An Examination of State Estimates Using Multiple Years of Data from the Medical Expenditure

Panel Survey, Household Component

John Sommers

Agency for Healthcare Research and Quality Working Paper No. 06004 May 2006

Suggested citation: Sommers J. An Examination of State Estimates Using Multiple Years of Data

from the Medical Expenditure Panel Survey, Household Component. Agency for Healthcare

Research and Quality Working Paper No. 06004, May 2006, http://gold.ahrq.gov.

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

issues. The papers have not undergone external 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.
 

 

 

An Examination of State Estimates Using Multiple Years of Data from the Medical 

Expenditure Panel Survey, Household Component 

John Sommers 

May 2006 

ABSTRACT 

For smaller subsets of population, such as, states, the sample size from a single year 

sample from the Medical Expenditure Panel Survey (MEPS), Household Component 

(HC), is not enough to provide quality estimates for many variables. Because of the 

importance of these estimates non standard methods need to be developed to obtain 

estimates for these small subsets of the population. Two possible methods that can be 

considered are pooling of multiple years of data or use of small subpopulation estimation 

techniques. 

This paper first examines the decrease in errors by using two or three consecutive years 

of data from the MEPS-HC rather than a single year. Due to sample overlap between 

years in the MEPS – HC, data from year to year are correlated and additional sample has 

less effect on total error than it would if the years had independent samples. The loss of 

sample efficiency depends on the correlations of the variables estimated. 

In this paper a variety of estimates are produced and improvements in standard errors 

using multiple years are calculated and compared to the errors obtained using one year of 

data. The improvement in errors over single year estimates are compared to the 

theoretical decrease in errors that would be obtained if the data across years were 

uncorrelated. 

The paper then examines the effect of using one type of small subpopulation estimation 

technique on the same variables. This technique is applied to earlier estimates 

constructed from one, two and three years of MEPS-HC data. Finally, the effects of 

using both multiple years and the special estimation technique are examined and 

reported. 

John Sommers 

Mathematical Statistician 

Center for Financing, Access, and Cost Trends 

Agency for Healthcare Research and Quality 

540 Gaither Road 

Rockville, MD 20850 

E-mail: John.Sommers@ahrq.hhs.gov 

2
 
An Examination of State Estimates Using Multiple Years of Data from the Medical 

Expenditure Panel Survey, Household Component 

Background 

The demand for state estimates of health expenditures, health status, percentages of 

persons with certain health conditions, and uninsurance rates is growing. In a recent 

report (Sommers, 2005), the possibility of making state level estimates with data from the 

Medical Expenditure Panel Survey (MEPS), Household Component (HC) was examined. 

This work showed that for larger states many quality estimates can be made either 

directly or using some simple small area estimation procedures. However, the paper also 

showed that as the sample size decreased, either due to the size of the state or due the 

uncommon nature of the event, the size of the error for both the direct and the small area 

estimates increased to a size that was problematic. One can assume other estimates for 

smaller sub populations within a state would have worse results. 

A common method to improve estimates is to pool several years of data. The Census 

Bureau produces poverty and income estimates using data from 2 or 3 years of data. 

(Census Website). This same technique can be applied to the types of estimates 

examined in the earlier work with the MEPS HC data. 

This paper presents results using estimates made with HC data from the years 2001 

through 2003. Combined year estimates are made for the identical variables as the 

previous report by Sommers, 2005, and estimates are also made for subpopulations of 

persons age 18 or older in the survey that were either diabetic, hypertensive, asthmatic, 

arthritic or obese. Although these groups overlap and the classification of persons into 

these groups is based upon self reported information and the results are still useful since 

the study is intended to explore the effects of using multiple years of data on estimated 

errors for small populations. 

If samples of independent data are pooled it is a relatively simple matter to estimate the 

effects of using a larger sample. However, this is not the case if one pools data from the 

MEPS HC across years. Samples from different years of the MEPS HC are not 

independent. The HC has overlap in both persons and PSU’s (Cohen, 2000). Thus, the 

values are correlated across years. 

