One way to answer this question is to use the Oaxaca decomposition.  This approach was originally formulated by Ronald Oaxaca. This document provides a nice overview of how to use the Oaxaca Decomposition and I apply that framework to the health spending case.

Differences in Health Spending

Assume that there are two regions: Region A and Region B. The spending for the two regions can be modeled using a linear regression framework:

• Y^A = β^AX + ε^A
• Y^B = β^BX + ε^B

The Y term represents spending and the variable X represents the patient’s health status. Health status could be measured as a vector of factors or as a single indicator (e.g., healthy or sick). The term β describes much an area spending on medical resources to treat a patient with a health status of X. Thus, average difference in spending per person the two regions is:

• Y^A – Y^B = β^AX^A – β^BX^B

where X^A is the average case mix in the area.

Determinants of Health Spending Differentials

Now the question is whether case mix or spending practices conditional on case mix is the key driver of the differences in spending between regions A and B. One can differentiate these two components using the following Oaxaca Decomposition:

• Y^A – Y^B = ΔXβ^B + ΔβX^A
• Y^A – Y^B = ΔXβ^A + ΔβX^B

In the first equation, the differences in health status (X‘s)are weighted by the coefficients for region B and the differences in the coefficients are weighted by the X’s from region A, whereas in the second, the differences in the X‘s are weighted by the coefficients of from region A and the differences in the coefficients are weighted by the X‘s of from region B.

There are basically three factors that effect health spending in the region: i) differences in health status across regions ii) differences in treatment patterns conditional on health status, and iii) the interaction of health status and conditional treatment effects. One can see this clearly below:

• Y^A – Y^B = ΔXβ^B + ΔβX^B + ΔXΔβ
• Y^A – Y^B = H + T + HT

The equations above show the health status effect (H), the treatment effect (T) and the interaction (HT).

The specification chosen for the Oaxaca decomposition determines whether the interaction effect is placed with the health status effect or the treatment effect.  More precisely:

• Y^A – Y^B = ΔXβ^B + ΔβX^A = H + (HT + T)
• Y^A – Y^B = ΔXβ^A + ΔβX^B = (H+ HT) + T

In effect, the first decomposition specification incorporates the interaction term with the treatment effect whereas the second specification places the interaction term together with the health status effect.

Sources:

• Oaxaca, R. 1973. “Male-Female Wage Differentials in Urban Labor Markets.” International Economic Review 14: 693–709.
• Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff, Magnus Lindelow “Explaining Differences between Groups: Oaxaca Decomposition” Chapter 12, Analyzing Health Equity Using Household Survey Data, World Bank, WBI Learning Resources Series, 2008.

For instance, this article examines how to align the Medical Expenditure Panel Survey (MEPS) to aggregate U.S. benchmarks provided in the National Health Expenditure Accounts (NHEA).  Today, I review some of these adjustments.

The article by Selden and Sing (2008) compares NHEA Personal Health Care (PHC) expenditures against MEPS expenditures. Whereas total NHEA in the U.S. was $1.603 trillion in 2003, PHC was only $1.341 trillion since it excludes administrative costs, public health, research, and construction, none of which are captured by MEPS. Using the PHC as the starting point, here are some other key differences between the MEPS and NHEA PHC measure.

