October 2006

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Ordered Probit (or Logit) Estimation

October 19, 2006 in Econometrics | Permalink

What is one to do when the dependent variable under investigation is categorical?  Well if these categories are ordered, then an ordered probit (or logit) estimation technique is a sensible means for estimation.  An example where ordered probit estimation should be used is for an integer index ranking of physician quality between one and five.    On the other hand, if the dependent variable is the number of surgeries a patient has, a Poisson estmation methodology would be best since ’y’ is a count variable. 

Let us continue with the physician ranking example.  Suppose there are three ranking categories: excellent (2), average (1), and poor (0).  We assume there is a latent variable y* which is a function of a vector of covariates (‘x‘).  The latent variable determines which category the physician falls into.

  • y* = xβ + ε; ε|x~N(0,1) 
  • y=0 if  y*<α_1
  • y=1 if  α_1
  • y=2 if  y*>α_2

Now we can calculate the probabilities that a physician will fall into each category.

  • P(y=0|x)=P(xβ + ε<α_1)=P(ε<α_1-Xβ )=Φ(α_1-Xβ)
  • P(y=1|x)=P(xβ + ε<α_2) - P(xβ + ε<α_1) = Φ(α_2-Xβ)-Φ(α_1-Xβ)
  • P(y=2|x)=P(xβ + ε>α_2)=1-Φ(α_2-Xβ)

Using maximum likelihood estimation, we can now derive the α and β parameter vectors.  The log-likelihood function becomes:

  • l(α,β)=1{y_i=0}log[Φ(α_1-Xβ)] + 1{y_i=1}log[Φ(α_2-Xβ) - Φ(α_1-Xβ)] + 1{y_i=2}log[1-Φ(α_2-Xβ)]

If we instead assume that the cdf of ε|x is ‘exp(Xβ)/[1+exp(xβ)]‘, then we can use the logit model instead. 

The end statistic of interest is P(y=j|x).  This can be calculated as follows:

  • ∂p_0(x)/∂x_k= -β_kφ(α_1-Xβ)
  • ∂p_1(x)/∂x_k= β_k[φ(α_1-Xβ)-φ(α_2-Xβ)]
  • ∂p_2(x)/∂x_k= β_k[φ(α_2-Xβ)]

For more information on ordered probits, see the Tokyo Climate Center’s ordered probit explanation as well as the treatment in Econometric Analysis of Cross Section and Panel Data (pp. 504-509) by Wooldridge.

UCSD Medical Center in the news

October 18, 2006 in Current Events, Hospitals, Supply of Medical Services | Permalink

The University of California San Diego (UCSD) is where I currently attend graduate school.  The UCSD Medical Center has been in some hot water lately.

  • The Office of the Inspector General (OIG) of the Department of Health and Human Services has alleged that UCSD has overcharged Medicare $48 million for pension costs.  According to a UCSD Guardian report (“Med Center…“), “…the OIG reported that the medical center overstated pension wage costs by $22 million, and overstated postretirement wage costs by $25 million. The newly-issued corrections propose a 19-percent decrease from the UC-released hourly wage averages, from $41.74 to $33.75.“
  • UCSD has two Medical Centers.  The first is on the UCSD’s main campus in the affluent neighborhood of La Jolla.  The second center is situated in an the urban, central city Hillcrest area (only a few blocks from where I live).  The University has decided to begin closing down operations in Hillcrest while expanding service offerings at their La Jolla location.  According to the UCSD Guardian (“Study says…“) the plan may overburden some of the city’s hospitals located in poorer areas.  ” ‘We fully expect that once the UCSD Hillcrest Medical Center is gone as a full-service hospital, other hospitals in the area will see a gigantic influx in patients,’ said Don Stanziano, a spokesman for Hillcrest’s Scripps Mercy Hospital [another San Diego area hospital]. ‘We don’t have the capacity to be the only hospital in the area. To us, it’s a hostile closure.’ “  The University responds to this criticism by citing the fact that the Hillcrest hospital has “aging” facilities and the La Jolla location is more “cost-effective.”

Defining Managed Care

October 17, 2006 in Academic Articles, Managed Care | Permalink

As insurance markets began to develop in the U.S., we observed two types of insurance emerging: indemnity plans and health maintenance organizations (HMOs).  Indemnity plans compensated providers on a fee-for-service basis and HMOs used a capitation scheme.  Typically, HMOs used gatekeepers to restrict services while indemnity plan restrictions were few and far between.  Typical analysis of managed care’s affect on patient utilization involved simply comparing the average medical service usage in the two groups–after controlling for patient covariates and adverse selection.

