Econometrics

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Add to Your Skills Toolkit: The Oaxaca Decomposition

January 26, 2012 in Econometrics, Economics - General | No comments

Suppose you look at health care spending in two different regions and observe a significant difference.  You may want to know what the cause of this difference is.  Is it because one region has a mix of people who are sicker; or is because the reason treat patients with a given disease more intensively?

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:

  • YA = βAX + εA
  • YB = βBX + εB

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:

  • YA – YB = βAXA – βBXB

where XA 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:

  • YA – YB = ΔXβB + ΔβXA
  • YA – YB = ΔXβA + ΔβXB

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:

  • YA – YB = ΔXβB + ΔβXB + ΔXΔβ
  • YA – YB = 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:

  • YA – YB = ΔXβB + ΔβXA = H + (HT + T)
  • YA – YB = ΔXβA + ΔβXB = (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:

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MEPS vs. NHEA

December 20, 2011 in CHIP, Data, Econometrics, Medicaid | No comments

Many researchers use household data sources to examine a variety of hypothesis.  The use of household data has many benefits including allowing for more detailed socioeconomic information (e.g., education, income) beyond what is contained in administrative claims files.  One drawback of household data is that extrapolations made from household survey data may not match national estimates.

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.

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Kappa Statistic

November 2, 2011 in Econometrics | No comments

Many research studies aim to figure out if a physicians did a good job.  Many studies use administrative claims data to evaluate performance.  Other times, researchers use medical record review.

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)]
Where P(a) is the observed level of agreement and P(e) is the expected level of agreement from pure chance.  In essence, the kappa measurement compares the observed level of inter-rater agreement against the level of agreement that would be expected by pure chance.  

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.

 

Biases

June 28, 2011 in Econometrics | No comments

All economists are familiar with the problem of selection bias.  In non-randomized samples, patients may choose to be in either the treatment or control group based on factors which are also related to the outcome of interest.  Even if researchers can design a study that fully controls for selection bias, robust studies must also account for other biases.  These include:

  • 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

 

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Quantile Regressions

May 10, 2011 in Econometrics | No comments

Understanding quantiles is fairly intuitive. A physician would rank in the τth quantile of in terms of quality of care if he performs better than the proportion τ of the reference group of physicians and worse than the proportion (1–τ). For physicians at the median, half of physicians will perform worse than this doctor and half will perform better.

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 (yi – μ)2
  • Quantile: min ξ∈ℜ Σ ρτ(yi – ξ)

where the function ρτ(x) = x(τ – I(x<0)). In essence, the function ρτ 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 (yi – Xβ)2
  • Quantile Regression: min βτ∈ℜ Σ ρτ(yi – Xβτ)

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.”

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Testing precision and accuracy

May 3, 2011 in Econometrics | No comments

How does one determine if a test is accuracy?  What does accuracy mean? One measure of test precision it is the positive predictive value, or the share of positive test results which are actually positive.  Alternatively, the negative predictive value determines the share of negative test results which are true (rather than false) negatives.  Better positive and negative predictive value indicates a better test.

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.

 

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Determining Population Size

April 26, 2011 in Econometrics | No comments

How do ecologists determine the size of a population?    One method is the mark and recapture (a.k.a. capture/recapture method).  This method relies on having two separate trials to capture (either physically or in data) members of certain population and determines the population size based on the proportion of specimens who are captured in both trials.

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)]

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Algorithms to Predict Breast Cancer Stage

April 5, 2011 in Econometrics, Operations Research | 2 comments

Cost effectiveness and quality analysis of the treatment of cancer has long been a goal of health services researchers.  In particular, researchers aim to determine whether various treatments provide cost-effective methods to improve longevity and quality.  Physicians, however, use different treatments depending on the patient’s cancer stage.  Although most cost-effectiveness researchers want to take into account patient cancer stage in their analyses, these data are not available in many administrative data files, such as the Medicare claims files.

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:

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Selecting Medicare Cohorts

March 16, 2011 in Econometrics, Medicare | 1 comment

Medicare administrative data provides a rich source to conduct health services research.  Researchers who wish to use this data, however, often have to restrict their sample population in order to  have a similar types of patients and consistent data available.  Today I review some popular methods to restrict Medicare samples for research use.

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.

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A Cohort Framework for Describing Medicare Expenditure Growth

February 22, 2011 in Econometrics, Medicaid/Medicare | No comments

Medicare spending changes over time for multiple reasons.  First, for any cohort of individuals, these individuals the age as time passes.  As their age increases, expected medical expenditure will also rise.   Second, the individual will likely received different medical services as the standards of care change over time.  The standards of care can change due to improved technology, policy, cultural factors, medical education, and other causes.

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) + uc,α

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