Examination of Skewed Health Expenditure Data from the Medical Expenditure Panel Survey

(MEPS)

William W. Yu and Steven Machlin

Agency for Healthcare Research and Quality Working Paper No. 04002 October 2004

Suggested citation: Yu WW, Machlin S. Examination of Skewed Health Expenditure Data from

the Medical Expenditure Panel Survey (MEPS). Agency for Healthcare Research and Quality

Working Paper No. 04002, October 2004, http://www.ahrq.gov.

AHRQ Working Papers provide preliminary analysis of substantive, technical, and methodological

issues. The papers are works in progress and have not undergone a formal peer review. They

are distributed to share valuable experience and research. Comments are welcome and should

be directed to the authors. The views expressed are those of the authors and no official

endorsement by the Agency for Healthcare Research and Quality or the Department of Health

and Human Services is intended or should be inferred.
Examination of Skewed Health Expenditure Data from the Medical Expenditure Panel 

Survey (MEPS) 

William W. Yu and Steve Machlin 

October 2004 

ABSTRACT 

The Medical Expenditure Panel Survey Household Component (MEPS-HC) is designed 

to provide nationally representative annual estimates of health care use, expenditures, 

sources of payment, and insurance coverage for the U.S. civilian noninstitutionalized 

population. The expenditure data from MEPS have been shown to exhibit a marked 

positive skewness, with a few high expenditure respondents and many low or zero 

expenditure respondents. As a consequence of this departure from the normal 

distribution, the frequency with which a conventional confidence interval for a MEPS 

expenditure estimate will not capture the true population parameter may be higher than 

the probability stated for the confidence interval. Based on repeated sample simulations 

using data from the 1996 to 2001 MEPS-HC, this paper evaluates and compares the 

actual probability achieved for confidence intervals derived from expenditure data by 

types of expenditure and varying sample sizes. The results are also compared to 

estimated confidence probabilities obtained from repeated sample simulations for other 

types of variables that do not exhibit as marked a positive skewness as health care 

expenditures. 

William W. Yu 

Statistician, Center for Financing, Access, and Cost Trends 

Agency for Healthcare Research and Quality 

540 Gaither Road 

Rockville, MD 20850 

E-mail: wyu@ahrq.gov 

Steve Machlin 

Senior Statistician, Center for Financing, Access, and Cost Trends 

Agency for Healthcare Research and Quality 

540 Gaither Road 

Rockville, MD 20850 

E-mail: smachlin@ahrq.gov 

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Examination of Skewed Health Expenditure Data from the 

Medical Expenditure Panel Survey (MEPS)
 

Introduction 

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

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

insurance coverage for the U.S. civilian noninstitutionalized population. It is cosponsored by the Agency for Healthcare Research and Quality (AHRQ) and the National 

Center for Health Statistics (NCHS). 

The expenditure data from MEPS have been shown to exhibit a marked positive 

skewness, with a few high expenditure respondents and many low or zero expenditure 

respondents. As a consequence of this departure from the normal distribution, the 

frequency with which a conventional confidence interval for a MEPS expenditure 

estimate will not capture the true population parameter may be higher than the probability 

stated for the confidence interval. 

Based on repeated sample simulations using data from the 1996 to 2001 MEPS, this 

paper evaluates the “actual” probability achieved for confidence intervals derived from 

expenditure data by types of expenditure and varying sample sizes. The results are also 

compared to estimated confidence probabilities obtained from repeated sample 

simulations for estimated proportions that do not exhibit as marked a positive skewness 

as health care expenditures. 

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MEPS Household Component 

The core survey for MEPS is the Household Component (HC). The MEPS-HC collects 

data through an overlapping panel design. In this design, data are collected through a 

series of five rounds of interviews over a period of two and a half years. Interviews are 

conducted with one member of each family who reports on the health care experiences of 

the entire family. Two calendar years of medical expenditure and utilization data are 

collected in each household and captured using computer-assisted personal interviews. 

This series of data collection rounds is launched again each subsequent year on a new 

sample of households to provide overlapping samples of survey data that provide 

continuous and current estimates of health care expenditures (Cohen JW, 1997). 