With correlation, if we had the same variance for each year of the HC and we were 

simply to average the same estimate for two years of the survey, then the variance for this 

estimate would be: 

σ2 var = (.5*( (1+ ρ)))

where ρ is the correlation between the estimates for the two years. One can see as the 

correlation increases towards + 1 there are diminishing returns in this approach. If the 

correlation were 1, then the average of the two years would be no better than that for a 

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single year. If the correlation were 0 then the result would be the equivalent of doubling 

the sample. It is unlikely that the correlation is negative since, for example, with an 

expenditure estimate; this would require persons who were the highest spenders one year 

to be lower than average the next. Research has shown that persons with high 

expenditures in one year tend to have high expenditures the following years. (Monheit, 

ref) 

Similar formulas that depend upon the pariwise correlations between two years can be 

developed for averages across three years of data. In general, addition of each extra year 

with the same sample size, errors and equal correlations with the previously added years 

will result in a smaller reduction in error relative to the error for a single year. For 

instance, if there were no correlation between years, the standard error using two years of 

data would be .707 times the error of the one year sample. Using three years of data 

would yield an error of .577 times the error of the one year sample and four years would 

result in an error of .5 times the error of a single year sample. As one can see the 

reduction in error relative to the original year one of sample is less for each additional 

year of sample. 

Although the MEPS HC does not follow this simplified model since samples and 

correlations for the MEPS HC are not equal for all years, this model gives an indication 

of how correlation can effect the reduction in errors of estimates using multiple years of 

data relative to the error of similar estimates made with a single year of data. Reduction 

of errors is decreased by positive correlation between years. Further, there is a 

diminishing effect on the reduction in error with the addition of each additional year of 

data. How, much extra reduction in error one gets using three years of the MEPS - HC 

rather than one or two is part of the focus of this work. 

Estimates Analyzed 

For this analysis, estimates were produced using three years of HC data, 2001, 2002 and 

2003. Estimates were made for each single year, for 2001 and 2002 combined, 2002 and 

2003 combined and for the combination of all three years. Since one of the key reasons 

for analysis is to determine the possibility of producing state estimates, estimates were 

made for each of the twenty largest states by population for each of five conditions for 

persons age 18 and over. The five conditions were obesity, diabetes, hypertension, 

asthma and arthritis. A person was classified as obese using their height and weight 

measurements from the survey. A person was classified as having one of the other four 

conditions based upon questions on the survey that asked if they had ever been diagnosed 

with the condition. For each state by condition by year’s combination, three different 

direct estimates were produced: the percent of persons with the condition, the percent of 

those persons with the conditions who had a health expenditure during the year and the 

conditional mean expenditure for those who had an expenditure. For each of these 

estimates, a corresponding small area estimate was made using a compositing technique 

similar to that used in previous work. (Sommers, 2005). These small area estimates have 

a relative mean squared error smaller than that of the standard direct estimate. These 

were made to determine the average effect of this process when applied to direct 

estimates for different numbers of years of data. Other types of estimates by type of 

4
 
expenditure were also made, but will not be discussed because the results relative to the 

total gain from using the same number of years of data or the small area technique are 

similar to the results that are reported in this paper. 

Terminology 

Before the analysis of the results is presented, it would be of value to establish some 

useful terminology. An important factor being considered is the ratio of errors for the 

same type of estimate, made with multiple years versus a single year of data. In the 

previous section, it was discussed how under ideal conditions with the same sample size 

and no correlations between years, how this value would be .707 for two years of data , 

.577 for three years of data and .500 for 4 years of data. This ratio of errors will be 

referred to in this paper as the multi year error ratio for the type of estimate. For a 

specific number of years, for example, for a two year estimate it will be called the two 

year error ratio. An average of this value over a set of estimates, say a set of states, will 

be referred to as the average error ratio. The values of .707, .577 and .500 will be 

referred to as the ideal error ratio. 

Another term used will be state size group. There are two groups used: group 1 is the ten 

largest states by population, and group 2 is the second ten largest states by population. 

