May 2011

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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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Health Reform made a number of changes for State’s health care policies. But states themselves have also been enacting legislation to alter health care payment policies and regulations. The CHCF describes some examples of legislative changes in California:

  • Safety Net Care Pool (SNCP) – covers uncompensated costs in public hospitals and finances other state health care programs.  This Section 1115 Waiver designated California public hospitals (including University of California hospitals) continue to able to draw down funding from the SNCP for uncompensated care through their own expenditures.
  • Low Income Health Program (LIHP) provides Medi-Cal Coverage to uninsured adults under 200% of the federal poverty line.  This initiative is basically an early-stage implementation Medicaid expansions required by Health Reform.
  • Delivery System Incentive Reform Payments (DSIRP) support infrastructure development and redesign in public hospitals.  Examples of initiatives covered by DSIRP include telemedicine and improved interpretation services.

 

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The best diseases, from a business point of view, would be those that cause lingering illnesses. Ideally–that is, for maximum profit–the patient should either get well or die just before all of his or her money runs out. It’s a fine calculation.

…and three other questions about physician care.

Do Medicare patients have shorter waiting times than those with commercial insurance?

  • In the 2010 survey, among those seeking an appointment, most beneficiaries (75 percent) and most privately insured individuals (72 percent) reported “never” having to wait longer than they wanted for an appointment for routine care.
  • Another 17 percent of Medicare beneficiaries and 21 percent of privately insured individuals reported that they “sometimes” had to wait longer than they wanted for a routine appointment.Finding a primary care physician was more difficult for privately insured individuals than for Medicare beneficiaries.  Seventy nine percent of Medicare beneficiaries reported that they had no problem finding a PCP compared to 69 percent of privately insured individuals.

Is Medicare the new Medicaid?

The answer is not yet; providers are still accepting Medicare patients at high rates, but the trend is towards fewer PCPs accepting Medicare.

  • “For 2008, among physicians with at least 10 percent of their practice revenue coming from Medicare, 90 percent accepted new Medicare patients. By specialty, 83 percent of primary care physicians and about 95 percent of physicians in all other specialties accepted new Medicare patients. The rate of primary care physicians accepting new Medicare patients fell from 88 percent in 2007.”
  • Medicare’s payment for physician fee-schedule services in 2009 averaged 80 percent of commercial rates for preferred provider organizations (PPOs)

Is concierge medicine the wave of the future?

Not yet.  In the fall of 2009, researchers found that there were 750 retainer-based or “concierge” physicians.  Thus number represents less than 1 percent of the total number of physicians practicing in the United States.  However, there is a trend towards more concierge medicine.  There was a 50% annual increase in the number of retainer-based practices from 2005 to 2009.

Where types of physician care is growing the fastest (and slowest)?

  • Volume per beneficiary grew 3.3 percent in 2009.
  • However, there was a decrease in 2009 of coronary artery bypass grafts (CABG), cardiovascular stress tests, colonoscopy, standard chest imaging, hip fracture repair, brain MRIs, and coronary angioplasty.
  • Increases in service volume per beneficiary were found in advanced, non-standard computed tomography (CT) scans, outpatient rehabiliation, and spine surgery.

What recent legislation will affect the provision of physician services in the coming years?

  • Since 1991, physicians and other health professionals who practice in designated health professional shortage areas (HPSAs) automatically receive a 10 percent bonus (relative to the fee schedule amount) on all Medicare services they provide.
  • Starting in 2010, CMS no longer recognizes the billing codes for consultation services
  • Starting in 2010, CMS started a four-year transition to practice expense relative values that incorporate data from the Physician Practice Information Survey.
  • Starting in 2011 and ending in 2016, primary care practitioners will receive a 10 percent increase in payments for selected Medicare services, as will general surgeons practicing in HPSAs
  • Under the Physician Quality Reporting System (PQRS), physicians and other health professionals may qualify for a 1 percent bonus on all Medicare services they provide in 2011 and a 0.5 percent bonus in 2012 through 2014.
  • Starting in 2015, those who do not satisfactorily report PQRS measures will be subject to a financial penalty starting at 1.5 percent of their Medicare services.
  • EHR incentive programs provides physicians with incentive payments for meaningful use of electronic health records (EHR).
  • Starting in 2015, eligible physicians who do not satisfy the EHR criteria will be subject to a financial penalty starting at 1 percent of their Medicare services.
  • Reimbursement changes from Health Reform (PPACA) can be found here.

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The latest edition of the Cavalcade of Risk (the Naked Beasts Run Wild edition) is up at David William’s Health Business Blog.

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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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Here’s how the killing of Osama Bin Laden may affect:

Note that the ‘markets in everything’ phrasing was gratuitously stolen from Tyler Cowen’s Marginal Revolution blog.

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Nearly 23 million Americans watched a British Prince and his fiancee get married last week.  Yet you don’t have to be royalty to enjoy a luxurious wedding.

In the U.S., the average wedding costs about $30,000.  Weddings in India are well known for their extravagance.

“India’s legendary nuptial shindigs risk emptying not just the country’s wallets, but its bellies too. In February the food minister estimated that close to 15% of all grains and vegetables in the country are wasted through ‘extravagant and luxurious social functions’, such as lavish wedding banquets.”

On the other hand, other countries are trying to reign in spending on nuptials.

“…the Afghan authorities have been considering a proposal to limit the boom in weddings, sombre affairs under the Taliban. The suggested limit is 300 guests and a few dollars per head.

…Wedding laws in Tajikistan now maintain that only one course may be served.”

When do wedding festivities excess become excessive.  Like love, the answer is in the eye of the beholder.

 

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