The latest edition of the Health Wonk Review is up at Hank Stern’s always interesting InsureBlog.
Tags: HWR
Currently, Medicare and private insurers are attempting to put in place incentives to reduce the number of readmissions. Visits to the hospital are costly and reducing the frequency of hospital visits is the best means to reduce medical costs. In particular, if readmissions are the fault of the care the patients receive during the initial admissions, hospitals should be liable for subsequent care.
On the other hand, a recent letter to the New England Journal of Medicine, argues that high readmission rates may in fact indicate high quality care.
“A higher occurrence of readmissions after index admissions for heart failure was associated with lower risk-adjusted 30-day mortality. Our findings suggest that readmissions could be ‘adversely’ affected by a competing risk of death — a patient who dies during the index episode of care can never be readmitted. Hence, if a hospital has a lower mortality rate, then a greater proportion of its discharged patients are eligible for readmission. As such, to some extent, a higher readmission rate may be a consequence of successful care.”
Tags: Hospitals, Readmissions
- California Workers Comp: Parts I and II.
- Decriminalizing drugs in the Czech Republic.
- Bad news for Alzheimer’s Treatment
- The solution to obesity: school playgrounds?
- An interview with a nurse practitioner.
- Homo economicus in Paris.
Tags: Links
Oftentimes, people use the following rule of thumb: if the dependent variable is continuous, use OLS; if binary use a logit or probit. But what should you do if your dependent variable is fraction between 0 and 1. To use a logit or probit one would have to unnecessarily transform the dependent variable into binary form. If one would use OLS, the estimation of the coefficients would likely be incorrect. Because the dependent variable is bounded between 0 and 1, the effenct of any explanatory variably xj cannot be constant through its entire range. Additionally, the predicted values from an OLS regression often produce figures outside the range of 0 to 1.
A paper by Papke and Wooldridge (1996) examines potential econometric alternatives when your dependent variable is fractional.
LOG-ODDS RATIO
One option to estimate a fractional response variable is to transform the dependent variable into a a log-odds ratio. For instance:
- E(log[y/(1-y)]|x) = xβ
This model is simple and can be estimated with OLS techniques onces the depenent variable is transformed. It only works, however, when the dependent variable is strictly between 0 and 1. [If y=0 the you have the log(0) and if y=1 then you get the log(1/0) which is ∞]. Additionally, using this framework, it is difficult to recover E(y|x). Under the model specified above:
- E(y|x)=∫ {exp(xβ+ν)/[1+exp(xβ+ν)]} * f(ν|x)dν
If the residuals are independent of the explanatory variables (i.e., ν⊥x), one can use Duan’s (1983) smearing technique to estimate f(•). If not, one must make functional form assumptions regarding the distribution of the error terms.
QUASI-LIKELIHOOD METHODS
Papke and Wooldridge support using quasi-likelihood methods. Assume the following relationship:
- E(y|x) = G(xβ)
where 0<1 for all z∈ℜ. The most popular choice for G(z) is the logistic function where G(z)=exp(z)/[1+exp(z)]. In this model, one can estimate the parameters β using the following Brenoulli log-likelihood function:
- li(β) ≡ yilog[G(xiβ)] + (1-yi)log[1-G(xiβ)]
This method has several advantages. First, it is fairly easy to estimate. Secondly, the equation above is a member of the linear exponential family thus the quasi MLE method will produce a consistent estimator of β where β is normally distributed. Assuming a logit function for G(z) produces the following variance:
- Var(yi|xi) = σ2 * G(xiβ)[1-G(xiβ)]
The Papke and Wooldridge (1996) also describe how to compute the asymptotic variance of the estimator β.
- Papke LE and Wooldridge JM (1996) “Econometric methods for fractional response variables with an application to 401(k) plan participation rates“, Journal of Applied Econometrics, v11:619-632.
Tags: Econometrics, Fractional Dependent Variable, Fractional Response Variable, Statistics
Stephen Zuckerman has a nice summary of the key provisions in the Health Reform law (i.e., PPACA). There are six broad changes: i) the creation of health insurance exchanges, ii) an excise tax on high-cost health plans, iii) creating the Independent Payment Advisory Board (IPAB), iv) Medicare policy changes v) additional emphasis on prevention and wellness, and vi) increased efforts to reduce waste fraud and abuse. The following sections will discuss each of these changes in more detail.