Matching MEPS to NHEA PHC using MEPS definition of medical expenditures

• Institutionalized population and active military.  PHC includes these individuals, but MEPS excludes these individuals.
• Medicaid capitated payments.  The authors “…modified the NHEA allocation of capitated Medicaid payments across types of service using the MEPS expenditure distribution, rather than the fee-for-service Medicaid distribution used in the construction of NHEA. This adjustment shifted expenditures from Medicaid Hospital to Medicaid Physician.”
• Drug Rebates. NHEA includes rebates public insurance entities receive from pharmaceutical companies.  These rebates are not captured in MEPS.  The authors remove drug rebates from the NHEA PHC estimates.
• Medicaid/CHIP underreporting.  Like most household surveys, the MEPS data contains fewer observations of individuals stating that they have Medicaid or Children’s Health Insurance Program (CHIP) coverage than is the case when these figures are reported in administrative data.  To correct for this underreporting, the authors used “a 10 percent upweighting of Medicaid and SCHIP recipients, using a raking post-stratification to preserve the MEPS distribution of poverty level, age, sex, Medicare enrollment and uninsurance.”
• Underreporting of high cost cases.  The authors cite other research (Zuvekas, Cohen and Pylypchuk, 2005; Zuvekas, Olin, 2009) which claim that MEPS underreports high cost cases.  This could be due in part because severely ill individuals may be have higher attrition rates.  Thus, the authors modify the MEPS sampling weights to increase the prevalence of high-cost cases.  They do this using a partial non-response model. “Our upweighting strategy targets the top three percent of the expenditure distribution in each of four (hierarchically defined) coverage groups: ever on Medicare, ever on non-Medicare Medicaid and SCHIP, ever on Private, and full-year uninsured. A raking post-stratification was implemented to preserve MEPS distributions by age, sex, race/ethnicity, and poverty level (along with coverage). The average increase in weight was 18.1 percent…”
• Laboratory Tests. “One area in which MEPS is particularly low is separately-billed laboratory tests, the number and financing of which are difficult to ascertain either from household respondents or from follow-back visits to providers ordering the tests.”  The authors allocated that additional lab spending test to individuals in a proportional fashion based on each individual’s use of physician services.
• Other adjustments. For the remaining adjustments, the authors simply scaled the MEPS amounts to match the NHEA figures.

Adjusting MEPS to match NHEA definition of medical expenditures

The list above describes how to calibrate MEPS to match NHEA figures for a MEPS-based definition of medical expenditures. However, the NHEA PHC figures include some expenditures which are not included in MEPS. These costs include:

• Non-medical assistance with activities of daily living. These costs are born mostly by Medicaid. The authors allocated these costs in proportion to home health care by source of payment.
• Hospital Subsidies.  These include Medicare and Medicaid disproportionate share (DSH) payments, Medicare graduate medical education subsidies, State and local subsidies to public hospitals, Medicare retrospective adjustments and capital pass-throughs.
• Public health, public research, public investment in structures and equipment.
• Administrative Costs.  For public programs, the authors allocate administrative costs in proportion to spending on care.  For private insurance, the authors use a regression-based model which compares health expenditures against insurance premiums paid by households and employers.
• Tax Expenditures.  Tax expenditures include: i) the exemption of employer health insurance contributions to from employee income and payroll taxes and ii) the exemption of medical care from state and local sales taxes

Comparing MEPS to Medicare claims data

Not only does MEPS underreport utilization compared the NHEA, similar differences are found when comparing to Medicare claims data. Zuvekas and Olin (2009) find a 19 percent gap between MEPS and Medicare claims data. The The key factors driving these differentials are underreporting of ehalth care utilization by respondents and underrepresentation of high expenditure cases in MEPS.

Specifically, quantities in MEPS come from household responses. Generally, household accurately report inpatient stays, but underreport emergency department and office visits. Further, household generally estimate their out of pocket cost accurately, but most “…may not know third-party payments at all or report them inaccurately because of confusion about discounts, adjustments, and contractual arrangements.”

Underrepresentation of high cost cases about $25,000 is also a problem. Whereas the top decile spending levels in the claims data spend $23,900, in MEPS the figure is $26,700. For the top five percentiles, Medicare claims has average spending of $38,500, compared to $34,600 in MEPS.

Sources:

• Thomas Selden, Merrile Sing, “Aligning the Medical Expenditure Panel Survey to Aggregate U.S. Benchmarks,” AHRQ Working Paper No. 08006, July 2008.
• Samuel H. Zuvekas, Gary L. Olin, “Validating Household Reports of Health Care Use in the Medical Expenditure Panel Survey” Health Services Research, VOLUME 44 | NUMBER 5 | OCTOBER 2009.
• Samuel H. Zuvekas, Gary L. Olin, ”Accuracy of Medicare Expenditures in the Medical Expenditure Panel Survey” Inquiry, 209 Spring; 46(1):92-108.

