April 2009

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Convex States

April 15, 2009 in Economics - General | No comments

What is a convex set?  An object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object.  Mathematically, we can define a convex set as follows.

  • C is a convex set if: αx+(1-α)y ∈ C, ∀ α ∈ [0,1], ∀ x,y ∈ C.

In other words, this means that if we connect any two elements in the set C with a straight line, all the points on the strait line must also be contained within the set.

Let us use an example of U.S. states.  We can consider a state a ‘convex state’ if we can drive in a strait line between any two places in the state and never leave the state.  Let us look at this map of Colorado.  Let us look at the two lines connecting Denver with Grand Junction and the other connecting Fort Collins with Colorado Springs.  We see that when we drive in a straight line between any two cities in Colorado, we will never leave the state.

On the other hand look at the following maps of Texas.  You can see that if we drive in a straight line from El Paso to Amarillo, we will pass through New Mexico.  Similarly, if we drive from New Orleans to Monroe, Louisiana, we will pass through Mississippi.  Thus, neither Texas nor Louisiana can be considered convex states.

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53% of American adults believe capitalism is better than socialism

April 14, 2009 in Economics - General | No comments

According to Rasmussen Reports:

  • 53% of American adults believe capitalism is better than socialism,
  • 20% believe socialism is better, and
  • 27% are undecided.

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Dr. Jason Shafrin

April 13, 2009 in My Papers | 8 comments

Today, April 13th, I successfully defended my dissertation.  I now officially have a Ph.D. in Economics from the University of California, San Diego.

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Why have disability rates decreased?

April 12, 2009 in HC Statistics | 2 comments

“Although the evidence was mixed for the 1980s and it is difficult to pinpoint when in the 1990s the decline began, during the mid- and late 1990s, the panel found consistent declines on the order of  0-2.5% per year for two commonly used measures in the disability literature: difficulty with daily activities and help with daily activities.”

From the quotation above, we see that disability trends have been decreasing over time.  The question is, why is this?  Was the decrease in disability cause by decreasing rates of chronic disease or were decreasing disability rates caused by decreased disability rates among those with chronic diseases?  This is the question Aranovich, Bhattacharya, Garber and MaCurdy attempt to answer in their recent working paper “Coping with Chronic Disease?”

Let us assume an individual has a disability in year t when Dt=1 and the person has a chronic disease when Ct=1. According to the equation below

  • P[Dt]=P[Dt|Ct]*P[Ct=1] + disability from non-chronically ill population.

The authors calculate the probability an individual has a chronic disease P[Ct], using data from the National Health Interview Survey (NHIS).  The authors calculate [Dt|Ct] using Bayes rule as follows:

  • P[Dt|Ct]=P[Ct|Dt]*P[Dt]/P[Ct]

The numerator is calculated using the National Long Term Care Survey (NLTCS) and the denominator we already calculated from the NHIS.  Now we can decompose the changes in disability rates into the following:

  • ΔP[Dt] = ΔP[Dt|Ct=1]P[Ct=1] + P[Dt|Ct]ΔP[Ct=1] + change attributable to non-chronically ill pop.

This says that the change in disability is a mixture of the change in the prevalence of chronic disease and the change in th probability of being disabled given that you have a chronic disease.

Results

Disability can be defined in one of two ways: IADLs or ADLs.  ”IADLs include everyday behaviors such as grocery shopping, managing money, and preparing meals and are considered a measure of moderate disability.  The ADL measure, which encompasses more basic, mechanically-oriented  activities, including dressing, eating, and bathing, is considered a gauge of more severe forms of functional impairment.”