Direct Estimates 

Table 1 shows average rse’s, relative standard errors, for the percent of persons with each 

of the five conditions for the single year 2003, for the combination of 2002 and 2003 and 

the combination of 2001 through 2003. The table also shows the average two and three 

year error ratios for cells defined by state size group and condition. The error used was 

the rse for each estimate. (Note, since the rse is the error over the mean and the means are 

about equal for the one, two and three year estimate, when error ratios are created with 

rse’s they are very similar to the error ratios for standard errors. Rse’s were used because 

of convenience.) 

(Also, note that the average error ratios given in the tables are the average ratios of the 

rse’s for one and either the two or three year estimate for the same item. Although many 

times this average of ratios is similar to the ratio of the average of all rse’s for one year 

estimates and the average of the rse’s for the set of two or three year estimates, they are 

not the same. Sometimes with sample sizes used in this paper they can be noticeably 

different.) 

Although, the average rse’s differ considerably by condition and state size group, the 

effect on the relative standard errors of using two and three years of data on the different 

groups of states and conditions is very similar for all the groups of estimates. The 

average two year error ratio for all estimates is slightly more than 84 percent. The 

average 3 year error ratio for all estimates is about 70 percent. 

5
 
 

One can see the effect of the correlations across the years. As was discussed earlier, the 

estimated value of the two year and three year error ratios, if there were no correlations 

across years would be approximately 71 and 58, percent respectively. Since the average 

error ratios are significantly larger than these values, this is an indication of significant 

correlations of the percent that have any of these conditions across the years. 

TABLE 1 

Comparisons of Relative Standard Errors for Direct State Estimates of the Percent 

of the Population with Selected Conditions: Multiple Years versus a Single Year of 

Data: Adults Age 18 Years and Older 

COMBINATION OF YEARS 

CONDITION STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave 

Rse 

Ave 

Rse 

Ave Two Year 

Error Ratio 

Ave Rse Ave Three 

Year Error 

Ratio 

Arthritis 1 .076 .067 .867 .053 .717 

2 .098 .079 .818 .078 .720 

Asthma 1 .121 .097 .831 .093 .704 

2 .161 .131 .817 .130 .719 

Diabetes 1 .139 .121 .861 .101 .677 

2 .187 .153 .832 .145 .704 

Hypertension 1 .061 .049 .824 .046 .706 

2 .086 .072 .870 .065 .700 

Obesity 1 .079 .062 .852 .049 .667 

2 .105 .088 .860 .076 .708 

Table 2 shows results for percents of persons who have any expense or a dental expense 

for 3 of the conditions for the two state size groups and a single year, two years and three 

years of data. These results are representative of the estimates of percents with 

expenditures. 

6
 
 

 

 

 

For any of the conditions whether less prevalent, such as, diabetes, or more visible, such 

as, arthritis or obesity, the relative errors for the estimate of percent of persons who have 

any expense are very low. This is because the percents are very close to 100, almost all 

these individuals have expenditures every year, and a binomial variable with that 

probability of occurrence has a very small relative error. The percent, which have a 

dental expenditure, is of more interest. These estimates are closer to 50% and have more 

representative relative standard errors. These errors using one year of data, are very high 

for diabetes, because the sample size of persons with diabetes is small. The values for 

one year are better for persons with arthritis or who are obese. These are the more 

frequent in occurrence of the 5 conditions. 

On the average for all estimates over all conditions, the two year error ratio is about 77%. 

The variation from 77 percent by condition or state size groups is not large. The 

comparable average three year error ratio is 65 percent. 

These values are lower than those obtained for estimates of the percentages of the 

population with a particular condition. This indicates that the correlation of whether a 

person in the overlapping sample has a condition is higher than the chance that they will 

have an expenditure across the two years. However, there is still significant correlation 

across the years of data for whether a person with a particular condition has an 

expenditure for different types of medical care. This can be seen by comparing the 

average two and three year error ratios obtained for these estimates of the percentages 

that have expenditures, 77 and 65 percent with the comparable ideal error ratios of 70.7 

and 57.7, percent respectively. 

