April 2009

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FDA bans import of Indian Pharmaceuticals

April 28, 2009 in Pharmaceuticals | No comments

Marketplace reports that the FDA has blocked sales from one of India’s largest drug producers, Ranbaxy Pharmaceuticals.  “It prevented sales of Ranbaxy’s generic versions of the antibiotic Cipro and the cholesterol pill Zocor.”

This begs the question: should the FDA put office in foreign countries?  On the one hand, it is important to ensure that imported drugs are safe.  However, FDA decisions to ban certain drugs could be influenced by protectionist concerns rather than patient health. 

Ajay Sahai, executive director of the Federation of Indian Export Organizations: ”In many of the cases, Indian companies do have a case where they have been stopped by large companies present in the importing countries. They have tried to restrict the imports at whatever cost or citing whatever reason.”

Is the FDA doing a diligent job or protecting the safety of the U.S. drug supply, or is it engaged in protectionism.  Finding the true answer is exceedingly difficult.

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Why not to use a normal distribution to approximate a binomial distribution

April 28, 2009 in Econometrics | No comments

Most people know that under the central limit theory claims, the distribution of the mean of a distribution will be normally distributed as the number of observations gets large.  The question is, if we have a series of discrete events that we want to approximate the distribution of the mean with a continuous distribution, should we estimate them with a normal distribution?

For instance, let us assume we have 20 observations on patient admittance to the hosptial and in 3 of those cases, the individual died.  we can use a binomial distribution to estimate the distribution of the prior as:

  •  nCr*πr(1-π) n-r. 

We can estimate π with the 3/20 = 0.15.  For our prior distribution, we could fit a normal distribution.  Using a normal distribution, however, would include values less than 0.  This is especially problematic if there is a small samples sizes (e.g., n=20).  A truncated normal would solve the problem of negative values, but eliminating one portion of the distribution will change the distribution’s mean and variance.

Another option is to use the beta distribution for the prior.  The beta distribution for the value of π is:

  • p(π) = {Γ(α + β)/[Γ(α)Γ(β)]} πα-1(1-π)β-1

If we apply Bayes’ theorm to the binomial data with a beta prior, we get:

  • p(π) ∝ πr(1-π)n-rπα-1(1-π)β-1
  • p(π) ∝ πα+r-1*(1-π)β + n-r -1

Now we have that the posterior distribution is Beta(α+r-1,β + n-r -1).  We already know r and n, and can match α and β with the methods of moments.

  • E(θ) = α/(α + β)
  • var(θ) = αβ/[(α + β)2(α + β+1)]

Now we estimate E(θ) and var(θ) with the sample moments. If 3/20 people died, then we estimate E(θ) with 3/20 = 0.15. Further, with a binomial distribution, we can estimate var(θ) with p(1-p)/n = .15*.85/20 = .00638. This means that the s(θ)=.006381/2 = .07984. Thus we can solve for α and β since we now have 2 equations and two unknowns.

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Swine Flu Update: Monday

April 27, 2009 in Contagious Disease | No comments

Closing public spaces may be a good idea to stop the spread of the flu:

Hong Kong uses technology to fight the spread of disease

  • Ever since the 2003 outbreak of SARS, or severe acute respiratory syndrome, Hong Kong has used infrared scanners to measure the facial temperatures of all arrivals at its airport and at its border crossings with mainland China. Dr. Thomas Tsang, the controller of the Hong Kong government’s Center for Health Protection, said Sunday afternoon at a news conference that any traveler who had passed through a city with laboratory-confirmed cases and who arrived in Hong Kong with a fever and respiratory symptoms would be intercepted by officials and sent to a hospital to await testing. “Until that test is negative, we won’t allow him out,” he said.

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Markov Modelling for Pharmaceuticals

April 27, 2009 in Economics - General, Pharmaceuticals | No comments

How do you create a Markov Model for the effectiveness of pharmaceuticals?   Below is an example from Briggs, Claxton and Sculpher’s book titled “Decision Modelling for Health Economic Evaluation.”

Example

The main characteristic of a Markov Model is that it defines different states and then defines transition probabilties between each state.  Let us examine the case of someone with an HIV infection.  There are 4 possible states in this simplified model:

  • State A: cd4 levels are between 200 and 400
  • State B: cd4 levels are less than 200
  • State C: The individual has AIDS
  • State D: Death

Transition Probabilities

Now we must find a baseline transition probability matrix.  In this case, the baseline will be no treatment, but the baseline could also be one form of treatment to be compared to another.  This table gives the transition probabilities.  You can read the table as follows: A person in state A has a 72.1% chance of being in state A next period, a 20.2% chance of being in State B next period, a 6.7% chance of being in state C next period and a 1.0% chance of being in state D next period.

