March 2008

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Serial Corelation and the Durbin Watson Statistic

March 25, 2008 in Econometrics | Permalink

What is the effect a country’s GDP on health? What about the country’s literacy rate on infant mortality rates? Often researchers try to answer these questions using time-series data. With time series data, we have observations of a few units (e.g.: countries or individuals) over many years.

Let the subscript i represent the the individual or country and the subscript t indicate the year. We can have a regression framework as follows:

  • yit = βxit + εit

As long as cov(xit,εit)=0, then ordinary least squares (OLS) will provide an unbiased estimate of β1.

One frequent problem which occurs with time series data is that there will be serial correlation. Serial correlation (or autocorrelation) occurs when the error terms are correlated over time. For instance,

  • εit=ρεit-1+ηit

Serial correlation means that if your predicted y value is overestimated in period, it is likely to be overestimated in another period. This is likely due to some persistent variable omitted the regression. For instance, if we regressed test scores on a vector of explanatory variables, it is likely that student who scored higher than their predicted test score in one period would also score higher then their predicted test score in another period.

Fortunately, our coefficient vector (β) is still unbiased even in the presence of serial correlation. However, OLS is inefficient. In this case, the standard errors are too small.

One way to test for serially correlation is to use the Durbin-Watson test. Let uit be the fitted values of the error terms after we conduct and OLS regression (uit = yit – βols xit ).

The Durbin Watson statistic is:

  • d= [Σ(t=2 to T) (uit - uit-1)2] / [Σ(t=1 to T) (uit)2]

With panel data we have:

  • d= [Σ(i=1 to N)Σ(t=2 to T) (uit - uit-1)2] / [Σ(i=1 to N)Σ(t=1 to T) (uit)2]

This page will help you interpret the statistic as to whether or not you should accept or reject serial correlation. If there is serial correlation in your data, you may want to include a lagged dependent variable as one of your right hand side variables. This will result in an AR(1) specification.
Yuting Wang of Notre Dame has a good explanation of the problems that occur with serial correlation.

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The Spread of Obesity in Social Networks

March 24, 2008 in Obesity | Permalink

Are you friends members of the Marathon Runner’s of America club or the Bratwurst and Philly Cheesesteak club? If the answer is the later, you are much more likely to be obese than the former.

This is the finding of a 2007 NEJM paper by Christakis and Fowler. Obese individuals are more likely to be friends, relatives, or spouses with other obese people (and vice versa). The authors contend that there are 3 explanations for why this could be the case empirically.

  1. Homophily. This means that individuals choose to associate with people who look like them. In this case, social networks would not cause obesity, it is just that obese individuals choose to hang out with other obese individuals.
  2. Counfounding factors. Siblings have the same genes. Obesity social norms within a particular geographic area may affect friends and family in a similar manner. These unobserved, confounding variables may also be the true cause of why
  3. Induction. Social influence and peer effects may effect the obesity level of each person in a group. The authors hypothesize that this explanation to be the major avenue by which social networks affect obesity.

The paper tracks a database of 12,067 individuals over 32 years. The regressions use a lagged dependent variable to eliminate problems of serial correlation.

Results

Let us define the ‘ego‘ the person as the person whose behavior is being analyze and the ‘alter’ as a person connected to the ego by a social network. When the ego’s alter is a friend and becomes obesity, there is a 57% chance that the ego will become obese. This impact is larger for same sex friendships (71% probability of become obese if the alter becomes obese) than opposite sex friendships (effect not different from zero).

How does the obesity of one’s spouse affect the ego’s obesity? According to the authors, “[a]mong married couples, when an alter became obese, the spouse was 37% more likely (95% CI, 7 to 73) to become obese. Husbands and wives appeared to affect each other similarly (44% and 37%, respectively).”

What explains this phenomenon that the alter’s obesity will affect the ego’s obesity. It is possible that the social network as a whole experiences similar life events which affect obesity. However, even when alter’s live geographically far from the ego–and thus likely have different life experience over time–this does not change the effect the alter’s obesity has on the ego. Christakis and Fowler claim that this supports their perception that social norms heavily influence obesity. Also, the spread of smoking behavior does not affect the spread of obesity. One would guess that social networks would have a similar effect on smoking and obesity. The authors claim that this finding, “…suggests that the psychosocial mechanisms of the spread of obesity may rely less on behavioral imitation than on a change in an ego’s general perception of the social norms regarding the acceptability of obesity.”

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How to declare bankruptcy

March 21, 2008 in Miscellaneous | Permalink

With the stock market in decline, the credit crunch hovering over, and the fear of a recession growing, I think its time for some Friday humor.

I’ll let personal finance guru Michael Scott of the TV show The Office show us all how to declare bankruptcy.

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Zagat rates your doctor

March 21, 2008 in Healthcare IT | Permalink

According to Insurance and Technology, health insurer WellPoint has partnered with Zagat’s Survey to allow WellPoint’s members to rate their doctors.  Zagat’s will use its 30 point rating system to evaluate all doctors.  According to Spirit magazine, patients can grade doctors based on “including doctor availability, office environment, trustworthiness, and communication.”

Other websites, such as RateMDs.com, already offer patients the ability to rate doctors, but WellPoint is the first health insurer to offer this service to its members.

