Producing State Estimates with the 

Medical Expenditure Panel Survey, 

Household Component 

Agency for Healthcare Research and Quality

U.S. Department of Health & Human Services December 2005 

 
ABSTRACT

In recent years, there has been a growing need for estimates of health care 

expenditures at the state level. The Household Component of the Medical 

Expenditure Panel Survey (MEPS-HC) is a survey designed to collect information 

on and to produce national and regional estimates of health care expenditures. 

However, while the sample design allows for some state estimates to produced, 

there is no assurance that the quality of these estimates are adequate for use, since

the original purpose of the survey did not include production of state estimates. 

This paper describes the results of research using data from the MEPS-HC to

produce a selected group of state-level estimates for the 30 states with the largest 

populations. Three methods of estimation are used. Each method is evaluated 

using standard measures, and conclusions about the quality of these estimates, 

along with recommendations, are given. 

Suggested Citation: 

Sommers, J. P. Producing State Estimates with the Medical Expenditure Panel 

Survey, Household Component. Methodology Report No. 16. December 2005. 

Agency for Healthcare Research and Quality, Rockville, Md. http://www.meps. 

ahrq.gov/papers/mr16/mr16.pdf 

∗ ∗ ∗

The estimates in this report are based on the most recent data available at the time 

the report was written. However, selected elements of MEPS data may be revised 

on the basis of additional analyses, which could result in slightly different 

estimates from those shown here. Please check the MEPS Web site for the most 

current file releases. 

Center for Financing, Access, and Cost Trends 

Agency for Healthcare Research and Quality

540 Gaither Road 

Rockville, MD 20850 

www.meps.ahrq.gov

ii
The Medical Expenditure Panel Survey (MEPS) 

Background 

The Medical Expenditure Panel Survey (MEPS) is conducted to provide nationally

representative estimates of health care use, expenditures, sources of payment, and 

insurance coverage for the U.S. civilian noninstitutionalized population. MEPS is 

cosponsored by the Agency for Healthcare Research and Quality (AHRQ), formerly the 

Agency for Health Care Policy and Research, and the National Center for Health 

Statistics (NCHS). 

MEPS comprises three component surveys: the Household Component (HC), the 

Medical Provider Component (MPC), and the Insurance Component (IC). The HC is the

core survey, and it forms the basis for the MPC sample and part of the IC sample. 

Together these surveys yield comprehensive data that provide national estimates of the 

level and distribution of health care use and expenditures, support health services 

research, and can be used to assess health care policy implications. 

MEPS is the third in a series of national probability surveys conducted by AHRQ on the 

financing and use of medical care in the United States. The National Medical Care

Expenditure Survey (NMCES) was conducted in 1977, the National Medical 

Expenditure Survey (NMES) in 1987. Beginning in 1996, MEPS continues this series 

with design enhancements and efficiencies that provide a more current data resource to 

capture the changing dynamics of the health care delivery and insurance system. 

The design efficiencies incorporated into MEPS are in accordance with the Department 

of Health and Human Services (DHHS) Survey Integration Plan of June 1995, which 

focused on consolidating DHHS surveys, achieving cost efficiencies, reducing 

respondent burden, and enhancing analytical capacities. To accommodate these goals, 

new MEPS design features include linkage with the National Health Interview Survey

(NHIS), from which the sample for the MEPS-HC is drawn, and enhanced longitudinal 

data collection for core survey components. The MEPS-HC augments NHIS by selecting 

a sample of NHIS respondents, collecting additional data on their health care 

expenditures, and linking these data with additional information collected from the 

respondents’ medical providers, employers, and insurance providers. 

Household Component 

The MEPS-HC, a nationally representative survey of the U.S. civilian noninstitutionalized population, collects medical expenditure data at both the person and household 

levels. The HC collects detailed data on demographic characteristics, health conditions, 

health status, use of medical care services, charges and payments, access to care, 

satisfaction with care, health insurance coverage, income, and employment. 

The HC uses an overlapping panel design in which data are collected through a 

preliminary contact followed by a series of five rounds of interviews over a two and a 

half year period. Using computer-assisted personal interviewing (CAPI) technology, data 

on medical expenditures and use for two calendar years are collected from each

household. This series of data collection rounds is launched each subsequent year on a 

new sample of households to provide overlapping panels of survey data and, when 

ii
combined with other ongoing panels, will provide continuous and current estimates of

health care expenditures. 

