Free Money Finance hosts the latest edition of the Cavalcade of Risk.
Tags: CoR
If you are evaluating the treatment effect of a policy or medical intervention, does it matter if some of your subjects leave the sample? In many cases, the answer is ‘yes’.
The Problem
As outlined in Grasdal (2001), the effect of the treatment is simply:
- Δ = E(Y|X, T=1) − E(Y|X, T=0)
However, in some cases we may not observe Y. For instance, if there is attrition in the study, we will not observe their outcomes. Thus, we can decompose the two components from the equation above as follows: The effect of treatment with attrition is:
- E(Y|X, T=1) = pTE(Y|X, T=1, A=0) + (1-pT)E(Y|X, T=1, A=1)
- E(Y|X, T=0) = pCE(Y|X, T=0, A=0) + (1-pC)E(Y|X, T=0, A=1)
where pT is the probability someone in the treatment group drops out of the sample (pT=p(A=0|X, T=1) and pC is the probability someone in the control group drops out of the sample (pC=p(A=0|X, T=0).
Rearranging terms we get:
- Δ = [E(Y|X, T=1, A=0)-E(Y|X, T=0, A=0)] + pT[E(Y|X, T=1, A=0)-E(Y|X, T=1, A=1)] + pC[E(Y|X, T=0, A=1)-E(Y|X, T=0, A=0)]
The first term in brackets is what we observe. The second term in brackets is the difference between is the outcome in the treatment group for the attrition and non-attrition group; the third term in brackets gives the difference between is the outcome in the control group for the attrition and non-attrition group. With random attrition, the two expressions inside the square brackets will cancel out. If attrition is random, then estimating the treatment effect using the first equation will produce unbiased estimates.
Potential Solutions
If one knows the source of the attrition bias, one can explicitly model the source of the attrition. Explicit models are typically sample selection model in which two simultaneous regression
models are calculated. “The first model is a regression model that addresses the research question, with the hypotheses of the study being examined by the regression of the dependent variable on the key independent variables in the study. The second model includes the variables that are causing attrition, with the dependent variable being a dichotomous variable indicating either continued participation or nonparticipation in the study. The error terms of the substantive dependent variable in the first regression model and the participation dependent variable in the second regression model are correlated. A significant correlation between the two error terms indicates attrition bias.”
If the source of the bias is unknown, one can use the Heckman selection model. The first step of the Heckman selection model “…not only tests for attrition bias but also creates an outcome variable, which Heckman calls λ (lambda). Thus, a λ value is computed for all cases in the study, and it represents the proxy variable that explains the causation of attrition in the study…The second step of Heckman’s procedure is to merge the λ value of each participant into the larger data set and then include it…in the regression equation that is used to test the hypotheses in the study. Including λ in the equation solves the problem of specification error and leads to more accurate regression coefficients.”
Empirical Investigation
A study by Grasdal looks at attrition in a randomized field trial of a rehabilitation programme designed to bring long-term sick listed workers with musculoskeletal problems back to work in Bergen, Norway. In this case, they found that “Both the parametric and the semi-parametric sample estimators that were considered indicated that sample attrition biased outcome data regarding posttreatment earnings, while the data regarding sick leave status remained unbiased. The sample selection estimators of post-treatment earnings perform quite well in terms of correcting for attrition bias and estimating treatment effects not very different from the experimental benchmark.”
…The analysis also demonstrates an inherent paradox in the ‘common support’ approach, which prescribes exclusion from the analysis of observations outside of common support for the selection probability. The more important treatment status is as a determinant of attrition, the larger is the proportion of treated with support for the selection probability outside the range, for which comparison with untreated counterparts is possible.”
Source:
- Astrid Grasdal, “The Performance of Sample Selection Estimators to Control for Attrition Bias” Health Economics. Volume 10, Issue 5, Article first published online: 16 JUL 2001
Tags: Attrition Bias, Econometrics, Toolkit
Medicare’s Hospital Compare website evaluates hospital quality. One of the most recent measures to be added to Hospital Compare is a measure of efficiency. The measure calculates a price-standardized, case-mix adjusted measure of spending during period before, during and after a hospital admission. The Healthcare Economist (Jason Shafrin) and a team at Acumen (including Tom MaCurdy, Sajid Zaidi, Elen Shrestha, and David Pham) worked closely with CMS to develop this measure. Additional information on this measure is available here or see the results for San Francisco General Hospital here.
“The Spending per Hospital Patient with Medicare measure shows whether Medicare spends more, less, or about the same per Medicare patient treated in a specific hospital, compared to how much Medicare spends per patient nationally. This measure includes any Medicare Part A and Part B payments made for services provided to a patient during the 3 days prior to the hospital stay, during the stay, and during the 30 days after discharge from the hospital.
This result is a ratio calculated by dividing the amount Medicare spends per patient for an episode of care initiated at this hospital by the median (or middle) amount Medicare spent per patient nationally.