TABLE 2 

Comparisons of Relative Standard Errors for Direct State Estimates of the Percent 

of the Population with a Dental or Medical Expenditure among Persons with 

Selected Conditions: Multiple Years versus a Single Year of Data: Adults Age 18 

Years and Older 

COMBINATION OF YEARS 

CONDITION 

AND 

EXPENDITURE 

GROUP 

STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave 

Rse 

Ave 

Rse 

Ave Two Year 

Error Ratio 

Ave Rse Ave Three 

Year Error 

Ratio 

Arthritis 

Dental expenditure 1 .089 .072 .817 .058 .660 

7
 
 

 

 

Dental expenditure 2 .133 .107 .821 .100 .697 

Any expenditure 1 .013 .008 .745 .008 .626 

Any expenditure 2 .012 .010 .772 .010 .667 

Diabetes 

Dental expenditure 1 .199 .158 .752 .126 .620 

Dental expenditure 2 .312 .208 .742 .185 .613 

Any expenditure 1 .014 .009 .824 .008 .730 

Any expenditure 2 .005 .004 .808 .004 .805 

Obesity 

Dental expenditure 1 .100 .078 .778 .060 .595 

Dental expenditure 2 .128 .115 .839 .101 .716 

Any expenditure 1 .030 .019 .663 .016 .557 

Any expenditure 2 030 .023 .750 .019 .615 

Table 3 gives results for estimates of conditional mean expenditures for persons with 

representative conditions who had a dental or any expenditure. As is the general case 

with estimates for expenditures, the relative standard errors are much higher than those 

for estimates percent of persons who had an expenditure. This type of estimate is one of 

the main reasons that one would use multiple years of data to make an estimate. For 

diabetes, even with 3 years of data, the relative standard errors for conditional mean 

expenditures are very marginal in quality 

The average value of the multiple year error ratios over all conditions and states for the 

average conditional mean expenditure are very similar to those for estimates the 

percentage of persons with an expenditure. They do vary by condition, expenditure type 

and state size group. 

TABLE 3 

Comparisons of Relative Standard Errors for Direct State Estimates of the 

Conditional Mean Expenditures for Dental and All Medical Expenditures for 

Persons with Selected Conditions: Multiple Years versus a Single Year of Data: 

Adults Age 18 Years and Older 

8
 
 

 

 

 

 

 

COMBINATION OF YEARS 

CONDITION 

AND 

EXPENDITURE 

GROUP 

STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave 

Rse 

Ave 

Rse 

Ave Two Year 

Error Ratio 

Ave Rse Ave Three 

Year Error 

Ratio 

Arthritis 

Dental expenditure 1 .160 .143 .767 .116 .655 

Dental expenditure 2 .193 .177 .840 .144 .620 

Any expenditure 1 .117 .097 .797 .087 .665 

Any expenditure 2 .151 .124 .798 .111 .695 

Diabetes 

Dental expenditure 1 .339 .259 .760 .259 .734 

Dental expenditure 2 .331 .258 .816 .232 .733 

Any expenditure 1 .156 .141 .777 .099 .652 

Any expenditure 2 .283 .193 .768 .095 .622 

Obesity 

Dental expenditure 1 .215 .144 .739 .116 .634 

Dental expenditure 2 .252 .192 .797 .164 .665 

Any expenditure 1 .168 .132 .832 .102 .655 

Any expenditure 2 .165 .121 .754 .118 .651 

Composite Estimators 

As one can see, especially in Table 3, multiple years of data do not guarantee that the 

relative standard errors for the direct estimates will be less than 20 percent. For instance, 

average relative standard errors for estimates of conditional mean dental expenditures for 

persons with diabetes, average over 20 percent. For more common conditions, these 

9
 
same types of estimates have relative standard errors that average over 10 percent. Many 

other multi year estimates that we have examined also have this problem. 

While one could add even more years of data, averaging over larger numbers of years 

could be problematic because of changing conditions. For instance, a state’s ranking in 

health care costs could change over the years due to specific policies implemented by the 

state. Averaging over a large number of years might hide this change. Also, as we have 

seen, relative to the error obtained with one year of data, each additional year of data has 

a diminishing effect on the error. 

To avoid using more years of data, a composite type of small area estimator similar to 

that used in earlier work, Sommers, 2005, was applied to the conditions examined. Using 

the methodology described in that work, composite estimates and mean squared errors 

were created for one, two and three years of data by shrinking the direct estimates 

towards the regional estimates. Because these estimates are biased relative to the state 

values, errors include estimates of variance and bias. Errors also include estimates of 

addition to variances caused by estimation of a weighting parameter required to build the 

composite estimate from the direct regional and state estimates. 

