Vaccinations

Merrill Goozner of GoozNews has an interesting interview with Richard Ebright, a chemistry professor at Rutgers University.  The two discuss the Bruce Ivins, anthrax, and bioterrorism.  A few poignant excerpts.

• Ebright: “We’ve spent $57 billion in biodefense since 2001. The annual budget for NIH is only $30 billion. The spending has been disproportionate to the level of threat.”
• Ebright: “There are now 14,000 individuals authorized to handle bioweapons materials.”

Goozner also gets some answers about who benefited from the anthrax attacks of 2001.

• Ebright: “The administration has milked this for all it is worth by allowing the misperception to remain that this was an external attack, possibly from Iraq…The vaccine industry, particularly BioPort and its successors, have exploited this misperception.”

Contagious disease are spread (generally) when one person comes in contact with another. Thus, the number of links in a network (the number of connections one has) will go a long way to determining how fast diseases are spread.

One question which needs to be answered is whether a hub-and-spoke network or a more diffused network will spread diseases faster. On the one hand, if the hub gets infected, it is very likely that everyone else gets infected in the hub and spoke diagram. On the other hand, if the hub does not get infected, then a more diffused network likely will spread diseases more quickly.

A paper by Jackson and Rogers (2007) uses the concept of stochastic dominance to demonstrate which types of networks spread diseases the quickest. Today, I will summarize their model.

Model

All nodes (think of a node as a person) in a network can either be infected (have the disease) or susceptible (do not have the disease and are not immune). We will ignore immunity in this model. The probability a node is infected is: ν(d_iθ_i + x) where ν ∈ (0,1) describes the infection rate. The variable d_i represents the degree (number of connections) that node i has, θ_i ∈ [0,1] is the fraction of i’s neighbors who are infected and x is a non-negative scalar representing the rate at which infection sprouts up independent of social connections.

An individual recovers from a disease with probability δ.

Now we want to characterize how diseases spread through different social networks. Let P(d) be the probability a randomly chosen node has d connections (degree d). If ρ(d) equal the average infection rate among nodes with degree d, then the average infection rate can be calculated as:

• θ=(Σ_dρ(d)P(d)d)/(Σ_dP(d)d)

The variable θ is the average neighbor infection rate. We can estimate the change in the infection rate over time for nodes of degree d with the following equation:

• ∂ρ(d)/∂t=[1-ρ(d)] ν(θd+x) - ρ(d)δ

The first part of the fraction shows how quickly susceptible nodes (i.e.; 1-ρ(d)) are infected and the second part show how quickly infected nodes (i.e., ρ(d)) are cured. In steady state [i.e., ∂ρ(d)/∂t=0], we have that the average infection rate is:

• θ=m^-1Σ_d[(ν(θd²+xd)P(d)/δ]/[1+ν(θd +x)/δ]]
• m = Σ_dP(d)d

Network Comparisons

Let us now define networks according to the concept of stochastic dominance. Network P’ has first order stochastic dominance over P if Σ_{(d=0 to Y)} P’(d) ≤ Σ_{(d=0 to Y}) P(d) ∀ Y, with Σ_{(d=0 to Y})P’(d) < Σ_{(d=0 to Y)} P(d) for some Y. This means that network P’ has a higher fraction of nodes with lots of connections compared to network P. Jackson and Rogers prove the following:

1. If P’ strictly first order stochastically dominates P, then the steady state θ’ > θ and the steady state ρ’ > ρ.
2. If P’ is a strict mean-preserving spread of P, then θ’ > θ.

Theory (1) implies that if a network has more connections, it will have a higher steady state average neighbor infection rate (θ), and a higher overall average infection rate (ρ). This makes perfect sense.

One the other hand, theory (2) shows what happens as we move towards a hub and spoke system (i.e., a mean-preserving spread in P). A mean preserving spread means the average number of connections between nodes stays the same, but there are more likely to be nodes with very few connection or very many connection. Thus, a hub and spoke system will have a higher neighborly infection rate, but this does not mean that the average infection rate will be higher.

