My recent blog post on eradicating polio through vaccination ends with this:

Part of the reason why vaccination is challenging is because social networks play a critical role in disease transmission. Even if enough people have been vaccinated in aggregate to obtain herd immunity in theory, it may not be enough if there are hot spots of unvaccinated children who can cause outbreaks. There are hot spots in some areas in California and other states that have generous exemption policies.

I want to elaborate. It’s possible that we have both:

1. record levels of immunization, and
2. record levels of vulnerability to highly infectious diseases.

The CDC estimates that 95% of kindergarteners have had MMR and DTaP immunization and 93% have had varicella (chicken pox) immunization. [Link] And yet there are outbreaks! The CDC’s immunization goal is 95%. Given that some kids truly should not be immunized (like those with specific allergies or those who have had serious reactions to other vaccines), there isn’t much room to allow for parents to choose to opt out while maintaining herd immunity. In fact, just a few people opting out has been linked to several disease outbreaks [Links here and here]. This is especially critical for newborns, who cannot be immunized for anything except Hepatitis B, and babies under a year old who cannot get the MMR vaccine for the measles. There is a measles outbreak among babies who cannot be vaccinated against the measles yet in a Chicagoland day care. In other words: please vaccinate your children if you can.

<side note>The rotavirus vaccine was off the market from 1999 to 2006, so my oldest daughter wasn’t vaccinated. She came down with a bad case of rotavirus at age 3.5 when my second daughter was 3 months old. Luckily, my second daughter had received her first rotavirus immunization 2 weeks prior and didn’t get sick.<\side note>

Despite having record levels of immunization, we’ve seen a lot of cases of pertussis, measles, and other infectious diseases. It’s all about social networks!

Let’s return to herd immunity. Estimates from Wikipedia indicate that most diseases require an immunization rate of 85%-94% (the herd immunity threshold) in a “well mixed” population to achieve herd immunity. In other words, this might be an optimistically low threshold when kind of ignoring social networks. An article in The Atlantic reports a 92% herd immunity threshold for most diseases and a 95% herd immunity threshold for highly infectious diseases like the measles (they cite a World Health Organization document). A population being well-mixed is a big assumption. Kids within the same school may travel in different social circles that are more homogenous than the school as a whole. That’s important. A social circle that has a low level of immunization may introduce risk to the kids in the community even if the school as a whole is above the herd immunity threshold. That’s what happened in the Chicagoland day care with the unvaccinated babies who hung out together every day. But more generally, people who don’t vaccinate generally have friends who also don’t vaccinate.

The Guardian has a nice simulation about herd immunity and social networks. They consider a few different communities with different vaccination rates (from 10% to 99.7%) with vaccinated, unvaccinated (susceptible) and vaccinated but susceptible individuals (the CDC estimates that MMR only “takes” in 93%-97% of those vaccinated). A few random individuals then come in contact with the measles. The red individuals represent infections. There are measles outbreaks even with a 90% vaccination rate.

The Guardian simulation results for exposing a community to measles. Sometimes a vulnerable community is OK (see the 83.8% vax rate here) but in general there is an outbreak.

We need vaccines because they protect against highly contagious diseases. Epidemiologists use the “basic reproduction number” (R0) to estimate how infectious a disease is, where R0 is the average number of people someone with the disease is expected to infect. The smaller R0 is, the less a disease tends to spread. Exponential growth happens when R0 > 1, but there is exponential growth (flu R0=2.5) and then there is exponential growth (measles R0 = 16!!). While R0 can be lowered by actions like good hygiene, some diseases are inherently more contagious than others. We can’t get the measles to spread as “slowly” as seasonal flu no matter how much we encourage people to wash their hands and use hand sanitizer. This is why we need vaccines as well as a higher herd immunity threshold for diseases like measles than we do for the flu. When that one person who hasn’t been vaccinated infects 12-18 other people, we have an epidemic on our hands. From the Wall Street Journal:

“Imagine if you had a reproduction number of 15 for measles with everybody susceptible,” said Derek A.T. Cummings, a professor of epidemiology at Johns Hopkins Bloomberg School of Public Health. “If you go in and vaccinate half the people, the expected reproduction number goes down to 7.5.”

The Guardian provides a nice figure of deadliness (the y-axis) vs. the basic reproduction numbers (the x-axis) of various diseases. That cluster of diseases on the right hand side is composed of highly infectious. Measles, rotavirus, whooping cough are highly infectious in ways that the seasonal flu just isn’t. In fact, the CDC recommends vaccines for that entire cluster of highly infectious diseases over there on the right except for malaria (which isn’t a huge problem in the US) because they are really that bad.

Deadliness vs. Basic Reproduction Number.

I get the impression we keep having these debates without agreeing on what the problem is and what its consequences are. It’s reasonable to say that most people in my generation have no idea what a massive infectious disease outbreak looks like. It’s not like the seasonal flu, where you know just a few people who succomb to the flu every year but you’re usually OK. With these highly contagious diseases, outbreaks may be rare but then BOOM, everyone you know is sick. Chicken pox (R0 = 8.5) may be an exception. The chicken pox epidemic in my kindergarten class was the only time I experienced a massive infectious disease outbreak (class attendance dwindled to 3-5 students for a few days).