One problem with medical record review is that oftentimes experts will come up with differing opinions from reviewing the same medical record.  Thus, researchers often have at least two individuals review the medical record so that the results are not biased by a single person’t opinion.

A question of interest is how reliable are different evaluators of medical record.  Cohen’s kappa can provide a quantitative estimate of inter-rater reliability.  The formula is the following:

• [P(a)-P(e)]/[1-P(e)]

To give an example, consider the situation where two raters rate 10 blogs and can give them a rating of an A, B, or C. These data are available here.  You can see that Tester 1 is more likely to give positive ratings and Tester 2 is more likely to give negative ratings.  In this example, the value of Kappa is 0.44.

A general rule of thumb to follow is values < 0 as indicating no agreement, 0–.20 as slight, .21–.40 as fair, .41–.60 as moderate, .61–.80 as substantial, and .81–1 as almost perfect agreement.

• Recall bias: Patients in one group have better or worse memory of a given event.  If one wishes to compare changes in income for individual who received certain workforce training, individuals who participated in the program may be more or less likely to inflate their income levels over time.
• Interviewer bias: If new data is being collected and researchers use separate interviewers for the treatment and control groups, if one interviewer systematically over/understates the interviewee responses, the study results will be biased.
• Observation bias: This problem is particularly problematic for medical studies.  Observation bias occurs when physicians (or patients) are more likely to detect a disease.  Thus, a study identifying how pollution affected disease rates may underestimate the impact of the pollution if those affected are less likely to detect any disease than those who are not.  For instance, if poor individuals are more likely to drink polluted water than rich individuals, but also less likely to go to the doctor, the disease incidence from polluted water would be underreported and the causal impact of water pollution would be underestimated.

Outside of purely statistical biases, the research community at large may suffer from other biases as well.  These include:

• Funding bias: Researcher bias towards interpreting quantitative results in favor of the entity which funded their study.
• Status quo bias: Survey respondents may base their opinions closer to the status quo or researchers can interpret their results in a fashion more likely to coincide with the existing academic literature.
• Publication Bias: tendency of researchers, editors, and pharmaceutical companies to handle the reporting of experimental results that are positive (i.e. showing a significant finding) differently from results that are negative (i.e. supporting the null hypothesis) or inconclusive, leading to bias in the overall published literature.
• Hindsight bias: is the inclination to see events that have already occurred as being more predictable than they were before they took place

Quantile regressions, however, offer the power to evaluate whether the predicted effect of selected explanatory variables on the outcome of interest differs depending on the where in the distribution the individual is located. Koenker and Bassett (1978) created these regression models and based them on the same intuition used to calculate the median. Today I review contrasts how quantile regressions work compared to ordinary least squares (OLS).

Mean vs. Quantile

The simplest way to compare OLS against quantile regression is to compare optimization methods for the mean and quantiles (e.g., median). Most people know the mean and median formulas, but the following specifications detail how to calculate these values for any sample using optimization techniques.

• Mean: min _μ∈ℜ Σ (y_i – μ)²
• Quantile: min _ξ∈ℜ Σ ρ_τ(y_i – ξ)

where the function ρ_τ(x) = x(τ – I(x<0)). In essence, the function ρ_τ tilts the absolute value function towards the quantile under investigation. For the mean, the goal is to pick the a parameter (the mean) which will minimize the sum of squared deviations. For the quantile, the goal is to pick a parameter which will minimize the sum of absolute deviations. For the median, the absolute deviations are weighted equally whereas for other quantiles deviations closer the quantile of interest receive more weight than those further away.

I have created this spreadsheet to more clearly demonstrate how calculating quantiles can be done in practice.  Wikipedia also has a nice example.

OLS vs. Quantile Regression

Again, compare the mechanisms by which OLS and quantile regressions choose the coefficients (i.e., β) to optimize the equations below.

• OLS: min _β∈ℜ Σ (y_i – Xβ)²
• Quantile Regression: min _βτ∈ℜ Σ ρ_τ(y_i – Xβ_τ)

When you calculate the sample mean, you are calculating the unconditional population mean [i.e., E(y)]. When you conduct the OLS regression, one calculates the conditional expectation function E(y|X)]. Similarly, the quantile regression is used to estimate the conditional quantile of the dependent variable.