Nowadays, all insurance plans are in some way ‘managed.’  If this is the case, how can a health economist measure the affect of managed care on service utilization?  Grembowski, et al. (2003) use a three tiered system to create an index of ‘managedness.’ Their system is described below:

  1. Plan level: The authors use an index to rank plans according to the following characteristics: gatekeeping and lock-in provisions, the plan’s referral preauthorization requirements, and whether the plan versus the provider was at financial risk (FFS vs. capitation).  They also included an two benefits indexes measuring the benefits covered by the plan as well as cost-sharing (copayments, coinsurance, deductibles) for providers both inside and outside of the plan’s network.  The first benefits index looks at only in-network information and the second benefits index examines out-of-network data.
  2. Office managed care: This was measured by examining office use of: utilization management, financial incentives (the percentage of the office’s revenue from capitation), and whether or not the office uses referral guidelines. 
  3. Physician managed care: This measure was developed by examining whether the physician was compensated via a capitation or FFS scheme, whether financial withholds for referrals were put into place, and the number of Agency for Health Care Policy and Research (AHCPR) guidelines read or employed by the physician.

With these continuous indexes in place, healthcare economist can now perform a more subtle analysis of how managed care affects utilization.

Grembowski; Martin, Dieher; Patrick; Williams; Novak; Deyo; Katon; Dickstein; Engelberg; Goldberg (2003) “Managed Care, Access to Specialists, and Outcomes among Primary Care Patients with Pain” Health Services Research, v38(1 Pt 1) pp. 1-19.

 

UnitedHealth Group CEO stepping down; agrees to reprice $1.6 billion of stock options

October 16, 2006 in Current Events | Permalink

The dealings of William McGuire, CEO of UnitedHealth Group, have been topic occasionally touched on by the Healthcare Economist (see May 19th and February 14th posts).  Today, Yahoo! News reported that Mr. McGuire will step down as chairman and CEO after questions arose regarding Mr. McGuire’s possibly illicit stock option compensation.  More from the Yahoo! article:

“McGuire has been under pressure since The Wall Street Journal reported in March that he received stock options on the days the company’s stock price hit yearly lows in 1997, 1999, and 2000. The timing is unlikely unless the grants were backdated.  Since the option’s price is set according to the stock price on the day of the grant, a low stock price makes an option more valuable.  Backdating stock options isn’t always illegal, but failing to disclose it can trigger tax and regulatory problems. Indeed, on May 11, UnitedHealth acknowledged a “significant deficiency” in its handling of stock options and said it may have to restate as much as $286 million in earnings for 2003, 2004, and 2005.  The company said McGuire had agreed to reprice his stock options to their yearly highs in 1994 through 2002 ‘and take any other appropriate action to eliminate any possible financial benefit from options-related issues identified in the report.’

McGuire had $1.6 billion in exercisable options as of the end of 2005, before the repricing announced Sunday.”

Economist wins Nobel Peace Prize

October 13, 2006 in Current Events | Permalink

Muhammad Yunus, founder of the Grameen Bank, won the Nobel Peace prize today (New York Times – “Microloan Pioneer“). I report on Mr. Yunus in an earlier blog post (“Father of Microcredit“).  If you are interested in contributing to a microcredit organization, the following organizations are two good choices.

Who to vaccinate

October 13, 2006 in Current Events | Permalink

An October 6th Wall Street Journal article asks “If we must ration vaccines for a flu, who gets the shots?“  Currently, the U.S. gives children, the elderly, and the sick priority in obtaining flu shots.  Journalist Sharon Begley of the WSJ wonders if this is the best policy:

“In May, scientists at the National Institutes of Health stirred things up with a paper calling into question the policy that aims to save the most lives by first vaccinating the old, the very young and the sick, putting last those who are two to 64 years of age.

The value of a life, they argued, depends on age. A 60-year-old has invested a lot (measured by education and experience) in his life, but has also reaped most of the returns. A child has minimal investment. A 20-year-old has great investment but has reaped almost none of the returns. Conclusion: To maximize investment in a life plus years of life left, 13- to 40-year-olds should have first claim on rationed vaccine, explains NIH’s Ezekiel Emanuel.”

The article wisely goes on to state that not only does the economic value of a life matter, but the probability that the vaccine will be effective is also important to consider. 

P4P

October 12, 2006 in Academic Articles, Medical Studies | Permalink

Can Pay for Performance (P4P) improve care and slow spending growth in the U.S.?  Joe Paduda is doubtful.  So is John Wennberg of the Dartmouth Medical School.  In his report (“Variation…“) for The Commonwealth Fund, Wennberg says that P4P initiatives can be very effective in creating incentives for physicians to operate under best practices.  For instance, practice guidelines are for diabetics to have an eye examination at least every two years.  We could compensate physicians more whose diabetic patients made visits on average every two years.