Tables 4, 5 and 6 show the effects of this process on the estimates presented in Tables 1, 

2 and 3. Errors used in these tables are the relative standard error for the unbiased direct 

estimates and the relative mean squared errors for the composite estimates. The latter 

estimates are made up of both variance and bias components. Note any improvement 

from this process is in addition to any improvement resulting from combining multiple 

years of data to make an estimate. In order to obtain estimates of overall average error 

ratios for estimates which combine the compositing methodology with addition of 

additional years of data, one must multiply the error ratios obtained from using multiple 

years of data shown in Tables 1, 2 and 3 times comparable error ratio values in Tables 4, 

5 and 6 which show the effects of compositing. For instance, for states in group 1, from 

Table 1 one can see that use of two years of data for estimates of the percent of persons 

with arthritis yields an error that is .867 times the average for a single year. On table 4 

for the same two year estimate the RSE is .843 times that of the direct estimates. Thus, 

the improvement using both two years of data and the composite methodology gives an 

estimate with a standard error that is about .731 times the error for a direct estimate made 

with a single year of data. 

Although the numbers on the tables vary considerably, when the data are analyzed using 

an analysis of variance model, only one factor showed a significant effect on the 

prediction of the improvement due to using the composite estimation methodology. This 

factor was the state groups. The use of this methodology reduced errors more for the 

smaller states in state group 2 compared to the improvements for the larger states in state 

groups 1. Neither condition type, item estimated (percent with expenditure versus 

conditional mean); type of expenditure nor did number of years of data have a significant 

effect on the average error ratio of the composite estimate versus the direct estimate. On 

average this ratio was about .66. The average for the set of larger states was about .70, 

while the average for the smaller states was about .62. 

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TABLE 4 

Comparisons of Relative Errors for Composite versus Direct State Estimates of the 

Percent of the Population with Selected Conditions Made with One, Two or Three 

Years of Data: Adults Age 18 Years and Older 

COMBINATION OF YEARS 

CONDITION STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave Error Ratio 

of Composite 

versus Direct 

Estimates 

Ave Error Ratio 

of Composite 

versus Direct 

Estimates 

Ave Error Ratio of 

Composite versus 

Direct Estimates 

Arthritis 1 .831 .843 .848 

2 .628 .610 .540 

Asthma 1 .655 .624 .654 

2 .544 .453 .428 

Diabetes 1 .594 .601 .678 

2 .608 .689 .657 

Hypertension 1 .705 .795 .777 

2 .658 .655 .586 

Obesity 1 .759 .682 .814 

2 .490 .584 .560 

11
 
 

 

 

 

 

 

TABLE 5 

Comparisons of Relative Standard Errors for Composite versus Direct State 

Estimates of the Percent of the Population with a Dental or Medical Expenditure for 

Persons with Selected Conditions Made with One, Two or Three Years of Data: 

Adults Age 18 Years and Older 

COMBINATION OF YEARS 

CONDITION 

AND 

EXPENDITURE 

GROUP 

STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave Error Ratio of 

Composite versus 

Direct Estimates 

Ave Error Ratio 

of Composite 

versus Direct 

Estimates 

Ave Error Ratio of 

Composite versus 

Direct Estimates 

Arthritis 

Dental expenditure 1 .760 .552 .835 

Dental expenditure 2 .761 .746 .686 

Any expenditure 1 .684 .726 .748 

Any expenditure 2 .578 .684 .709 

Diabetes 

Dental expenditure 1 .600 .601 .643 

Dental expenditure 2 .671 .585 .526 

Any expenditure 1 .641 .660 .653 

Any expenditure 2 .612 .655 .528 

Obesity 

Dental expenditure 1 .776 .783 .833 

Dental expenditure 2 .644 .767 .675 

Any expenditure 1 .618 .637 .664 

Any expenditure 2 .841 .737 .695 

12
 
 

 

 

 

 

 