The sampling frame for the MEPS-HC is drawn from respondents to the previous year’s 

National Health Interview Survey (NHIS), conducted by NCHS. NHIS provides a 

nationally representative sample of the U.S. civilian noninstitutionalized population, with 

over sampling of Hispanics and blacks. 

Source of Data 

This study is based on six years of use and expenditure data from MEPS (1996-2001). 

Expenditures in MEPS are defined as the sum of direct payments for health care provided 

during the year, including out-of-pocket payments and payments by private insurance, 

Medicare, Medicaid, and other sources. Payments for over the counter drugs, alternative 

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care services, and phone contacts with medical providers are not included in MEPS total 

expenditure estimates. Indirect payments unrelated to specific medical events such as 

Medicaid Disproportionate Share and Medicare Direct Medical Education subsidies also 

are not included (Cohen JW, Machlin SR, Zuvekas SH, et al., 2000). 

The use and expenditure data included in this paper were derived from the MEPS-HC and 

Medical Provider Components (MPC). MPC data were collected for some office-based 

visits to physicians (or medical providers supervised by physicians), hospital-based 

events (e.g. inpatient stays, emergency room visits, and outpatient department visits), and 

prescribed medicines. HC data were collected for physician visits, dental and vision 

services, other medical equipment and services, and home health care not provided by an 

agency. Data on expenditures for care provided by home health agencies were collected 

only in the MPC. MPC data were used if complete; otherwise HC data were used if 

complete. Missing data for events where HC data were not complete and MPC data were 

not collected or not complete were derived through an imputation process (Machlin S. 

and Dougherty D., 2004). 

Distribution of MEPS Expenditure Data 

MEPS expenditure data, as show in Figure 1, exhibits a marked positive skewness, with a 

few high expenditure respondents and many low or zero expenditure respondents. 

Furthermore, this skewness or concentration of medical expenditures has also been 

shown to be consistent over time. Figure 2 (Berk ML and Monheit AC, 2001), updated 

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with 2001 MEPS data, shows that the concentration of health care expenditures among 

the U.S. population has remained stable: the top 1% of the population accounts for 25­

29% of total expenditures, the bottom 50% of the population accounts for only 3% of 

total expenditures, and this degree of concentration has been consistent over time. 

Confidence Limits by Normal Approximation 

In sample surveys, the normal approximation typically is used to calculate confidence 

limits. For example, 1-α (e.g., 95%) confidence limits are computed for the population 

mean Y by the normal approximation as follows: 

6
 
 y − Z − α 2 ) S y < Y < y + Z (1 − α 2 (1 ) S y 

Figure 1 - Distribution of Health Expenditures for the U.S. Population, 2001 

MEPS 

0 

10 

20 

30 

40 

50 

0 

1­ 1,000 

1,001­ 2,000 

2,001­ 3,000 

3,001­ 4,000 

4,001­ 5,000 

5,001­ 6,000 

6,001­ 7,000 

7,001­ 8,000 

8,001­ 9,000 

9,001­ 10,000

10,000+ 

Total Health Care Expenditure ($) 

Percentage 

Figure 2 - Concentration of Medical Expenditures 

0 

20 

40 

60 

80 

100 

Top 1% Top 5% Top 10% Top 50% 

Percentage 

1987 1996 2001 

(1)

Another form of the normal approximation to 95% confidence limits for population 

proportion P is: 

7
 
 α	 1 

p ± {Z (1 − 2 ) 1 − n N pq /(n − 1) + } 2n 

 

 

 

E ( y − Y )

3 1 N 

3 G1 =	 i 

= ∑ ( yi − Y )

σ3 Nσ3 

i =1 

 (2) 

where q = 1-p, (1 - n/N) is the finite population correction, and the last term on the right, 

1/2n, is a correction for continuity. With repeated sampling, we claim that statements of 

this kind will not hold for only 5% of the time. However, for highly skewed data, the 

probability that the statement above will not hold is often higher than 5% unless the 

sample size is very large. 