A result of 1 means that Medicare spends ABOUT THE SAME amount per patient for an episode of care initiated at this hospital as it does per hospital patient nationally.
A result that is more than 1 means that Medicare spends MORE per patient for an episode of care initiated at this hospital than it does per hospital patient nationally.
A result that is less than 1 means that Medicare spends LESS per patient for an episode of care initiated at this hospital than it does per hospital patient nationally.
Lower numbers are better.“
Tags: hospital, HVBP, P4P, Quality, Value-Based Purchasing, VBP
U.S. life expectancy after cancer diagnosis is higher than that those for ten European countries. A recent study in Health Affairs cites these statistics as evidence that the more expensive treatments American physicians employ is worth it.
“We found that US cancer patients experienced greater survival gains than their European counterparts; even after considering higher US costs, this investment generated $598 billion of additional value for US patients who were diagnosed with cancer between 1983 and 1999. The value of that additional survival gain was highest for prostate cancer patients ($627 billion) and breast cancer patients ($173 billion).”
Some critics are not convinced.
“‘This study is pure folly,” said biostatistician Dr. Don Berry of MD Anderson Cancer Center in Houston. “It’s completely misguided and it’s dangerous. Not only are the authors’ analyses flawed but their conclusions are also wrong.’”
Why aren’t some experts convinced? Philipson and colleagues look at survival rather than mortality. Survival means how long the patient lives after the patient is diagnosed with cancer. One thing the U.S. is good at is screening for cancer. Thus, patients may be surviving longer not due to better care, but because because these patients are diagnosed earlier. U.S. mortality rates from cancer are no better than in Europe.
Another problem with the American approach is over-diagnosis. According to Doverdiagnosis. From Merrill Goozner:
“Because cancer screening is much more widespread in the United States than in Europe, especially for breast and prostate cancer, ‘we find many more cancers than are found in Europe,’ [Dr. Berry] said. ‘These are cancers that tend to be slowly growing and many would never kill anyone.’
Screening therefore turns thousands of healthy people into cancer patients, even though their tumor would never threaten their health or life. Counting these cases, of which there are more in the United States than Europe, artificially inflates survival time, experts said.”
Sources:
- Tomas Philipson, Michael Eber, Darius N. Lakdawalla, Mitra Corral, Rena Conti and Dana P. Goldman “An Analysis Of Whether Higher Health Care Spending In The United States Versus Europe Is ‘Worth It’ In The Case Of Cancer” Health Aff April 2012 vol. 31 no. 4 667-675
- Merrill Goozner. “Critics Pounce on Cancer Care Costs Study” GoozNews. 2012.
The movement of mental health care from mental hospitals to treatment in outpatient settings and nursing homes began in the 1950s. Here is how it happened.
“The field of medicine where the ‘rediscovery of community’ found an immediately welcome reception was mental health services. A movement away from mental hospitals had already begun in the mid-1950s. The national census of mental hospitals declined from a peak of 634,000 in 1954 to 579,000 by 1963. The predominant, though contested, explanation for the drop is that the discover and introduction of major tranquilizers (e.g., Thorazine) was the decisive event. Patients who were previously hospitalized could now be safely treated, or at least more safely ignored, on an outpatient basis. Another interpretation points to the adoption by Congress in 1956 of amendments to Social Security that provided greater aid to states to support the aged in nursing homes. Mental hospitals had been filled with unwanted older people suffering only from a harmless senility. By transferring such patients from mental hospitals to nursing homes, the states could transfer part of the cost of upkeep to the federal government. Probably both drugs and nursing homes had some effect on the decline of mental hospitalization.”
- The Social Transformation of American Medicine, Paul Starr.
Tags: Mental Health, Nursing Homes
- Is rationing gaining acceptance?
- New Hampshire bill prohibits health exchanges.
- Does increasing the number of nurses improve hospital care?
- U(h,w) = h · log(w).
- SF-8 vs. SF-36.
- Is customized drug prescribing on the horizon?
- Getting fired for biopsying Warren Buffet’s prostate.
Plus…
- Jennifer Salopek and Sarah Sonies have posted Health Wonk Review: Shiny Happy (Mostly) Edition at Wing of Zock
The answer is because using more intensive services does reduce mortality.
This is the finding of a recent JAMA paper. After controlling for patient case mix, the authors examine variation in hospital spending in the last year of a patient’s life. The authors note that “Higher-spending hospitals differed in many ways, such as greater use of evidence-based care, skilled nursing and critical care staff, more intensive inpatient specialist services, and high technology, all of which are more expensive.” Higher spending hospitals (on a per patient basis) tend to be hospitals with a larger volume of patients. They are also more likely to “be located in urban areas; be associated with regional cancer centers; have on-site computed tomography and magnetic resonance imaging scanners, cardiac catheterization laboratories, and cardiac surgery capability; and be early adopters of critical care response teams.”