To conduct the quantile regression in SAS, on can perform the QUANTREG function. In Stata one can use the qreg function.

Quantile Regression in Practice

An example of a paper using Quantile Regression includes the following: Johar, M. and Katayama, H. (2011), Quantile regression analysis of body mass and wages. Health Economics, 20: n/a. doi: 10.1002/hec.1736. This paper uses the National Longitudinal Survey of Youth 1979, to explore the relationship between body mass and wages. The researchers use quantile regression to provide a broad description of the relationship across the wage distribution. “Our results find that for female workers body mass and wages are negatively correlated at all points in their wage distribution. The strength of the relationship is larger at higher-wage levels. For male workers, the relationship is relatively constant across wage distribution but heterogeneous across ethnic groups.”

Sources:

• Koenker, Roger and Gilbert Bassett. 1978. “Regression Quantiles.” Econometrica. January, 46:1, pp. 33–50.
• Koenker, Roger and Kevin F. Hallock 2001. “Quantile Regression.” Journal of Economic Perspectives. 15:4, pp. 143–156.
• Colin (Lin) Chen. “An Introduction to Quantile Regression and the QUANTREG Procedure” Paper 213-30, SAS Institute, Inc.
• Brian S. Cade, Barry R. Noon, (2003) “A gentle introduction to quantile regression for ecologists“, Frontiers in Ecology and the Environment, 1 (8), 412–420.

In addition, sensitivity and specificity uses the gold standard (i.e., “true”) results as the denominator.  Sensitivity indicates the share of true positives as a fraction of total people who actually have the condition. Similarly, specificity gives the number of true negatives as a share of the number of test subjects who actually had the disease.

The formulas for these four metrics  describing the accuracy of various diagnostic testing procedures is shown below:

• Positive Predictive Value:  TP/(TP+FP)

• Negative Predictive Value:  TN/(TN+FN)

• Sensitivity:                TP/(TP+FN)

• Specificity:                TN/(FP+TN)

This example below from Wikipedia provides a simple example.

The key assumption for the capture/recapture method is that the probability of capturing any given specimen is independent for each trial.  If one was doing a capture/recapture study and one could more easily capture fat and old birds, then the likelihood of catching the same bird in the second trial would increase.  This would inflate the value of m, and thus the approximation of the population would be too low.

One application of the capture/recapture method is McClish et al. (1997)‘s examination of the size of the elderly cancer population in Virgina.  The authors estimate  the likelihood cancer patients appear in both the Virgina Cancer Registry (VCR) and the Medicare claims files (MEDPAR) for Virginia resident 65 and older.

“Capture-recapture techniques were used to estimate the actual cancer population size, based on the concordance and discordance of the data sources. If VCR identifies M cases and MEDPAR identifies n cases, m of which are common to both sources, then the estimated number of cases in the entire population of cases at reporting hospitals will be N = [(M + 1) X (n + 1 )/(m + 1)] – 1. With this estimate of the population, the sensitivity of each source alone, as well as those of the combined sources, was estimated.”

The variance of the total population is simply:

• var(N) = [(M+1)(n+1)(M-m)(n-m)]/[m+1)(m+1)(m+2)]

What explains the discrepancy between the VCR and MEDPAR data.  This study claims:

“Cases not reported to the VCR were more likely to have their cancer diagnosis found in the second through fifth position in the MEDPAR record rather than in the first. That implies that cancer may not have been the primary reason for the hospitalization, so that MEDPAR may have identified a prevalent rather than an incident case. While the method used here has been used by others, some cases termed incident may have been prevalent cases seen as a recurrence after more than 2 years. More complex methods to identify incident cases that look at the position of cancer diagnostic code and the surgical interventions might improve this, but at the expense of missing more cases.”

Source:  Donna Katzman McClish, Lynne Penberthy, Martha Whittemore, Craig Newschaffer, Diane Woolard, Chnstopher E. Desch, and Sheldon Retchin. Ability of Medicare Claims Data and Cancer Registries to Identify Cancer Cases and Treatment.  Am J Epidemiology. 1997, 145(3): 227-233.