The sampling frame for the MEPS-HC is drawn from respondents to NHIS, conducted

by NCHS. NHIS provides a nationally representative sample of the U.S. civilian 

noninstitutionalized population, with oversampling of Hispanics and blacks. 

Medical Provider Component 

The MEPS-MPC supplements and validates information on medical care events reported 

in the MEPS-HC by contacting medical providers and pharmacies identified by household respondents. The MPC sample includes all hospitals, hospital physicians, home 

health agencies, and pharmacies reported in the HC. Also included in the MPC are all 

office-based physicians:

 Providing care for HC respondents receiving Medicaid. 

 Associated with a 75 percent sample of households receiving care through an HMO 

(health maintenance organization) or managed care plan. 

 Associated with a 25 percent sample of the remaining households. Data are collected 

on medical and financial characteristics of medical and pharmacy events reported by

HC respondents, including: 

 Diagnoses coded according to ICD-9 (9th Revision, International Classification of 

Diseases) and DSMIV (Fourth Edition, Diagnostic and Statistical Manual of Mental

Disorders). 

 Physician procedure codes classified by CPT-4 (Current Procedural Terminology, 

Version 4). 

 Inpatient stay codes classified by DRG (diagnosis related group). 

 Prescriptions coded by national drug code (NDC), medication names, strength, and 

quantity dispensed. 

 Charges, payments, and the reasons for any difference between charges and 

payments. 

The MPC is conducted through telephone interviews and mailed survey materials. 

Insurance Component 

The MEPS-IC collects data on health insurance plans obtained through private and 

public sector employers. Data obtained in the IC include the number and types of private 

insurance plans offered, benefits associated with these plans, premiums, contributions by

employers and employees, and employer characteristics. 

Establishments participating in the MEPS-IC are selected through three sampling 

frames: 

 A list of employers or other insurance providers identified by MEPS-HC respondents 

who report having private health insurance at the Round 1 interview. 

 A Bureau of the Census list frame of private-sector business establishments. 

 The Census of Governments from the Bureau of the Census. 

To provide an integrated picture of health insurance, data collected from the first 

sampling frame (employers and other insurance providers) are linked back to data

provided by the MEPS-HC respondents. Data from the other three sampling frames are 

collected to provide annual national and State estimates of the supply of private health 

iii
insurance available to American workers and to evaluate policy issues pertaining to 

health insurance. Since 2000, the Bureau of Economic Analysis has used national 

estimates of employer contributions to group health insurance from the MEPS-IC in the 

computation of Gross Domestic Product (GDP). 

The MEPS-IC is an annual panel survey. Data are collected from the selected

organizations through a prescreening telephone interview, a mailed questionnaire, and a 

telephone follow-up for nonrespondents. 

Survey Management 

MEPS data are collected under the authority of the Public Health Service Act. They are 

edited and published in accordance with the confidentiality provisions of this act and the

Privacy Act. NCHS provides consultation and technical assistance. 

As soon as data collection and editing are completed, the MEPS survey data are released 

to the public in staged releases of summary reports and microdata files. Summary reports 

are released as printed documents and electronic files. Microdata files are released on 

CD-ROM and/or as electronic files.

Printed documents and CD-ROMs are available through the AHRQ Publications 

Clearinghouse. Write or call: 

AHRQ Publications Clearinghouse 

Attn: (publication number) 

P.O. Box 8547 Silver Spring, MD 20907 

800-358-9295 

703-437-2078 (callers outside the United States only)

888-586-6340 (toll-free TDD service; hearing impaired only) 

To order online, send an e-mail to: ahrqpubs@ahrq.gov. 

Be sure to specify the AHRQ number of the document or CD-ROM you are requesting. 

Selected electronic files are available through the Internet on the MEPS Web site: 

http://www.meps.ahrq.gov/

For more information, visit the MEPS Web site or e-mail mepspd@ahrq.gov. 

iv
Table of Contents

Background ..................................................................................................................... 1

Need for State Estimates from the MEPS-HC ................................................................. 2

State Estimates with MEP-HC Data ................................................................................ 3

The MEPS-HC ............................................................................................................. 3

Number of PSUs .......................................................................................................... 3 

Design-based state estimates........................................................................................ 3

Design-based estimates with weights post-stratified by state ....................................... 5

Composite estimation................................................................................................... 7

Conclusions and Recommendations .............................................................................. 10

Acknowledgments..........................................................................................................11 