TABLE 6 

Comparisons of Relative Standard Errors for Composite versus Direct State 

Estimates of the Conditional Mean Expenditures for Dental and All Medical 

Expenditures for Persons with Selected Conditions Made with One Two or Three 

Years of Data: Adults Age 18 Years and Older 

COMBINATION OF YEARS 

CONDITION 

AND 

EXPENDITURE 

GROUP 

STATE 

SIZE 

GROUP 

2003 2002-2003 2001-2002-2003 

Ave Error Ratio of 

Composite versus 

Direct Estimates 

Ave Error Ratio of 

Composite versus 

Direct Estimates 

Ave Error Ratio 

of Composite 

versus Direct 

Estimates 

Arthritis 

Dental expenditure 1 .798 .726 .748 

Dental expenditure 2 .535 .684 .709 

Any expenditure 1 .621 .675 .737 

Any expenditure 2 .564 .560 .584 

Diabetes 

Dental expenditure 1 .599 .573 .545 

Dental expenditure 2 .720 .585 .651 

Any expenditure 1 .670 .802 .773 

Any expenditure 2 .381 .495 .609 

Obesity 

Dental expenditure 1 .456 .566 .693 

Dental expenditure 2 .537 .498 .496 

Any expenditure 1 .688 .653 .715 

Any expenditure 2 .723 .667 .623 

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Conclusions and Recommendations 

Use of multiple years of data can decrease the standard error of a mean or proportion. If 

one assumes equal sample sizes and independence across years, the ratio of the standard 

errors of direct estimators using two and three years of data could be .71 or .58 of the 

standard error for a similar estimate using one year of data. However, due to use of the 

same set of PSU’s and overlap between about half the persons in the sample in two 

consecutive years of data, MEPS-HC data are not independent across years and are 

positively correlated. This correlation lowers the reduction in the standard errors for 

direct estimates using multiple years of data versus the errors obtained for similar 

estimates using a single year of data. For highly correlated data, such as, whether a 

person has a certain chronic illness, we found that the errors using two and three years of 

data were on average .84 and .70 of the errors for similar estimates made using one year 

of data. For less correlated data, such as, average expenditures errors for estimates using 

2 and 3 years of data were on average .77 and .65 of the errors using a single year of data. 

The use of a composite estimation methodology produced reductions in errors compared 

to the errors of direct estimates. This was in spite of the additional errors caused by bias 

and parameter estimation that were included in the errors of the composite estimates. 

These reductions were consistent whether the compositing methodology was applied to 

estimates made with 1, 2, or 3 years of data. The only factor that seemed to influence the 

reduction gained, was the size of the states estimated. Reductions were higher for smaller 

states. 

Although, the gain in precision of direct estimates made using multiple years of data is 

less than optimal due to the correlation in MEPS data across years, the gains can still be 

substantial. Further, the largest gains are for estimates of expenditures which tend to 

have the highest relative standard errors (Sommers, 2005). Using multiple years of data 

combined with the small area methodology can yield impressive reductions of over 50% 

in errors compared to the errors obtained using direct estimates and a single year of data. 

As with direct estimates, the best gains come for some of the worst estimates, in this case, 

estimates for smaller states. 

The downside of using multiple years of data is interpreting what a multiple year average 

represents. It may be possible to calculate estimates using multiple years of data which 

are controlled so that when they are combined they produce the regional or national 

estimates for the year of interest. Future research should be performed to assess such 

estimates and compare their results to those of single year estimates. 

References 

Census Bureau Website: 

http://www.census.gov/prod/2005pubs/p60-229.pdf 

14
 
Cohen SB. Sample Design of the 1997 Medical Expenditure Panel Survey, Household 

Component. MEPS Methodology Report No 11. AHRQ Pub. No. 01-0001. Rockville, 

MD: Agency for Healthcare Research and Quality. 2000. http://www.meps.ahrq.gov/ 

papers/mr11_01-0001/mr11.pdf 

Monheit, A. Persistence in health expenditures in the short term: Prevalence and consequences. 

Medical Care, July 2003; 41(7): III-53-III-64. 

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://meps.ahrq.gov/mepsweb/data_files/publications/mr16/mr16.pdf 

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