Tags: Health Reform, PPACA
- The politics of breast cancer.
- Are gulf shrimp safe?
- High journal rejection rates and the probability of erroneous results.
- The uninsured in Massachusetts.
- How to reduce malpractice lawsuits.
- Roboscout and the Four Factors of Basketball Success.
- ObamaCare threatens college health plans.
- Using the iPad for EMR.
Tags: Links
As a Wisconsin-native, you may be surprised that this is my first post about Beers. I do like beer. My preference is for either dark beers (e.g., porters, stouts) or Belgian ales. Today, however, I am not going to endulge you in a discussion about beer.
Instead, I want to talk about the Beers criteria. The Beers criteria lists a number of medications that are considered inappropriate to prescribe to the elderly. Generally, the side effects of these drugs outweigh the potential benefits for more frail seniors. The list has been updated numerous times, most recently in 1997 and updated in 2003.
Many medication therapy management (MTM) programs use the Beers list to identify high risk drugs. Computer algorithms can use data on the beneficiary’s age and the drug prescribed to determine if the medication meets the Beers criteria. If this is the case, the pharmacist can alert the patient and/or prescribing physician in order to alter the treatment plan.
Tags: Beers List
Tyler Cowen thinks that one way to reduce the fiscal burden on States is to move Medicaid to the Feds. Wisconsin may be taking a first step in that direction. Wisconsin Governor Jim Doyle, having to make $400 million in Medicaid cuts, left these cuts up to Federal Medicaid officials. Newsweek reports that “The fixes, most of which kicked in this summer, were a predictable mix of new contracts and procedures (incentives for natural birth will save $4 million in C-sections).”
Although the State/Federal funding arrangement is the same, Wisconsin’s shifting decisionmaking power to the Feds may augur for a more centralized Medicaid program. Governor Doyle believes that shifting these decision reduce the power of lobbyists. According to teve Barton, president of the hospital lobby Wisconsin Hospital Association believes that shifting decisions to the Feds means lobbyists lost influence, officials were insulated from blame, and lawmakers were shielded from “tough votes.”
This politics-free honeymoon, however, will likely be short-lived. If State Medicaid decisions are made at the Federal level, lobbyists will simply move from Madison to Washington. In fact, lobbying may increase since the cost of these political wrangling will be less expensive if all Medicaid decisions are centralized.
As long as some form of government–State or Federal–runs healthcare, believing that these decisions will be free of lobbying influence interests is naive.
The latest edition of the Cavalcade of Risk (#112) is up at The Notwithstanding Blog. This new entry into the blog-o-sphere is not only entertaining and informative, but also contains pictures. Using the latest exchange rate (1 picture=1000 words), this edition of the CoR is sure to have enough information to enlighten even the most veteran risk analyzers.
In particular, I enjoyed the following articles:
Tags: CoR
How will health reform affect small, medium and large size businesses? Linda Blumberg answers this question in this RWJ policy brief. Blumberg summarizes the legislation as follows:
“Small employers, those with fewer than 50 workers, will face no new requirements but will have new insurance options made available to them through the new health insurance exchanges. These new options have the potential to save money for small businesses that wish to offer insurance to employees.
Medium-size employers, those with 50 to 100 workers, will have access to these new coverage options as well, but may face some financial penalties if their modest income, full-time workers obtain federal subsidies due to a lack of affordable coverage available through the workplace. New coverage sold to small and medium-size groups will be subject to regulations that will make insurance more affordable to groups with higher than average health care needs. Healthier groups will share in these costs more than they do today.
The vast majority of large employers (more than 100 workers)…are the least likely to be significantly affected by health care reform. However, they may experience greater employee participation in their current insurance plans and will face penalties if their full-time workers obtain subsidized coverage through the exchanges.”
This spreadsheet summarizes how key provisions will affect each of these three types of businesses.
- Linda J. Blumberg “How Will the Patient Protection and Affordable Care Act Affect Small, Medium, and Large Businesses?” Timely Analysis of Immediate Health Policy Issues, Urban Institute and Robert Wood Johnson, August 2010.
Tags: Health Reform, PPACA
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