Now there is a drug treatment on the market which has a relative risk of 0.509.  This means that the chance of moving to a worse state has decreased by about half.  The book’s authors note that “Often it is assumed that baseline event probabilities should be as specific as possible to the location(s) and subgroup(s) of interest, but that the relative treatment effect is fixed.”

To get the new transition probabilties after treatment, we multiply the transition probabilities by 0.509 if the represent a worsening of the state.  The remaining ‘extra’ probability is moved to the probability of transitioning to the current state.  In this model, no one can transition to a better state (i.e., remission) so we do not have to worry about the relative risk of getting better.

Look at the first row of the transition probabilities matrix with the therapy.  State A transition probabilities to states B, C, and D are multiplied by 0.509 to get the new transition probabilities (i.e., .202*.509 = .103; .067*.509=.034;  0.010*.509 = .005).  The probability of staying in state A after treatment is just one minus the other probabilities (i.e., 1 – .103 – .034 – .004 = .858).

Survival

Now we want to find out how many people will survive.  We can do this with a simple simulation.  The baseline simulation is shown here and the simulation with the treatment is shown here.  To get the future probabilities, simply multiply the transition probabilities by the people in each state.  For instance, to find out how many people will be in state C in year 5, we need to look at year 4.  We know that of the people in state A, 0.067 will go to state C; Of the people in state B, .407 will go to state C; of the people in state C, 0.750 will state in state C, and of the people in state D, 0.000 move into state C.  Thus we calculate the number of people in state C in year 5 as: .27*.067+.23*.407+.34*.75+17*0 = 0.36.

We could also accomplish this with matrix algebra.  The vector of people in each state is equal to [1 0 0 0]*Tn.  This means that in year 0, we have 100% of people in state A.  The transition matrix is represented by T and n is the number of years in the future we want to view.

In our analysis, we see that the baseline 20-year survival rate is only 3.2%, but with the treatment, this increases to 33.2%.

Cost

We can also determine the costs of the treatment and baseline.  The treatment has the added expense of purchasing the drug for $2278.  However, with the treatment fewer people are moving into the more expensive stages B and C.  Thus there is a tradeoff.

We can see from the simulation, that the treatment is more expensive than the baseline.  To calculate this, you simply multiply the proportion of people in each state by the cost in each state to get the cost per year.  It is also important to discount the costs to get the expenses in terms of net present value.  In this example, I used a 6% discount rate.

Markov with Memory

In general, Markov models are memoryless, meaning they do not care how long an individual has been in each state.  It is possible to create ‘memory’ using tunnel stages.  Let us examine the following example for disease X.  In this model there are 5 stages, 1 having the disease, 3 remission stages, and death.  An individual with disease X has a 60% chance of keeping the disease, a 20% chance of remission less than 1 year and a 20% chance of death.  Of course, they have a 0% chance of being in remission for 1-2 years or >2 years after only 1 period.  If a person does go into remission, we see that they have a 40% chance that the disease reoccurs, a 50% chance of getting to the remission for 1-2 years stage, and a 10% chance of death.  By making these stage related to time, we have created a Markov model that simulates memory.

Summary

With Markov modelling, we can estimate the effect a drug has, both in terms of its health implications–such as survival rates and the number of people in each stage–as well as its cost implications.  The key assumption is that the treatment effect is constant across all stages.


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Swine Flu: Public Health Emergency in the U.S. and Mexico

April 26, 2009 in Contagious Disease | 2 comments

The World Health Organization (WHO) declared Swine Flu to be an international public health emergency.

MÉXICO

La Jornada claims that there swine flu has killed 81 people in México and infected 1324.  The entire country of México has closed schools until May 6th according to La Prensa:

“El gobierno federal ordenó la sus­pensión de misas, clases–hasta el 6 de mayo– y todo tipo de eventos abiertos o cerra dos en estadios, teatros, cines, bares y discotecas donde se generen aglomeraciones.”

Mexico is also considering shutting down all public transportation.

U.S. and CANADA

According to the New York Times, swine flu has been spreading and risks becoming a pandemic.  In fact, the U.S. has declared a public health emergency.  In the U.S. there have been at least 20 confirmed cases:

SPAIN

After a visit to Mexico, 6 Spaniards have possibly contracted swine flu.

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NHS Privatization

April 25, 2009 in International Health Care Systems | No comments

The Guardian reports that the UK considering privatizing sections of the National Health Service (NHS):

A Treasury-commissioned report yesterday recommended measures to chop £6bn from public services budgets over the next two years, with further measures intended to save £15bn a year by 2013.

It calls for a shake-up of “back office” administrative and support services across government departments, the NHS and local government, a move likely to see thousands of jobs lost or outsourced.