The authors expound on theory (2) in more detail below:

The change in infection rate due to a change in the degree distribution comes from countervailing sources, as more extreme distributions have relatively more very high degree nodes and very low degree nodes. Very high degree nodes have high infection rates and serve as conduits for infection, thus putting upward pressure on average infection. Very low degree nodes have fewer neighbors to become infected by and thus have relatively low infection rates. Which of these two forces is the more important one depends on the ratio λ=ν/δ, i.e., the effective spreading rate. For low λ, the first effect is the more important one, as nodes recover relatively rapidly, and so there must be nodes with many neighbors in order keep the infection from dying out. In contrast, when λ is high, then nodes become infected more quickly than they recover. Here the more important effect is the second one, as most nodes tend to have high infection rates, and so how many neighbors a given node has is more important than how well those neighbors are connected.

Conclusion

For fast spreading disease where people recover slowly, a diffuse network increases the average infection rate. For slow spread diseases, or diseases where people recover relatively quickly, a hub-and-spoke system increases the average infection rate.

• Jackson, Matthew O. and Rogers, Brian W. (2007) “Relating Network Structure to Diffusion Properties through Stochastic Dominance,” The B.E. Journal of Theoretical Economics: Vol. 7 : Iss. 1 (Advances), Article 6.

Most people believe that vaccines are for kids. The CDC and public health departments have done a good job of keeping vaccination rates high for children. With the advent of new vaccines for adults, the key now is to increase vaccination rates for these older groups.

The Wall Street Journal (”Get your shots“) details a few of the vaccines that adults should receive.

Not included in the list is the HPV vaccine against cervical cancer.

Another point of interest is that it is increasingly difficult for physicians to supply vaccines to patients. With so many vaccines, the logistics of ordering all these perishable vaccines is very difficult. Further, as vaccines costs have increased, physicians will have to invest more and more capital into vaccine inventory.

For this reason, alternative providers such as pharmacies may a solution. With a vast experience in storage of drugs and supply chain management, pharmacies can easily absorbed the increased adult vaccine demand.

In the Wall Street Journal article, we have the following story:

The doctor didn’t have the shingles vaccine in stock, and recommended they try a walk-in clinic at a nearby drugstore, where the nurse practitioner provided a two-page handout on the vaccine and answered some of their questions. Though the price was about $219 each, all but $40 was covered by their drug benefit plan.

The next time you get a shot, it may be at your local CVS or Walgreens and not at the doctor’s office.

Have scientists found a vaccine for brain tumors? Scientists have found that the cytomegalovirus is present in the 90% of glioblastoma brain tumors.  The Economist reports on two doctors who are attempting to create a vaccine for the cytomegalovirus which (hopefully) can greatly reduce the incidence of brain tumors around the world.

Vaccines work well because of an adjuvant. The adjuvant boosts immunity but physicians did not know how it worked until now. The Economist reports (”A shot in the dark not more“) that Stephanie Eisenbarth, Richard Flavell an co-authors have discovered that the adjuvant “works by stimulating bits of the immune system called NOD-like receptors.”

Why is this discovery important?

“The value of that is shown by another piece of news. This week GlaxoSmithKline, a big British drug company, won the European Union’s approval for a ‘pre-pandemic’ vaccine that promises protection against multiple strains of bird flu. This vaccine depends, according to Emmanuel Hanon, who helped develop it, on an oil-in-water-emulsion adjuvant so good that only a twentieth of the normal amount of antigen is needed. So how does this amazing adjuvant work? Dr Hanon admits that his team does not actually know.“

ABC News reports that immunization rates are falling.  Who’s fault is this?

“Traditionally, the government has measured immunization noncompliance by tallying up only missed doses of a vaccine. In this new research, the CDC recalculated immunization compliance to include vaccine lapses in addition to missed doses. Based on these new criteria, the CDC found that immunization compliance was actually 9 percentage points lower than previous estimates, dropping the compliance rate from 81 percent to 72 percent.”