Shop around

March 20, 2008 in Current Events | Permalink

People who are sick are not able to shop around for medical care.  This statement may be true in some cases, but not for the majority of illnesses.  Those without insurance are especially sensitive to the price of medical care and are in fact very likely to shop for the combination of the lowest price, best quality care they can afford.

The RNCentral website gives some tips to the uninsured regarding how they can increase their access to care, improve the quality of care they are receiving, and reduce their out of pocket expenditures.  One interesting company is TelaDoc.  This firm provides a service which enables patients to phone a doctor 24 hours a day, 7 days a week to receive diagnosis and treatment information.  While TelaDoc won’t cure cancer, it will help patients to find the correct treatment for minor illnesses.

Health Wonk Review

March 20, 2008 in Carnivals | Permalink

The latest edition of the Health Wonk Review is up at Joe Paduda’s Managed Care Matters website.

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Paying kids to go to school

March 20, 2008 in Public Policy | Permalink

In Mexico there is a government program named Oportunidades which gives families cash payments if their children go to school, get vaccinated, and have regular health checkups.  The program has been a success and similar conditional cash transfers (CCTs) programs are being run in Nicaragua, Brazil and New York City.

New York City?  Should the NYC government pay for local children to go to school?  On the one hand, this will likely increase school attendance and decrease the number of drop outs.  On the other hand, the government is paying residents to do certain actions which seems to be a very paternalistic attitude.

The Economist  reports (“When bribery pays…“) that CCTs have been used in other settings as well:

Offering cash to change long-term bad habits, such as smoking or over-eating, has not worked. But disbursements tied to short-term transactions, such as getting drug addicts to take treatments for tuberculosis or depressed patients to see their psychiatrists, have already shown promise.

While paying children to go to school is not in and of itself a bad idea, I am concerned that the government will continue to pay people to do things that it thinks are in its best interest.  If we want to decrease inequality in society, it would be much better to increase cash transfers to the poor and allow them to decide for themselves what they should do with the money.

Vaccine Logistics

March 19, 2008 in HC Economist Models, Vaccinations | Permalink

Vaccination is one of the most cost effective medical treatments we have.  It is important that providers vaccines in a timely manner.

In attempt to streamline vaccine distribution systems, the CDC created Vaccine Management Business Improvement Project (VMBIP).  Instead of having providers place orders with the grantee (i.e.: state health department), and then having the grantee ship them to a local distributor, VMBIP is an attempt to reduce warehouse costs by shipping vaccines from a centralized warehouse directly to the provider.  This may save money, if the vaccines are sent in a timely manner.

My presentation at the National Immunization Conference analyzed some data from southern California providers and found that the time from the vaccine order being place to delivery increased from 1.6 work days to 13.5 workdays after VMBIP was implemented.  I received other anecdotal evidence that these delays were affecting the vaccine supply of many California providers, but I did not know how efficiently the VMBIP program was operating in other states.

I found that California’s 13.5 day delay may not be so bad compared to the rest of the country.  One nurse from Texas said that vaccines delivery could take as long as 6 weeks.  There was significant variability so that the clinic would run out of vaccines occasionally so would have to place their orders early.  Sometime the vaccines would arrive within 2 days, but since the provider had anticipated a 2-4 week delay, there was no room in the refrigerator to store the vaccine.

Another conference attendee explained to me her experience in Minnesota.  Vaccines must be stored at a certain temperature to ensure they do not spoil.  Some winter days are so cold in Minnesota that the state public health department would advise distributors not to ship on those days to insure that they would not freeze.  Under the new, centralized VMBIP system, the national warehouse–which is run by McKesson–was not sensitive to these regional variations.  Minnesota providers have received frozen vaccines since McKesson did not know about how Minnesota winters effect vaccines.  These frozen vaccines are completely useless and must be discarded.

Overall, I doubt that centralized vaccine distribution is a good model.  Wal-mart can operate a centralized distribution system because all the stores are on the same computer network, they work under the centralized location, and receive extensive logisitcs training.  Further, Wal-mart is a hierarchical organization.  On the other hand, physicians are not integrated into a public health IT database–VACMAN not withstanding.  Further, providers are well trained on medical issues, but not logistics or filling out forms.  Since vaccine distribution is not a hierarchical system, a more flexible, less centralized, system would likely be optimal.

I would like to thank all the people who attended my presentation today at the National Immunization Conference and all the helpful feedback I have received.

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National Immunization Conference

March 16, 2008 in Vaccinations | Permalink

I will be in Atlanta for most of this week attending the National Immunization Conference. If you are interested in seeing me present my work regarding the efficiency of the Vaccine Management Business Improvement Project‘s new distribution system for the Vaccines for Children (VFC) program, my talk will be on Wednesday at 9am.

Blogging will resume later the week.

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Pay first, evidence later.

March 15, 2008 in Medicaid/Medicare | Permalink

Merrill Goozer reports (“CMS okays heart scan…“) on how Center for Medicare and Medicaid Services (CMS) has reversed a policy to stop paying for heart scans.  There has been no clinical evidence to show that these expensive heart scans identify heart disease any better than less expensive procedures (i.e.: stress tests).

Physician revenue, however, would be hurt by this decision and after extensive lobbying, CMS has decided that paying for heart scans may be a good decision after all.  In the words of Merrill Goozer: “Pay first, evidence later. It’s the American way.”

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