References..................................................................................................................... 11

v
Producing State Estimates with the Medical Expenditure 

Panel Survey, Household Component 

John P. Sommers, PhD, Agency for Healthcare Research and Quality 

Background 

An investigation of results produced from large-scale Federal household surveys, reveals 

few state estimates produced from these surveys. The exception is the Current 

Population Survey (CPS), conducted by the Census Bureau and sponsored by the Bureau 

of Labor Statistics, which is the source of state income, poverty, and health care 

uninsurance rate estimates (Census Bureau Web site: c). However, the state personal 

income and uninsurance rate estimates are multiple-year averages produced from 

combining several years of data (DeNavas-Walt et al., 2004). County- and state-level 

estimates of income and poverty are produced using special small area estimation 

techniques using CPS and other data. State estimates are rare, and design-based one-year 

estimates do not seem to be routinely published. State-level estimates are not routinely

produced from other large-scale Federal household surveys, including the following: 

 The National Health Interview Survey (NHIS), sponsored by the Centers for Disease 

Control and Prevention’s National Center for Health Statistics (NCHS) and 

conducted by the Census Bureau (NCHS Web site and Botman, et al., 2000) 

 The Survey of Income and Program Participation (SIPP), conducted by the Census

Bureau (Census Bureau Web site: a and Kostanich and Dippo, 2002) 

 The American Housing Survey (AHS), sponsored by the Department of Housing and 

Urban Development and conducted by the Census Bureau (Census Bureau Web site: 

b and Census Bureau Web site: d ) 

 The Household Component of the Medical Expenditure Panel Survey (MEPS-HC), 

sponsored by the Agency for Healthcare Research and Quality (AHRQ) (Medical 

Expenditure Panel Survey Web site and Cohen, 2000). 

A basic indication explaining why state-level estimates are not produced with these

surveys can be found in the estimates that are produced with the CPS data by the Census

Bureau. Multiyear averages and small area estimation techniques are used when the 

reliability of the design-based estimates is poor. Multiyear averages increase sample 

sizes and thus lower errors. Small area estimation techniques use modeling and other 

complex and time-intensive estimation methods to “borrow strength” from data outside

the state or outside the survey to improve results with poor precision that are produced 

using design-based survey estimation techniques, such as weighted means and totals.

(Ghosh and Rao, 1994) 

For the large national Federal surveys, unbiased design-based estimates for states are 

possible. An unbiased estimate of the state average for any variable is simply the 

weighted sum of the variable for all sample units within the state divided by the sum of

the weights for the sample units within the state (Cochran, 1977). There are two reasons, 

however, why design-based estimates for individual states are generally of poor 

1
precision for the large national surveys. The first reason is that to meet population subdomain and for key survey estimates for specified proportions, the survey sample sizes 

are generally allocated on a national basis. For general population-based national 

surveys, survey budgets do not allow adequate sample size in each state to produce state 

estimates with acceptable precision. There is generally no focus on state estimates, thus

no minimum state samples. Even for surveys with state-level stratification as a design 

feature, such as the NHIS, given that the top10 states have over half the population, the 

sample sizes for the remaining states can fall below an ideal sample size. 

Aside from the possible lack of adequate sample sizes in states, the sample designs used 

in the surveys listed above also make it difficult to produce high-quality design-based

estimates for states. All the surveys have stratified multistage cluster sample designs.

This involves sampling of clusters, sets of counties. This limits the samples in each state, 

no matter how many persons are in the final sample, to a limited number of counties 

within each state. This is done because of the costs of personal household visits to

collect the information if the sample of persons were spread widely and evenly across 

the entire country. This clustering of the sample can have a large impact on the sampling 

error. If the average values for the variables being estimated vary considerably across the 

clusters of counties, then the sampling error is effectively limited by the number of

county clusters. For further detail on the variances of cluster samples, see Cochran, 

1977. 

Need for State Estimates from the MEPS-HC 

In 2004, the increase in costs of health insurance was above 10 percent (Kaiser Family

Foundation, 2004). Further, large numbers of persons are without health coverage 

(DeNavas-Walt et al., 2004). At the same time, state budgets have been hard hit by loss 

of revenues and increasing health care costs from Medicaid spending. In 2003, Medicaid

spending increased 8 percent over 2002 levels and was 21.4 percent of all state spending.

As a result, most states reduced Medicaid benefits, reduced Medicaid eligibility, and 

implemented prescription drug cost control programs for Medicaid (National Association 

of State Budget Officers, 2003). 