APPENDIX

ICD-9-CM DIAGNOSTIC CODES

• Breast: 174-174.9; 233; 233.0
• Colorectal: 153-153.9; 154; 154.0; 154.1; 230.3;230.4
• Lung: 162-162.9; 231; 231.2; 231.9
• Prostate: 185–185.9; 233.4
• ICD-9-CM SURGICAL CODES

• Definitive surgical therapy: 85.4-85.48; 85.21-85.23
• Biopsy: 85.11; 85.12; 85.19

• Definitive surgical therapy: 45.4-45.43; 45.49;45.7-45.79; 45.8; 48.3-48.35; 48.4-48.49; 48.5;48.6-48.69
• Biopsy: 45.23-45.29; 48.23-48.29

• Definitive surgical therapy: 32.0-32.2; 32.28-32.29
• Biopsy: 33.22-33.29

• Definitive surgical therapy: 60.2-60.69
• Diagnostic procedure: 60.11; 60.12; 60.18; 60.2

To overcome this problem, recent studies have examined how to develop accurate algorithms to account for cancer stage in studies using claims data.  A paper by Cooper et al. has provided an initial attempt to accomplish this feat, but a more recent paper by Smith et al. 2010 offers an alternative.  Today, I will review the Smith paper.

Methods

The initial study population consisted of 150,764 women (age ≥ 65 years) diagnosed with breast cancer between 1992 and 2002 identified through Surveillance Epidemiology and End Results (SEER)-Medicare.   From this population, the following cohorts were excluded beneficiaries characterized by:

• Unknown SEER stage history
• In situ rather than invasive cancer
• Beneficiaries who were not continuously enrolled in Medicare FFS including beneficiaries who had had Medicare Advantage Coverage between 12 months prior and 9 months after diagnosis
• Age less than 66 to ensure a complete year of history
• Death

To determine the cancer stage, physicians typically use the following heuristic:

• Observe if there is a distant tumor, then the patient is stage IV.
• If the patient is not stage IV, then the patient is classified into stages based on tumor size and the extent of the disease.

This spreadsheet explains the cancer stage classification according to the American Joint Committee on Cancer (AJCC).

The study relied on demographic, tumor, and treatment characteristics to identify the cancer stage.  One of the key variables in the breast cancer algorithm was axillary lymph node involvement.  This spreadsheet also lists all the covariates included in the prediction algorithm.

To test the accuracy of the algorithm, the authors relied  on four metrics: sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV).  The authors calibrated the model on a baseline sample of the SEER data and tested the accuracy using a validation sample.

One drawback of the Smith et al. algorithm is that it requires both retrospective and prospective data for up to 1 year prior to and 1 year after the date of diagnosis.  Further, patients have to be continually enrolled in Medicare FFS for the algorithm to work properly.  Those who join a Medicare Advantage plan are dropped from the sample.

Conclusion

The authors claimed the following results:

“A claims-based algorithm was utilized to predict breast cancer stage, and was particularly successful when used to identify early stage disease. These prediction equations may be applied in future studies of breast cancer patients, substantially improving the utility of claims-based studies in this group. This method may similarly be employed to develop algorithms permitting claims-based epidemiologic studies of patients with other cancers.”

Source:

• Smith GL, Shih YC, Giordano SH, Smith BD, Buchholz TA. A method to predict breast cancer stage using Medicare claims. Epidemiol Perspect Innov. 2010 Jan 15;7:1.
• Cooper GS, Virnig B, Klabunde CN, Schussler N, Freeman J, Warren JL: Use of SEER-Medicare data for measuring cancer surgery. Med Care 2002, 40:43-48.
• Cooper GS, Yuan Z, Stange KC, Dennis LK, Amini SB, Rimm AA: Agreement of Medicare claims and tumor registry data for assessment of cancer-related treatment. Med Care 2000, 38:411-421.