The problem Wennberg brings up is that the money spent on procedures where there are clearly defined best practices is small compared to spending in areas where there is no established ‘optimal’ protocol.  Wennberg divides medical procedures into 3 groups.

  • Effective Care: This is where P4P can be effective (e.g.: the diabetic eye exam case).  There are clear best practices established and physicians should follow them.
  • Preference Sensitive Care:  For these procedures, there is no one ‘right’ way to treat the patient.  Wennberg’s report gives a clear example.:

“Preference-sensitive care typically involves significant tradeoffs that affect the patient’s quality or length of life. The surgical options for treating early stage breast cancer, for example, usually include mastectomy (complete removal of the breast) or lumpectomy (a local excision of the tumor), often called “breast-sparing surgery.â€? The consequences for women who choose mastectomy include the loss of the breast and, for some, the use of a prosthesis or the undergoing of reconstructive surgery. For women who choose breastsparing surgery, consequences can include radiation or chemotherapy, or both, and living with the risk of local recurrence, which would require further surgery.”

  • Supply Sensitive Care: Patients with chronic illnesses (e.g.: congestive heart failure, chronic lung disease, cancer) have a choice of how much treatment they seek.  There is no best practice for the number of procedures (physician visits, referrals, tests, etc.) a cancer patient should make.  Many studies show that physicians are over-treating these patients.  Regions which employ a large volume of medical procedures to treat illness often find their patients no better or even worse off than regions applying a less invasive protocol (a  note of caution that one must worry about reverse causation).

Wennberg estimates 50% of all medical spending is for supply sensitive care.  This tends to suggest that P4P should be promoted, but only on a narrow scale and only for procedures with clear best practice guidelines.  P4P may be a step forward but it is not a cure all for the modern medicine’s problems.

Roemer’s law

October 12, 2006 in Supply of Medical Services | Permalink

Supplier induced demand has become a common phrase for health policy wonks. Yet this phenomenon was first discovered by Milton Roemer when he investigated how the number of hospital beds per capita affected hospitalization rates. According to the Dartmouth Atlas Project, Roemer’s law can be stated as follows:

“Supply may induce its own demand where a third party practically guarantees reimbursement of usage.”

In his research Roemer found higher hospitalization rates in regions where the number of hospital beds per capita were higher. The length of hospital stays was also longer in regions with a higher supply of hospital beds.

One problem in this finding is that it could be the case that hospital stays are shorter in lower hospital bed per capita regions because of a deficit in supply (reverse causation). An increased number of beds may be due to patient preference for in-patient (rather than outpatient) care in a region. While Roemer’s law may not be entirely convincing, the finding of a strong correlation between that areas with above average supply of medical services and profligate utilization of these services is robustly shown empirically.

Helping the world see

October 12, 2006 in Current Events, Health Care in Developing Nations | Permalink

On Wednesday, Marketplace on NPR ran a story on how providing eye care to individuals in the developing world can not only improve their well-being, but increase economic productivity.  Fortunately, low cost solutions are available.  To view the story, click here.  Some excerpts are below:

“153 million people around the world live with poor vision that could be corrected with glasses. Ninety percent of them live in developing countries. Those with bad vision have problems working and going to school.”

“We know that in many countries we can provide cataract surgical services, say, from $30 to $50 per eye. For glasses, of course, it’s substantially less….And then there’s Vitamin A supplementation, which targets children’s vision. That runs a few cents a capsule”

Information on Referrals II

October 11, 2006 in Academic Articles, Specialists, Supply of Medical Services | Permalink

If my October 10th post did not satiate your desire for knowledge regarding referrals, today I give you even more information. 

  • Franks, Zwanziger, Mooney and Sorbero examine a large Rochester, NY Independent Practitioner Association (IPA).  The authors find a mean patient referred/patients seen/year of 0.37.  The data show that referral rates remain very stable by physician over time, likely due to physician stable case mix.  Franks et al. conclude that referrals are driven by physician recommendations, not patient demand.
  • Shea, et al. look at data from the 1992-1993 Medicare Current Beneficiary Survey (MCBS).  They find that only 36% of referrals are from primary care physicians to specialists.  Primary care to primary care and specialist to specialist referrals account for 45% of referrals and specialist to primary care referrals make up 4%.  The balance is made up from within-specialty referrals.  As opposed to Franks et al., the authors conclude that patient demand (not supplier recommendations) are the major driver of referrals. 

Franks, Peter; Zwanziger, Jack; Mooney, Cathleen; Sorbero, Melony (1999), “Variations in primary care physician referral rates,” Health Services Research, vol 34(1), pp. 323-329.

Shea, Dennis; Stuart, Bruce; Vasey, Joseph; Nag, Soma (1999),”Medicare physician referral patterns,” Health Services Research, vol 34(1), pp. 331-348.

 

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