When we measure compliance as missed vaccines, given that the child goes to the doctor, then we would believe that most of the fault of decreasing immunization rates is the doctors fault.  On the other hand, if we measure immunization rates as whether the child is “up to date” with their vaccines, then it could also be the fault of the parents who may not be bringing their child in for necessary check-ups.

Further, with an increasing number of vaccines required, it may be difficult for physicians to give all these vaccines.  Kids will only tolerate so many shots at a doctors visit before they start crying uncontrollably.  Elizabeth Luman of the National Center for Immunization and Respiratory Diseases says “It’s a complicated schedule … and there are also a lot of vaccines and figuring out when to time them can be a bit complicated.”

Vaccine shortages may also be to blame.  Dr. David Freedman, professor of medicine and epidemiology at the University of Alabama at Birmingham, says that “In many cases when there is a shortage, physicians can’t get any, stop giving it and are not rapidly informed when it is available again. In some cases shortages or nonavailability can last a year or more.”

Some doctors propose that an immunization registry, one that would store all an individuals immunization records, could be a solution.  This way, doctors and patients would be able to know which vaccines they have received and which ones they need to get.

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.

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.

According to Reuters (”All U.S. kids…“), the CDC’s Advisory Committee on Immunization Practices (ACIP) is recommending that all kids should receive an influenza vaccination. Previously, the CDC recommended that all children 0-6 receive a flu shot. Now, all children 18 and under should get the shot.

In addition to the direct health benefits the children will receive from a decreased likelihood of getting the flu, the probability that they will spread it to adults, teachers, other children, and senior citizens will decrease.

However, there will be costs to the flu vaccine expansion. According to the U.S. Census, there were 61.3 million children aged 5-19 in the U.S. Getting all these children vaccinated will be very costly and since the vaccines will be given in the fall, the logistics of providing 61 million additional flu shots will be difficult to manage.

Further, one of my working papers (”Adam Smith meets Jonas Salk: Estimating the Social Cost of Third-Party Influenza Vaccination Restrictions“) finds that when kids 0-18 year old must receive a flu vaccine efficiency losses could increase to as much as $560 million if insurance companies continue to prohibiting reimbursement to pediatricians for vaccinating adults.

According to the USA Today, the influenza vaccine may receive a complete overhaul for the 2008-2009 flu season.

All three flu viruses in this year’s vaccine should be swapped for others next year because of a dramatic change in the mix of circulating flu bugs…

The decision launches a “time-critical, highly orchestrated” effort by public health agencies and vaccine makers to produce roughly 100 million doses of vaccine — a dated process that involves growing the virus in eggs, he said. “From egg to vial, it takes six to eight months,” Baylor said in a background briefing with reporters this week.

The egg-growing process is done only in the U.S. In Europe, vaccines can be produced faster since they are developed artificially in a lab.

This year’s vaccine protects against just one of three viruses that are dominating this year’s flu season, now reaching its peak. The Centers for Disease Control and Prevention said last Friday that 44 states are reporting widespread flu activity, with cases mounting in five others.

Scientists are unable to explain why all of a sudden, new flu strains have grown so much in prevalence.

Reuters reports (”Too few…“) on the problem that U.S. adults not receiving necessary vaccines.

“Only 2 percent of U.S. adults last year got a shot that can protect them from painful bouts of shingles, health officials said on Wednesday in a study that shows what they call unacceptably low rates of adult vaccination against a range of diseases.

Adults also failed to get vaccines that can protect them against tetanus, whooping cough and even influenza — despite years of campaigning, the U.S. Centers for Disease Control and Prevention [CDC] found.”

There are a variety of vaccines and different vaccines only apply to certain demographic groups based on their age, sex and risk factors. Some risk factors are obvious (e.g.: being HIV positive, having sex with prostitutes) but others are more mundate (e.g.: working in the healthcare or public safety sectors, being a first-year college student, traveling abroad).
Here at the Healthcare Economist, I don’t just point out potential problems, I offer solutions:

If you do not know which vaccines you need to get, go to the CDC Immunization website and TAKE THIS QUIZ. Childhood immunization schedules are also available.