Given the variety of methods being implemented by the states to control Medicaid and 

other health costs and to increase the number of persons with health insurance, it is of 

great interest for all states to know which efforts have succeeded and which have not. To

assess these results, one must have reliable data. Health care usage and costs at the state 

level must be analyzed to determine if costs are increasing over time and if more people 

are using health care. It would also be of use to know who is using care and what types; 

for instance, how much care certain parts of the population use and what type, doctor 

visits, hospitals, etc. 

Because of these data needs, there is an emerging drive within the Department of Health 

and Human Services (DHHS) to examine the feasibility of producing state data from

population-based surveys and other sources. This paper examines the possibility of 

producing selected state estimates from one core DHHS data source. 

2
State Estimates with MEP-HC Data

The MEPS-HC 

National estimates of health care expenditures are an important resource for health 

policymakers and health services researchers. MEPS collects information regarding the 

use and payment for health care services from a nationally representative sample of the 

U.S. civilian noninstitutionalized population. In addition to the annual nationally

representative expenditures estimates from MEPS, there is a growing need for estimates 

at the subnational level. While MEPS was designed to ensure reliable estimates at the 

national and regional level for individuals, families, and selected population subgroups, 

recent research has focused on the capacity for subnational estimates. A 2004 MEPS

Statistical Brief (Machlin, et al., 2004) provided estimates of health care expenses and 

uninsured rates for the U.S. community population under age 65 in 10 large metropolitan

areas. This paper examines the capacity for producing expenditure estimates with 

acceptable precision at the state level using MEPS. 

The sample of households for the MEPS-HC is a subsample of households that 

responded to the prior year’s NHIS. The MEPS sample is drawn from approximately

one-half of the primary sampling units (PSUs) in the NHIS. Oversampling of households

with Hispanics and African Americans carries over from the NHIS to the MEPS sample

design. In addition, in forming strata for selection of the first-stage sampling units or 

PSUs in the NHIS, state was used as a stratification variable. This design feature carries 

over from the NHIS to MEPS-HC since the MEPS-HC uses approximately half of the 

NHIS PSUs. In this paper, the MEPS-HC design is investigated with respect to its 

capacity to support reliable state-level estimates for a selected number of states. 

Number of PSUs 

The first issue one must address when trying to make state estimates from a survey with 

a cluster sample is the number of PSUs available to make the estimates for each state. If

the between PSU variance is large compared with the within PSU variance, a very small

number of PSUs means a large error, regardless of the number of final stage sampling 

units (Cochran, 1977). For this reason, we checked the PSU structure for the MEPS. We

found that if we ranked states by total population that the 10 largest states each had 

either more than six PSUs and/or had a number of certainty PSUs that covered a large 

portion (60 percent or more) of the state population. For the second largest set of states, 

those with population ranks from 11 through 20, the states contained at least four PSUs 

and/or had a certainty PSU that covered a large portion of the state population. For states 

with population ranks from 21 through 30, the minimum number of PSUs was three, but 

most had four or more non-certainty PSUs and population coverage of the selected PSUs 

was limited. However, since there are enough PSUs to calculate an error for each of 

these states, this third set of states is also used in the analysis. Most of the remaining 

small states had either one or no PSUs, and these were not included in the analysis. 

Design-based state estimates 

The first step of the research was to develop simple design-based estimates using the 

MEPS-HC design structure and data for 2002 for six types of expenditures: total (all 

types combined), dental visits, inpatient facility stays, office-based visits, outpatient 

3
doctor visits, and prescription drugs. This was done using the weights that were created 

by post-stratification to national CPS values for cells defined by age, race, gender, and 

marital status. For each type of expenditure, an estimate for each state was made for the

percentage of persons who had that expenditure, the mean for those who had an 

expenditure, and the total expenditures. These estimates were created for each of the 30 

largest states defined by total population. Relative standard error results were averaged 

for each type of estimate for three state groups: the 10 largest states, the second 10 

largest states, and the third 10 largest states. These are called groups 1, 2, and 3 in order 

from the largest to smallest states. Results are shown in table 1. Maximum relative 

standard errors in each group are also shown.

The standard errors for the estimates shown in the tables in this report were produced 

using a set of 64 partially balanced half samples and the balanced repeated replication

method (Wolter,1985). This was done to take into account the post-stratification done to 

the sampling weights. For variance estimation purposes, the weights were post-stratified 

for each replicate. We found that use of Taylor Series methods for this first set of

design-based estimates gave similar results. However, this was not true for results 

produced and discussed latter in this paper and shown in tables 2 and 3. 