Higher spending hospitals had overall reduced mortality rates for four disease considered. “In the highest- vs lowest-spending hospitals, respectively, the age- and sex-adjusted 30-day mortality rate was 12.7% vs 12.8% for AMI, 10.2% vs 12.4% for CHF, 7.7% vs 9.7% for hip fracture, and 3.3% vs 3.9% for colon cancer.”
One reason for these differences could be that high-spending areas could be located in richer areas where mortality rates are lower for a variety of reasons. Although unobserved heterogeneity in patient case mix is a problem with any study, the authors do stratify their results based on neighborhood income and find similar results.
The relevance of this study to the United States, however, is hard to determine. Although high spending hospitals decrease mortality in Canada, almost all hospitals in the U.S. would be considered high spending by Canadian standards. Thus, it is unclear that marginal returns to additional spending in the U.S. would be similar to what was observed in this study. In fact, studies in the United States by Barnato et al. and Goodman et al. show “…a positive association between spending and outcomes among low-intensity hospitals or regions but no association at average or higher intensity levels.”
Read the rest of this entry »
Tags: Canada, End of Life, Hospitals, Spending
Many recent healthcare policies aim to consolidate the provision of medical services. For instance, Accountable Care Organizations consolidate providers with the goal of providing seamless, integrated patient care. Consolidation can increase efficiency and (potentially) drive down prices. If a market is highly concentrated, however, problems in a single supplier can lead to shortages. Consider the case of Sandoz in Quebec.
“On March 4 a fire broke out at a Quebec manufacturing facility of the multinational generic drug manufacturer Sandoz. The fire halted production and led to medication shortages across the country….
The resulting shortage has hit hospitals especially hard because the Sandoz plant manufactures the vast majority of injectable medications used in Canada….But why was one factory manufacturing such a large proportion of so many important drugs?…
Hospitals in Ontario purchase most of their drugs through group purchasing organizations (GPOs). The two largest GPOs in Ontario are Medbuy and HealthPRO. Both organizations are governed by their member organizations, which are mainly hospitals and other health care providers. GPOs were established to increase efficiency for member hospitals. Instead of each hospital signing its own contracts with multiple different pharmaceutical companies, GPOs deal with the pharmaceutical companies and the hospitals only have to deal with GPOs.
GPOs drive down prices by buying in bulk. But the downside of negotiating aggressively is that sometimes only one manufacturer remains willing to supply a particular drug at the negotiated price. And what appears to have occurred in Canada is that Sandoz was the only willing manufacturer not just for one important medication, but for dozens.”
There are parallels in the car industry as well.
“The company is a chemical plant in a town called Marl. That explosion there killed two people. It was a tragedy, but did not seem to have global significance….Until car companies realized that Marl is vital to their business….
In [Marl], there’s a plant that makes a chemical…that is used in another material called Nylon-12, which is a material that is used – it’s a very basic material. It’s simply a coating that’s used in some of the critical parts of the vehicle, like fuel lines and brake lines.
It’s the kind of thing where it’s so specialized, that not a lot of companies make the product, but a lot of companies end up using it. The plant is one of very few – less than a handful – that make the chemical in the world.”
Concentrating production in a single company can produce economies of scale. A lack of diversification of suppliers (whether its suppliers of medications or car parts) make producers vulnerable to disruptions in their global supply chain.
It is widely known that safety net hospitals provide less intensive care than hospitals whose patient base is mostly commercially-insured. One question is whether safety net hospitals discriminate the care provided based on their patients insurance status. In other words, do commerically insured individuals who visit safety net hospitals receive more care than patients treated at these same hospitals with no insurnce or who are covered by Medicaid?
Based on data from Virginia looking at surgery wait times and rates of breast re-construction surgery, the answer appears to be ‘no.’ A 2012 study by Bradley and co-authors finds the following:
“There is little evidence to suggest that safety net hospitals attenuate treatment differences between insurance and racial groups. The time between diagnosis and surgery was longer in safety net hospitals for all patients, regardless of insurance source or race. Perhaps safety net hospitals are operating at capacity and are unable to schedule surgeries in a timely manner. If this is the case, their resources may be further stretched following the passage of the PPACA. Alternatively, as these hospitals are teaching hospitals, they may perform additional diagnostic tests prior to scheduling surgery or physicians who treat low-income patients may have a slower referral process.”
Tags: Breast Cancer, Hospitals, Insurance
NBA Coaches and Spoiled Children
April 28, 2012 in Books, Economics - General | No comments
In honor of the start of the NBA playoffs…
“After personal fouls, points scored per minute have the largest impact on minutes per game. The result directly contradicts the rhetoric from coaches. Again, coaches tell players to focus on something besides scoring. Players, though, can see that the most effective way to get more playing time is to score more points. In essence, coaches are like the parents of a spoiled child. Although the coach may tell the player he will be sitting if he doesn’t look past scoring, the player knows this is an empty threat. If the player just shows the coach he can score, he will be rewarded with more playing time. In turn, additional playing time will inflate scoring totals, which will increase a player’s future salary.”
Tags: Books, NBA, Sports