Confidence that the normal approximation is adequate in most practical situations comes 

from a variety of sources (Cochran WG, 1963). It has been shown that for any population 

which has a finite standard deviation the distribution of the sample mean tends to 

normality as the sample size increases (Feller W, 1957). For populations in which the 

principal deviation from normality consists of marked positive skewness, Cochran 

recommends the following rule on minimum sample size for use of the normal 

approximation in computing confidence limits: 

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n > 25 G 1	 (3) 

where G1 is Fisher’s measure of skewness. 

8
 
 

 

 

 

(4) 

This rule is designed so that 95% confidence limits will not hold for not more than 6% of 

the time. Application of this rule to compute 95% confidence limits on MEPS total 

expenditures requires a sample size of ~ 4,000. While annual MEPS sample sizes are 

substantially larger than 4,000, many of MEPS analytic and policy relevant 

subpopulations of interest are smaller than 4,000. 

Evaluation of Impact of Skewness on Confidence Probability 

We designed a simulation study to evaluate coverage error of confidence 

intervals constructed with the normal approximation method. We constructed a 

hypothetical population based on five years of MEPS data (1996-2000) with 124,564 

records. Four variables listed in Table 1 with a wide range of skewness measures were 

selected for the study: 

Table 1 – Variables Analyzed 

Variables analyzed 

Hypothetical 

Population Mean 

Hypothetical 

Population Skewness 

Total expenditures $2,040 16.17 

Rx expenditures $294 9.43 

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Proportion with inpatient expenses 0.07 3.22 

Proportion with dental visits 0.38 0.48 

We selected 10,000 repeated samples of varying sizes (25 – 5,000) with replacement 

from the hypothetical population using a SAS uniform random number generator “ranuni 

(seed).” For each sample, confidence intervals about the means and proportions were 

computed based on (1) and (2), respectively at three different levels of α (.01, .02, .05), to 

determine if they cover the target hypothetical population parameters. The results are 

presented in Figures 3 to 6 for mean annual total health expenditures, mean annual Rx 

expenditures, the proportion with inpatient expenses, and the proportion with dental visits, 

respectively. 

As shown in Figure 3, the actual coverage of confidence intervals containing the 

hypothetical population mean of total health expenditures (skewness=16.17) was far from 

the stated coverage. For example, at a sample size of 500, the actual coverage was at 

95.4%, 93.9%, and 90.6% for the stated coverage of 99% (α=.01), 98% (α=.02), and 95% 

(α=.05), respectively. The coverage did not get close (within 1%) to the stated coverage 

until the sample size approached 4,000. 

 

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Figure 3 - Coverage of Confidence Intervals - Mean Total Expenditure 

75 

80 

85 

90 

95 

100 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 

Sample Size 

Percent Covered

α=0.01 α=0.02 α=0.05 

Figure 4 presents the simulation results for mean Rx expenditures which has a moderate 

skewness measure of 9.43. Compared to the coverages shown in Figure 3, the actual 

coverage increased to 97.7%, 96.5%, and 93.4% for the stated coverage of 99%, 98%, 

and 95% respectively and the coverage started to get close (within 1%) to the stated 

coverage when the sample size approached 1,000. 

Figure 4 - Coverage of Confidence Intervals - Mean Rx 

Expenditure 

75 

80 

85 

90 

95 

100 

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 

Sample Size 

Percent Covered

α=0.01 α=0.02 α=0.05 

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Table 2 – Sample Size Requirements to Approach True 95% Coverage for Expenditure 

Variables 

Sample Size 

Coverage of 95% C.I. for Mean 

Total Expenditures 

Coverage of 95% C.I. for Mean 

Rx Expenditures 

25 72.0% 81.2% 

100 83.7% 89.3% 

500 90.6% 93.4% 

1,000 92.0% 93.7% 

3,000 93.4% 94.4% 

5,000 94.0% 94.3% 

Comparing the simulation results for mean total expenditures and mean Rx expenditures, 

as shown in Figures 3, 4 and Table 2, we conclude that for estimates based on MEPS 

expenditure data with marked positive skewness, a large sample size (e.g., >1,000 for 

mean Rx expenditures or > 4,000 for mean total expenditures) may be needed to maintain 

validity of the normal approximation used to calculate confidence limits. 