  • Overall Disability.  Between 1982 and 1999, the authors found a decrease in IADL disability of 45% whereas ADL disability decrease by 9%.  
  • Chronic Disease Rates P[Ct].  In general, the authors found increases in the age-adjusted prevalence of chronic diseases.   The prevalence of being overweight increased by 10.4 percentage points, arthritis rates increased 3.0 and diabetes prevalence increased by 1.1.  There were small increases in the prevalence of stroke, chronic obstructive pulmonary disease (COPD).  On the other hand the prevalence hypertension and heart disease decreased by 2.6 percentage points and 3.3 percentage point respectively.
  • Probability of Disability for those with a Chronic disease: P[Dt|Ct]. Between 1982 and 1999, people with arthritis, hypertension, COPD, overweight and heart diseases all experienced about a 50% decline in IADL disability.  Disability of those with diabetes decreased by 25%.  ”Among the seven conditions evaluated, only overweight was associated with a statistically significant decline (p<.05) in ADL disability between 1982 and 1999, a decrease of about 20%.”  However, there were also smaller, non-statistically significant declines in ADL disability among those with heart disease, COPD and arthritis.

Conclusion

Overall, we see a trend of decreasing disability rates and increasing rates of chronic illness.  This means that disability levels have decreased for those who have chronic disease.  It does not seem to be the case that preventive care is decreasing the level of chronic illness.  It could be the case, however, that as more people live longer, observing more chronic illness is an improvement from the counterfactual of death rather than a counterfactual of no disability.  It is also important to note that IADL disability decreased more than ADL disability.  This could be explained by environmental factors.  For instance, “[i]nternet shopping, amplifying devices for phones, and street ramps” all would help to decrease IADL levels, but would have little effect on ADL levels.

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Adaptive Partial Drug Approval

April 10, 2009 in Pharmaceuticals | No comments

Currently the FDA requires that drug companies conduct 3 phases in order to secure the approval of a pharmaceutical. These are:

  • Phase I. These are smaller (20-80 participants), clinical trials which determine a drug’s safety and pharmacologic properties among healthy volunteers.
  • Phase II. This phase tests a drug’s efficacy and optimal dosage. Typically 100-300 individuals are enrolled and these volunteers have the disease which the drug is supposed to treat.
  • Phase III. The third phase is very similar to phase 2, except that the study is much larger. Often there are over 1000 participants in these trials. A drug can receive approval from the FDA if Phase III proves successful.

Is this the best way to insure a safe drug supply? Charles Manski argues no.  Instead, Dr. Manski argues that pharmaceutical companies should received approval to sell limited quantities of a drug after Phase II approval.  This would help reduce the amount of Type II error (not approving a drug that is beneficial).  Quantity limits would increase if the drug was shown to be effective over time.  Drug companies would submit annual reports to the FDA regarding the drug efficacy.

Further, Manski argues that Type III trials should be of much longer length and should focus more on outcomes than on surrogates.  ”For example, treatments for heart disease may be evaluated using data on patient cholesterol levels and blood pressure rather than data on heart attacks and life span.”

The Healthcare Economists Take

While I agree with much of what Manski proposes in theory, putting his proposals into practice will be exceedingly difficult.  The first matter is how much should the drug company be allowed to sell during the partial approval stage.  Manski claims that this decision should be made by a panel of experts, but it is possible that the experts in the field may have strong relationships with pharmaceutical companies.  Further, even an expert will not know if releasing 1000 or 1200 doses of a medicine is optimal.

From a political standpoint, a limited release is a difficult sell.  If the drug is beneficial, it will be hard to justify limiting its sale when it could help other people afflicted with the disease.  If it is potentially harmful, why sell it at all.  Further, one wonders when would insurance companies decide to cover the drug?  This would likely only happen after the full approval many years down the line.  

I agree with Manski that surrogates are a poor measure of health outcomes.  Nevertheless, mandating phase 3 trials of “considerably longer” duration will make the drug development process even more expensive.  Finding the optimal tradeoff between additional information and increased cost is an exceedingly difficult one.

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Minimum Efficiency Standards vs. Price Control

April 8, 2009 in Pharmaceuticals | No comments

When and how regulators allow drugs to come to market is an complex and fascinating process.