Restrictions to consider for Medicare population:

1. Continuously enrolled in Parts A and B.  This is needed for data completeness.  New individuals could enroll in Medicare throughout the year and thus the data on their spending and treatment patterns may be incomplete.
2. Medicare Advantage Enrollment.  Researchers may want to exclude beneficiaries who receive Medicare services through managed care, because they are currently not claim-level detail for MA-enrolled beneficiaries although this will change in 2012.
3. U.S. Residence.  Individuals residing outside the U.S. may receive their care through other countries’ medical systems and thus Medicare claims may not capture the full range of services they receive.
4. The Working Aged.  The working aged are individuals for whom a private group health insurance plan was the primary payer.  Medicare may not have a complete set of claims for working aged beneficiaries.
5. Hospice Beneficiaries.  Managed care plans cover all Parts A & B services except for hospice.  If one wants to predict Medicare Advantage spending, one would need to exclude hospice spending since hospices services are not covered by MA, only the Medicare FFS.
6. ESRD Beneficiaries.  Beneficiaries with End Stage Renal Disease (ESRD) are covered by Medicare through a specific carve out.  Anyone with ESRD qualifies regardless of age.  Thus, researchers may want to exclude/include these beneficiaries.
7. Medicaid Status.  Individuals who are dual eligible have much lower Medicare cost sharing and can also receive services covered by Medicaid.
8. Disability Status.  Some individuals qualify for Medicare prior to being 65 because they were disabled and qualify under the Supplemental Security Income program.  A researcher could restrict the sample to: i) individuals eligible for Medicare under SSI who are less than 65, or ii) individuals who are eligible for Medicare because they are over 65, but who were already enrolled in Medicare when they were under 65 because of their disability status.
9. Death.  For researchers analyzing cost analysis, patients who die causes a problem.  Patients who die are low cost; excluding these patients from the sample, however, may assign low-cost status to certain providers for whom a large number of patients die.  Thus, one does not want to reward providers whose patients die at a high rate and identify them as low-cost providers.

On the other hand, one could examine trends in Medicare spending for a certain age group over time.  For instance, how much did Medicare spend on care for 70 year-olds in 1970, 1990 and 2010?  In this case, medical expenditure change as the standards of care change over time.  In addition, certain cohorts may be more or less healthy than others when the reach a certain age, or the cohort may have difference preferences over medical treatment.

The post today review a method for describing differential growth rates in Medicare Expenditures.  For cohort c at age α, the following equation describes medical expenditures y.

• y(c,α) = g(c,α) +
  u_c,α

To identify the effects of the different components of this equation is not trivial.  In fact, there is an “…inherent identification problem, which is well known in the literature (e.g., Heckman and Robb, 1985), that prevents one from being able to distinguish among age, period, and cohort effects.”  In the MaCurdy and Geppert chapter, the authors use the follow specification to estimate the combined how aging affects medical expenditures for different birth cohorts.

• g(c,α) = Σ_j β_j(c) * φ_j(α)

The quantities β_j(c) determine the shape of a cohort’s lifetime profile with respect to age, and the function φ_j(α) captures cross-cohort variation in lifecycle profiles.  In the paper, the authors assume that there there are 3 separate cohorts. They parameterize the function g as follow:

• g(c,α) = β₀(c) + β₁(c)α + β₂(c)α²

where

• β_j(c) = β_0j + β_1j*c + β_2j*c²,       j=1, 2, 3

In addition, the authors assume that the error distribmances can be decomposed as follows:

• u_c,α = ū_t + ū_t,α

Here, ū_t are the common time effects and the errors ū_t,α are the idiosyncratic deviations from trends for cohorts c at age α after the removal of common year components.  One can then use a simple OLS specification to estimate the vector parameters β and fixed time deviations ū_t.
Sources:

• Thomas E. MaCurdy, Jeffrey Geppert “Characterizing the Experiences of High-Cost Users in Medicare” Analyses in the Economics of Aging (2005), David A. Wise, editor (p. 79 – 128), Published in August 2005.
• Heckman, J. J., and R. Robb. 1985. Alternative methods for evaluating the impact of interventions. In Longitudinal analysis of labor market data, ed. J. Heckman and B. Singer, 156–245. Cambridge: Cambridge University Press.