Simulation results for proportions with inpatient expenses and proportions with dental 

visits are shown in Figures 5 and 6, respectively. The sample size requirements to achieve 

the validity of normal approximation for these estimates were much smaller. For 

proportions with inpatient expenses (skewness=3.22), a sample size of 400 is needed to 

satisfy the requirement, while a sample size of 75 was sufficient for proportions with 

dental visits (skewness=0.48). 

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Table 3 – Sample Size Requirements to Approach True 95% Coverage for Proportions 

Sample 

Size 

Coverage of 95% C.I. for 

Proportion with Inpatient 

Expenses 

Coverage of 95% C.I. for 

Proportion with Dental Visits 

25 85.5% 93.5% 

50 89.6% 93.2% 

75 92.1% 94.0% 

100 94.1% 94.8% 

250 92.5% 95.3% 

500 94.7% 95.0% 

Comparing the simulation results for proportion with inpatient expenses and proportion 

with dental visits, as shown in Figures 5, 6 and Table 3, we conclude that for confidence 

intervals on estimates of proportions, sample sizes of about 100 appear sufficient for 

normal approximation to calculate confidence limits. 

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Figure 5 - Coverage of Confidence Intervals - Proportion with
 

Inpatient Expenses
 

Percent Covered

100
 

95
 

90
 

85
 

80
 

75
 

α=0.01 α=0.02 α=0.05 

0 100 200 300 400 500 600 700 800 900 1000
 

Sample Size 

Figure 6 - Coverage of Confidence Intervals - Proportion with Dental 

Visits 

75 

80 

85 

90 

95 

100 

0 50 100 150 200 250 300 350 400 450 500 

Sample Size 

Percent Covered 

α=0.01 α=0.02 α=0.05 

Conclusions 

•	 MEPS expenditure data are highly skewed. The extent of skewness varies by type of 

expense and population subgroup. This raises questions about the validity of the 

normal approximation used to compute confidence intervals because confidence 

levels (e.g., 95%) for intervals based on relatively large samples may be substantially 

overstated. 

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•	 Options to improve normal approximation: 

a.	 Increase sample size (pool multiple years of data); 

b.	 Reduce α level when constructing intervals. For example, Figure 3 shows that 

computing a 98% (α=.02) confidence interval for mean total expenditure with 

n=900 will result in a true 95% (α=.05) confidence interval. 

•	 Sample sizes of 100 appear generally sufficient for less skewed distributions and 

normal approximation to binomial. 

•	 Since the analysis is based on repeated simple random samples, results may 

understate the necessary sample sizes to achieve normality from complex sample data. 

•	 Analysts should consider extent of skewness when interpreting estimates and making 

inferences based on MEPS expenditure data. 

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References 

Cohen JW, “Design and methods of the Medical Expenditure Panel Survey Household 

Component.” Rockville (MD): Agency for Health Care Policy and Research; 1997. 

MEPS Methodology Report No.1. AHCPR Pub. No. 97-0026. 

Cohen JW, Machlin SR, Zuvekas SH, et al., “Health care expenses in the United States, 

1996.” Rockville (MD): Agency for Healthcare Research and Quality; 2000. MEPS 

Research Findings 12. AHRQ Pub. No. 01-0009. 

Machlin S. and Dougherty D., “Overview of methodology for imputing missing 

expenditure data in the Medical Expenditure Panel Survey.” 2004 Proceedings of the 

American Statistical Association, Section on Survey Research Methods, [CD-ROM], 

Alexandria, VA: American Statistical Association. 

Berk ML and Monheit AC, “The concentration of health care expenditures, revisited.” 

Health Affairs 2001; 20: 9-18. 

Feller W, “An introduction to probability theory and its applications.” John Wiley and 

Sons, New York, 1957; second edition. 

Cochran WG, “Sampling Techniques.” John Wiley and Sons, New York, 1963; second 

edition. 

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Acknowledgements 

The authors wish to thank Trena Ezzati-Rice and Jessica Banthin for their helpful reviews 

of the paper. 

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