Table 1. Average and maximum relative standard errors (RSEs) by state size group for typical estimates:

National post-stratification, estimates are given in order of column headings, from left to right,by expenditure

type, size group, mean r s e, and max r s e,

Conditional mean

expenditures

Percent of persons

with expenditure

Total 

expenditures

Expenditure type Size group Mean RSE Max RSE Mean RSE Max RSE Mean RSE Max RSE 

All types combined 1 0.0989 0.1697 0.0226 0.0327 0.2159 0.3437

All types combined 2 0.1602 0.3223 0.0291 0.0424 0.3336 0.5232

All types combined 3 0.1677 0.3377 0.0389 0.1007 0.4120 0.5737

Dental visits 1 0.1423 0.2361 0.0713 0.1035 0.2387 0.3130

Dental visits 2 0.1453 0.2528 0.0947 0.1538 0.3484 0.5089

Dental visits 3 0.2499 0.5821 0.1272 0.2031 0.4438 0.6494

Inpatient facility 1 0.2110 0.4049 0.1299 0.1834 0.2928 0.4152

Inpatient facility 2 0.2920 0.5901 0.2056 0.3031 0.4618 0.7730

Inpatient facility 3 0.3495 0.8165 0.2404 0.4383 0.5629 0.7007

Office based visits 1 0.1091 0.1621 0.0330 0.0514 0.2138 0.3180

Office based visits 2 0.1417 0.2558 0.0468 0.0765 0.3212 0.4930

Office based visits 3 0.1899 0.2571 0.0603 0.1372 0.4060 0.5495

Outpatient doctors 1 0.1746 0.2661 0.1231 0.1761 0.2782 0.4306

Outpatient doctors 2 0.338 0.6895 0.2111 0.3783 0.4673 0.7005

Outpatient doctors 3 0.3764 0.7446 0.2794 0.4949 0.5280 0.7346

Prescription drugs 1 0.0953 0.1923 0.0389 0.0532 0.2305 0.4494

Prescription drugs 2 0.1290 0.2104 0.0531 0.0912 0.3401 0.531 

Prescription drugs 3 0.1696 0.2695 0.0667 0.1392 0.4025 0.5868

Source: AHRQ, Household Component of the Medical Expenditure Panel Survey, 2002

4
Table 1 shows 

 State-level estimates with acceptable precision can be made for some states from the 

MEPS-HC, but there are still many estimates of poor precision. This can be seen

from the maximum RSE values for many of the groups. (Note: RSE ge 0.30 is 

considered as poor.) 

 Estimates for the percentage of persons with each type of expenditure have good 

precision, while the total expenditure estimates are of uniformly poor quality. 

 The estimates are generally of best quality for expenditure types that affect the most

people and thus have the greatest sample, such as all types combined or office-based 

visits, while the worst are inpatient facility and outpatient doctor estimates because 

the numbers of sample persons with these expenditure types are very small. None of 

the size groups of states could be published for the latter two types of expenditures. 

 The estimates decline in precision as the size of states decreases.

 With a goal of a maximum RSEs of 20 percent, for the majority of the cases only

estimates for the 10 largest states could be produced. 

Most of these results with respect to the reliability of the estimates could be expected.

Most are directly related to expected sample. For any type of expenditure, the percentage

of persons with an expenditure is the best estimate because this estimate is based upon 

the entire sample and the distribution. The conditional mean and total expenditure 

estimates are based upon subsets of the sample in each state. Further, these estimates are 

based upon the distribution of expenditures which can be highly skewed. The extremely

poor quality of the total expenditure estimates versus the conditional mean estimates can 

be attributed to the fact that the between PSU variances of population totals are much

higher than the between PSU variances of average usage. 

Design-based estimates with weights post-stratified by state 

After review of the first set of results, it was decided that the estimates could be 

improved using weights that were post-stratified to CPS population totals at the state 

level. For each state, the nonresponse adjusted weights were post-stratified by state, age, 

race, and gender. The use of these weights produced a marked improvement in the 

precision of the results. 

