

Standard error1982 1983 1984 of difference

Number of Standard Number of Standard Number of

CharacteristicStandard

days of care error days of care error days of care error 1982-83 1983-S4

Female . . . . . . . . . . . . . . . . . . . . . . . . . . .Male . . . . . . . . . . . . . . . . . . . . . . . . . . . .65years and over, . . . . . . . . . . . . . . . . . . .15–44years, .,, , . . . . . . . . . . . . . . . . . . .45–64years, . . . . . . . . . . . . . . . . . . . . . . .Mental disorders . . . . . . . . . . . . . . . . . . . . .Under 15years. .,.,..,,....,,.. . . . . .Famales with deliveries. . . . . . . . , . . . . . . . .Mental disorders, 15-44 years . . , . . . . .Acute myocardial infarction . . . . . . . . . . . .Atherosclerotic heart diseaee . . . . . . . . . . .Fracture ofneckof femur, 65 years and over .Malignant neoplasm of lung. . . . . . . . . . . . . .Malignant neoplasm of breast, female . . . . . . .Malignant neoplasm oflung, maie. ., . . . . . . .Inguinal hernia, male.,.,....,.. . . . . . . .Cataract . . . . . . . . . . . . . . . . . . . . . . . . . .Cataract, 65 years and over . . . . . . . . . .Congenital anomaly, under 15 years . . . , . , . .

146,117108,167100,80774,41663,51719,54115,54413,17210,5347,0744)1303,3183,2152,0822,0621,8721,5191,184

891

3,6583,0423,1482,4681,8601,6101,124

6951,131

35727619317314012188

10486

1a7

145,768109,100104)2e473,32861,51420,25915,74013,34111,1026,9803,6813,2673,3752,1672,0941,8201,4311,167

985

Number in thousands

4,083 134,5333,046 100,1613,348 96,0162,674 68,5861,717 56,1721,763 19,4201,375 13,919

756 12,8101,271 11,037

343 6,655245 2,386219 3,131174 3,089118 1,881116 1,91667 1,416

107 1,10591 897

206 932

3,7722,9el3,2192,3611,7241,6761,349

7201,239

310176202169149129777259

213

2,1891,4931,6541,2661,011

88650532950633820920218713513787585377

1,5411,2851,3941,035

62264137624246628215023017715814785736598

SOURCE National Center for Health Statistics, National Hospital Oiacharge Survey, 1982J34.

20

Table 3, Number of surgical procedures for patients discharged from short-stay hospitals, standard errors, and standard errors ofdifference, by selected characteristics: United States, 1982-84

Standard error1982 1983 1984 of difference

Number of Number of Number of

surgical Standard surgical Standard surgical StandardCharacteristic procedures error procedures error procedures error 1982-83 1983-84

All procedures:Total, .