The authors say the government should push ahead with full or part privatisation of state-owned assets such as the Royal Mint, Met Office and Land Registry, and identifies other bodies ripe for commercialisation, including the health service’s in-house staffing agency, NHS Professionals, the Central Office of Information, and Forestry Commission.

The British Medical Association thinks the privatization plan is just “barmy economics.”

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Swine Flu leads to at least 20 deaths

April 24, 2009 in Contagious Disease | No comments

In Mexico, there has been an outbreak of swine flu which has lead to 20 recorded deaths and likely 40 more.  The newspaper el Universal reports that, the Secretaría de Educación Pública suspended classes in the Distrito Federal and the Estado de México.  This means that in the Mexican capital, 5,201 public schools and 3,965 private schools were cancelled.  

Yet this is not just a Mexican issue.  Swine flu has been found among residents of San Diego and Austin.  Further, after a Canadian citizen contracted swine flu after a visit to Mexico, it was the Canadian government that informed Mexico of the possibility of a swine flu outbreak.

Fortunately, the Mexican government claims it has enough drugs to combat the swine flu outbreak.

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Economics 2.0: What caused the housing market boom

April 24, 2009 in Uncategorized | 2 comments

What caused the housing boom?  Did people really believe that a median home price of over $500,000 in San Diego  were realistic?  Were people caught up in the dot-com boom really rational?

 Economics 2.0, reviews a paper saying that rational people will often buy assets that they themselves believe are overvalued.  Why?

Let’s say I believe that most investors think of the market as being overvalued.  I also know, however, that most investors have not yet sold out.  My conclusion from that is that they expect a price increase, at least for the short term, and are therefore unlikely to sell tomorrow.  I will step up and buy.  

The same will occur tomorrow, with the effect that my daily predictions for the next day’s average market assessment will not be in line with my long-term forecast of the average market value assessment.  This discrepancy grows wider with each day as observant investors have an incentive to “ride the bubble.”

The book also reviews an article by Javier Estrada the thick tails of the stock market returns distribution.  This makes effective market timing very difficult:

Someone having invested a fixed daily amount in the Dow since 1900, but having missed the ten most profitable trading days, would have lost 65 percent of all returns.  By contrast, someone having managed to avoid the ten worst trading days would have increased his gains by 206 percent.  ”These magnitudes are enormous, given that ten days account for only 0.03 percent of the days considered,” Estrada writes.  Results are similar when viewed in the context of shorter time spans.  ”A negligibe proportion of days determines an enormous creation or destruction of wealth and, therefore, the odds against successful market timing are simply staggering.” 

This is more academic evidence supporting my own buy-and-hold investment philosophy.

“Say it ain’t so, Ben”

April 23, 2009 in Current Events, Economics - General | No comments

  • Bank of America shareholders approved the purchase of Merrill Lynch on December 5, 2008.  
  • Last year in the fourth quarter,  Merrill Lynch lost $15.84 billion.  
  • Bank of America President Ken Lewis knew that Merrill was at risk of huge 4th quarter losses.
  • Ken Lewis did not tell shareholders about Merrill’s impending large losses.  Why?

Under oath, Ken Lewis testified that “he believed Messrs. Paulson and Bernanke were instructing him to keep silent about deepening financial difficulties at Merrill, the struggling brokerage giant.”   

According to Lynn Turner, former chief accountant at the SEC, “If these allegations are proven true, both Bernanke and Paulson should be prosecuted by the SEC to the fullest extent of the law.”

Economists coercing business leaders to hide vital economic information…Say it ain’t so, Ben!

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Health care in India

April 23, 2009 in Health Care Around the World, International Health Care Systems | 3 comments

Highlights from The Economist’s article on Health Care in India:

  • India spends only about 5% of GDP in medical care.  Of this spending only one fifth is public spending.
  • With an overwhelmed public sector, relatively low levels of insurance, a premium is put on frugal innovation.  Fortis, a hospital chain in New Delhi, elects to have ‘world class’ scanners, but not necessarily the newest.
  • Surgical procedures are also innovative.  Vivek Jawali has developed an open heart surgery procedure where the patient is still awake.  ”Because such ‘beating heart’ surgery causes little pain and does not require general anaesthesia or blood thinners, patients are back on their feet much faster than usual. This approach, pioneered by Wockhardt, an Indian hospital chain, has proved so safe and successful that medical tourists come to Bangalore from all over the world.”
  • Health IT use in U.S. hospitals: 20%
  • Health IT use in Indian hospitals: 60%
  • Tiered pricing: Aravind, the world’s biggest eye-hospital chain, employs “a tiered pricing structure that charges wealthier patients more (for example, for fancy meals or air-conditioned rooms), letting the firm cross-subsidise free care for the poorest.”
  • “In health care, as in life, there is need for both Ferraris and Tata Nanos.”

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