5
Table 2. Average and maximum relative standard errors (RSEs) by state size group for typical estimates:

State level post-stratification, estimates are given in order of column headings, from left to right,by

expenditure type, size group, mean r s e, and max r s e,

Conditional mean

expenditures

Percent of persons

with expenditure 

Total 

expenditures

Expenditure type Size group Mean RSE Max RSE Mean RSE Max RSE Mean RSE Max RSE

All types combined 1 0.0744 0.1126 0.0152 0.0206 0.0756 0.1181

All types combined 2 0.1072 0.2112 0.0198 0.0283 0.1085 0.2179

All types combined 3 0.1250 0.2635 0.0256 0.0558 0.1340 0.2582

Dental visits 1 0.1128 0.2032 0.0512 0.0794 0.1288 0.2214

Dental visits 2 0.1123 0.1947 0.0703 0.1050 0.1252 0.1974

Dental visits 3 0.1804 0.4529 0.0921 0.1366 0.1988 0.4655

Inpatient facility 1 0.1631 0.2852 0.0972 0.1482 0.1759 0.2896

Inpatient facility 2 0.2229 0.5188 0.1427 0.2009 0.2738 0.5763

Inpatient facility 3 0.2591 0.6084 0.1870 0.3432 0.3183 0.6300

Office based visits 1 0.0869 0.1217 0.0227 0.0349 0.0887 0.1252

Office based visits 2 0.1037 0.1751 0.0335 0.0589 0.1112 0.1827

Office based visits 3 0.1376 0.2090 0.0429 0.0829 0.1564 0.2494

Outpatient doctors 1 0.1399 0.2267 0.0883 0.1278 0.1574 0.2294

Outpatient doctors 2 0.2406 0.3997 0.1561 0.2291 0.2717 0.3809

Outpatient doctors 3 0.2546 0.4987 0.2078 0.3453 0.3061 0.6082

Prescription drugs 1 0.0674 0.1496 0.0254 0.0357 0.0743 0.1534

Prescription drugs 2 0.0890 0.1529 0.0349 0.0582 0.0976 0.1592

Prescription drugs 3 0.1235 0.2644 0.0418 0.1015 0.1353 0.2463

Source: AHRQ, Household Component of the Medical Expenditure Panel Survey, 2002

The use of weights post-stratified with state population totals yielded the following 

results shown in table 2: 

 Results are uniformly better than those in table 1. 

 Of special interest are the results for total expenditures for each type. These

estimates are now of approximately the same quality as those for the conditional 

mean expenditures for the same type of expenditure. This improvement is likely the 

result of the stabilization of totals from the use of state-specific post-stratification.

This post-stratification essentially makes the estimates of totals a ration estimate 

which uses the average usage times the mean conditional expenditure times an 

outside population total for each state. As we saw earlier, the RSEs of average usage 

and mean conditional expenditure estimates were more precise, and this change in 

the estimates of total expenditures results in estimates with RSEs closer to those of 

the first two types of estimates. Nevertheless, there are still estimates with very large 

RSEs. 

 Although improved, estimates for inpatient facility and outpatient doctors are still 

problematic. 

 For all other expenditure groups, all types combined, office-based visits, dental 

visits, and prescription drugs, the improvements are such that one could make 

6
estimates for the 20 largest states in size groups 1 and 2, with very few estimates

with an RSE greater than 20 percent. 

Estimates in an AHRQ report titled Estimates of Health Care Expenditures for the 10 

Largest States, 2002, are based on this methodology (Machlin and Sommers, 2005). 

Composite estimation 

Given that we have produced estimates for every state, a small area estimation approach 

could potentially be used to adjust and improve these estimates by “borrowing strength

across states.” In this case, one can consider a random effects model or a Bayesian 

approach based upon such a model (Ghosh and Rao, 1994). However, it was decided to 

use a method that makes no assumptions about the relationships among estimates and is 

simple to apply across a large number of estimates.

It was decided to apply a composite estimation technique to estimates of the conditional

mean expenditures and percentages with an expenditure. Strength can be borrowed from 

sample estimates at the Census Division level, the regional level, or the national level. 