In order for drugs to be sold to the public, they must gain approval by the FDA (U.S.) or EMEA (EU).   This involves multiple stages of clinical trials, often costing many millions of dollars.  The uses these trials to evaluate if the drug has a minimum efficacy level and how severe the side effects are.  Approximately, only five in 5,000 compounds that are tested in the laboratory will end up in human trials and only one of these five will be approved by the FDA or EMEA.

After a drug is approved, many coutries regulate drug prices.  Price regluation varies siginificantly across countries.  For instance:

  • Germany: Allows price freedom only for innovative drugs.
  • United States: Prices are free but HMOs and Pharmacy Benefit Managers create formularies with price incentives to use “preferred drugs.”
  • France, Italy and Spain: Drug prices are set through negotiation between the government and industry.
  • United Kindgom: The government does not control individual prices, but instead regulates drug company profits.  Pharmaceutical firms set drug prices freely at product launch; only subsequent price increases require approval. Firms are penalized if profits exceed government guidelines. These are no universal guidelines on drug company profits.  Instead they are negoitated on a company by company basis.

So which framework is best: using a minimum efficiency standard (MES) only or also using price controls (PC)?  Atella, Bhattacharya, and Carbonari (2008) weigh in the debate using evidence from the U.S. and Italy.  Their theoretical model predicts that “average drug quality delivered is higher under the MES regime than in the PC regime or a in combination of the two.  Second, PC regulation reduces the difference in terms of high-low quality drug prices. The empirical analysis based on Italian and US data corroborates these results. ”

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Cavalcade of Risk: Risky Business Edition

April 8, 2009 in Carnivals | No comments

Healthcare Manumission hosts the 75th installment of the Cavalcade of Risk.  

My favorite insight was from the Colorado Health Insurance Insider:

  • “Patients are in the system because they have to be, but the same is not the case for doctors, nurses, and other health care providers.  Whatever health care reforms we consider…we need to make sure that we don’t create a system that is so distasteful to providers that they decide they’d rather spend their time doing something else instead of medicine.”

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When do patients find out how much they will pay for their drugs?

April 8, 2009 in Pharmaceuticals | 2 comments

Consumer Reports writes that “66% of those polled by Consumer Reports said they found out the cost of a drug when they picked it up at the pharmacy counter, while just 4% said they had a conversation with their doctor about the cost of a drug.”  Because doctors do not discuss cost with their patients, these patients often forego necessary medications.

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Adjusted Risk Ratios

April 7, 2009 in Econometrics | No comments

How do you estimate the specific risk a smoking has on the probability of being hospitalized.  If smokers on average have lower income and less educational achievement, is smoking truly causing the increase in hospitalization or could the covariates fully or partially explain the increased hospitalization rates?

A paper by Kleinman and Norton suggests using adjusted risk ratios with logistic regressions.  The formula for this procedure is as follows:

  • ARR = [n-1Σi=1 to N riski(Xi|as if exposed)] ÷ [n-1Σi=1 to N riski(Xi|as if unexposed)]   (1)
  • ARD = [n-1Σi=1 to N riski(Xi|as if exposed)] – [n-1Σi=1 to N riski(Xi|as if unexposed)]   (2)

The authors explain the first equation as follows:

  • “The denominator of equation (1) is the mean of this calculated risk for each observation when the exposure variable is assumed to be unexposed and represents an MLE of the unexposed (baseline) risk for a population whose covariates are distributed as for the observed covariates for the entire study population. The numerator in equation (1) represents an MLE of the adjusted risk among the exposed. This approach is a specific example of using what are called “recycled predictions.”

Standard errors can be calculated using either bootstrapping or the Delta Method.  However, the authors wisely recommend bootstrapping the standard errors since it reduces the computations resources needed and can also allow for asymmetric confidence intervals.

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A tax on sex?

April 6, 2009 in Current Events, Taxes | No comments

Nevada is contemplating ‘slapping’ a $5 tax on sex acts in brothels.

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