This type of estimate uses a weighted average

Y w c = + Y − w Y $ ( ) $ 1 1 2

1 2

( )

( )

 where Y and Y 

are usually a synthetic and direct estimates of the same item. The weight is determined 

by minimizing the mean squared error (MSE) of the linear combination of estimators. In 

this case, the sample Census Division estimate for a larger geographic area was chosen 

as the synthetic estimate and the state estimate as the direct estimate. The Division 

estimates were chosen as the synthetic estimate because there seemed to be good 

correlation between estimates of states within the same Division. Thus, it seemed that 

the other states in the Division would be most helpful in providing information and 

strength for one another within the Division. Under these conditions, assuming that the 

state estimate is an unbiased estimate of the state value, then the value of w which 

minimizes the MSE of the composite estimator is

w

Y Y Y

Y Y Y Y bias

s s d

s d s d

= −

+ − +

var( ) cov( )

var( ) var( ) cov( )

,

2 , 2

2 2 ( ( ) ( )) E Ys E Yd bias = −

where s denotes the design-based state estimator and d the division estimator for the 

larger geographic area. Bias squared in this case is the squared difference in expected

values of the state and synthetic estimates:

This result can be obtained simply by taking the MSE of the composite estimate and

using differentiation to calculate the value of w which minimizes the result. 

The terms in the numerator can be estimated using the half samples. The bottom term 

can be estimated using the square of the difference of the two estimators. However, that 

estimate can be very unstable. Thus, a method using the sum of squared differences of

the half sample estimates was developed to estimate the denominator term, which is the 

variance of the difference of the two estimators plus the squared difference in their 

expected values. Using these estimates for w, new estimates and their MSEs and RSEs

were calculated using 

7
Var Yc d w Var Y w Var Ys w w C Yd Ys ( ) = + ( ) ( ) − ( ) − ( ) − ( , ) 2 2 1 2 1

MSE Yc d w Var Y w Var Ys w w Cov Yd Ys ( ) = + ()( − ) ( ) + ( − ) ( , ) 2 2 1 2 1 +w bias 2 2

( )2 2 E Y Y Var(Y Y ) bias d − s = d − s +

( )2 2 E Y Y 2*Var(Y Y ) bias di − si = d − s +

This MSE was estimated using the individual parts developed in the calculation of w. Of 

special interest is the estimate of the bias. One can use the fact that 

One can just take the difference of the two estimates squared and subtract an estimate of

the variance of the difference of the two estimates to obtain an estimate of the bias. 

However, this is an unstable estimate. We instead take advantage of the following 

expected value for the difference of the two estimates for the ith half sample: 

Thus we average the values of the difference squared for each half sample and subtract 

the standard estimate of twice the variance to obtain an estimate of the bias. 

Because the value of w is an estimate, the sample estimate of this variance is only an 

estimate of the variance of the estimator given the estimate of w. This does not account 

for the expected variance due to the estimation of w. To account for this variation, w was 

estimated using groups of half samples. Specifically, w was estimated using these sets of 

half samples and half sample estimates of the composite were made by varying the 

estimates of w with the full sample values of the model and division estimates. Addition 

of this term was prompted by bias found by Prassad and Rao (1990) in formulas that did

not consider the variation caused by estimation of w. This term did not add large sums to 

the overall errors. This indicates that the estimates of variance and bias are generally

stable. However, when the value of w was very close to 1 or 0, the estimates of w 

became less stable. It was decided that the value of w would be limited to values

between .1 and .9 for the final composite estimates currently produced. 

Table 3 below shows values obtained using the composite estimation technique, 

comparable to those in tables 1 and 2 for conditional mean expenditures and percentage

with the expenditure type. This synthetic estimate was chosen because it gave better 

results than using the Census Division and about the same quality as combining state and 

national estimates while not changing the original value of the state estimates to the 

same degree as using the national estimates as the synthetic estimate. 

We should note that as with any set of error estimates made using sampling data, the 

estimates of mean squared errors used have errors also. Thus, some of the composite 

estimates could have less quality than the numbers indicate. This is true when making 

estimates of error for any set of estimates. However, we base our final evaluation of the 

quality of the composite estimates when compared to the other unbiased estimators not 

on the results for just one estimate, but on the fact that as a group the estimates of errors

for the composite estimators are almost uniformly better than those for the more standard 

design-based estimates. 

8
Table 3. Average and maximum relative mean squared errors (RMSEs) by state size

group for typical estimates: Composite estimation using regional estimates, estimates are 

given in order of column headings, from left to right, by expenditure type, size group, mean r m s e, max r m s e,

Conditional mean

expenditures

Percent of persons with

expenditure 

Expenditure Type Size Group Mean RMSE Max RMSE Mean RMSE Max RMSE 

All types combined 1 0.0587 0.0914 0.0107 0.0189

All types combined 2 0.0533 0.1116 0.0117 0.0176

All types combined 3 0.0758 0.1556 0.0143 0.0241

Dental visits 1 0.0699 0.1032 0.0418 0.0629

Dental visits 2 0.0688 0.1311 0.0536 0.0682

Dental visits 3 0.0912 0.1742 0.0719 0.1378

Inpatient facility 1 0.1086 0.1441 0.0694 0.0989

Inpatient facility 2 0.1217 0.1521 0.0587 0.1149

Inpatient facility 3 0.1750 0.3330 0.0872 0.2130

Office based visits 1 0.0598 0.1112 0.0163 0.0272

Office based visits 2 0.0609 0.1009 0.0182 0.0359

Office based visits 3 0.0657 0.1240 0.0261 0.0538

Outpatient doctors 1 0.0866 0.1223 0.0747 0.1212

Outpatient doctors 2 0.1119 0.2355 0.1243 0.1689

Outpatient doctors 3 0.1639 0.4506 0.1778 0.3118

Prescription drugs 1 0.0497 0.0841 0.0193 0.0252

Prescription drugs 2 0.0536 0.1053 0.0193 0.0459

Prescription drugs 3 0.0747 0.2189 0.0267 0.0513

Source: AHRQ, Household Component of the Medical Expenditure Panel Survey, 2002

One can see from table 3 that this technique provides several advantages. 

 In spite of their biased nature, estimates have uniformly better estimated relative

mean squared errors than the previous two methods.

 Improvement was greatest where it was needed most, i.e., in size groups 2 and 3 and 

inpatient facility and outpatient doctors. 

 Improvements were such that one could make estimates for all expenditure types for 

state size groups 1 and 2, the 20 largest states, and have very few estimates with 

greater than a 20 percent relative standard error and none with a relative standard 

error greater than 30 percent. With the exception of errors for inpatient facility and 

outpatient doctors, the vast majority of the estimates for the 20 largest states have

relative errors of less than 10 percent. 

 For all but the least common types of expenditures, inpatient facility and outpatient 

doctors, most of the estimates for the set of the smallest states, size group 3, are 

acceptable using a 10 percent relative error as the standard of acceptance. Few of 

these estimates for the smallest states have relative error measures of over 20

percent. 

9
One should note that although estimates of totals are not evaluated, if one has good 

estimates of means and proportions, one can make estimates of totals by multiplying 

means by total population estimates from other sources. 

Conclusions and Recommendations 

We made two sets of direct state estimates with 2002 MEPS-HC data for the 30 largest 

states. The first set was produced using standard nationally post-stratified weights, and 

the second used weights post-stratified within each of the largest states. Each set of 

estimates included estimates for six types of expenditures and three measures, an 

estimate for total expenditures, and estimates for conditional mean expenditure per 

person with an expenditure and for the percentage of persons with an expenditure. After 

this, estimates for the same six types of expenditures were made for the mean and the 

percentage with an expenditure using a small area technique where strength was 

borrowed for state estimates from data for the Census Division. Several patterns of

information surfaced: 

 Estimates decreased in quality as the population size of the state decreased and the 

number of PSUs decreased. 

 The best estimates in any group were for the percentage of persons who had

expenditures. Estimates of error for the conditional mean expenditure and total 

expenditures were correlated with the percentage of persons who had the 

expenditure, i.e., sample size used. 

 Overall, the relative errors of the estimates were best for the small area technique 

and worst based on the nationally stratified weights. 

 One can make estimates for the 20 largest states for the more common expenditures 

with the state post-stratified weights, and one can generally make improved 

estimates with the small area technique for each state for all the expenditure types 

tested. 

The research was very successful and confirms the feasibility for making state estimates 

with the MEPS-HC to help inform health policy decisions at the state level. Given these 

results, it seems that estimates could be produced for additional survey variables at the 

state level for the 20 largest states. Whenever possible, the method used should be the 

small area technique. Efforts should be focused on items that affect a large enough 

portion of the population so that enough sample is available to produce estimates with 

acceptable quality. Among the items that might be considered are expenditures for obese 

and overweight persons, persons with private health insurance or persons without health

insurance, all subsets that might have a large enough sample to produce reliable 

estimates. 

Given the simplicity of the process and that development of state stratified weights and

software to produce these estimates have been completed, additional estimates can and 

should be produced and assessed to determine how many state-level estimates can be

produced on a regular basis in the future. 

10
Acknowledgments

The author would like to thank Trena Ezzati-Rice and Steve Machlin for their valuable

ideas and comments which were used freely in the production of this work. 

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