<side note>I may have had the mildest case of the chicken pox ever recorded. I had just a few poxes/blisters and itched for maybe an hour. But I bear a scar on my face from one of the few poxes I had(!) </side note>

I’ll stop here for now. Let me know your thoughts on vaccination, social networks, herd immunity, and disease outbreaks.

Related posts:

• on vampires and stochastic processes
• how  to optimally prepare for a zombie outbreak
• exam question: find the size of the zombie population after an outbreak

I recently read an article on Forbes about a forthcoming JAMA article about screening test uncertainty and invasive medical procedures [Link]. In the study [Study Link], the researchers gave 727 men hypothetical PSA scores for screening for prostate cancer. The control group was not given a PSA result. Those who not in the control group were given one of three outcomes, leading to four groups.

1. Normal PSA test
2. No PSA test (control group) – no uncertainty
3. Inconclusive PSA test – high uncertainty
4. Elevated PSA test

Men in each group were asked if they would pursue a biopsy, an invasive and expensive medical procedure compared to the PSA test. Groups 2 and 3 are similar in that they don’t have conclusive of cancer. However, group 3 has more uncertainty.

Probability of patients who opted for a biopsy:

1. Normal PSA test – 13%
2. No PSA test (control group) – 25%
3. Inconclusive PSA test – 40%
4. Elevated PSA test – 62%

The issue here is that an inconclusive test gives the same information as doing no test at all, yet those with an inconclusive test want to get a biopsy at a higher rate. In the study, the biopsies are requested by the patients, but in real life, doctors often turn inconclusive tests into expensive and invasive medical procedures.

I had a few other reactions to the issues associated with screening for disease.

With limited resources, inexpensive screening in theory helps to keep health care costs down. A cheap test is supposed to be used to weed out some of the population that does not need more invasive screening test. If disease cannot be ruled out, it may make some sense to retest. Of course, the issue here is that biopsies are chosen at different rates for different inconclusive patients. The results of this study suggests that screening for disease starts a process that is hard to turn off – screening could result in more men being biopsied instead of fewer. This isn’t just an issue with PSA tests.

I also found it interesting that 13% of the population apparently refused to be weeded out.

Humans do not do a good job of figuring out how to effectively use resources to screen for and manage disease. And as we see in this study, humans do not always make better decisions with better information. This is why we need good models of disease and its treatment. With those models in place, we can explore how to effectively target limited healthcare resources at the patients who most need them.

This is a growing area for operations research – identifying how to make good decisions at the patient level for understanding when to do more testing and when to take a wait-and-see approach. For slow-growing cancers such as prostate cancer, a wait-and-see approach may be a good one most of the time (disclaimer: for what it’s worth, I’m not a medical doctor). Waiting and retesting was not an option considered in the study, and maybe the results would be different. A wait-and-see approach is often used for other types of cancers, such as for pre-cancerous legions that could lead to cervical cancer.

For more reading about screening policies, inaccurate screening tests, and unnecessary treatment, read this NY Times article about breast cancer: [Link] Breast cancer can be quite aggressive, especially when it affects younger people, and it is common. I’ll admit that delaying or avoiding mammography is hard to fathom. The article highlights how aggressive mammography policies have led to the discovery of more cancerous and pre-cancerous legions (and thus cancer survivors) but it has not led to higher cancer survival rates. Other issues such as self-exams are also discussed.

I’m looking forward to learning about the latest research in this area at the INFORMS Healthcare Conference in Chicago this summer [Link]. I hope to see many of you there.

In October, This American Life produced two interesting episodes about health interventions and evidence-based medicine that I am just listening to now. These This American Life shows seem fresh and interesting, largely because they try to discuss health insurance/care issues from a quantitative, evidence-based perspective, even though cite few numbers in the episodes.  To illustrate this point, part of the first episode is even titled “Every CAT scan has nine lives,” referring to the side effects of over-using advanced medical techniques such as CAT scans.

The More is Less episode is particularly interesting for OR folks.  It starts with a twenty-minute discussion of some of the cost and effectiveness problems with health care.  The episode steps through one of the problems that grappled the medical community from the 1970s: geographic disparities in hysterectomies and other medical procedures in Maine and Vermont.  This baffled the doctors, since the disparities in hysterectomies across the state could not be explained by demographics, age, religion, or other factors, as was initially suspected.  One of the doctors who performed some of the analysis (Wennberg) concluded that 70% of women would receive hysterectomies in some communities. Maine doctors concluded that disparities were in part based on the doctors choosing to over-perform certain surgeries rather than the patients asking for procedures.

The episode continues to discuss why performing more medical procedures leads to more side effects and potential destruction in some cases, including the PSA tests for prostate cancer, thus exploring the tradeoff between cost and effectiveness.  These issues have been in the news quite a bit lately, particularly with the chance in mammogram screening recommendations.  These discussions in the news have included too much pandering and too little math and analysis, for the most part.   I’ve struggled to find good resources for a lay audience that address the numbers, so this episode was much appreciated.  I’ll leave the rest of the episode a mystery, so you can listen to it yourself.  The second episode (Someone Else’s Money) is not nearly as good, but examines health insurance in more detail.

Podcast Links:  More is Less and Someone Else’s Money.

Link: The Numbers Guy (WSJ) on Mammogram Math is also an interesting read.

Have you found any good references on lay explanations of the numbers behind health care and health insurance?

After attending the second day of the Virginia Health Equity Conference, I have been convinced that public health is a function of much, much more than just medical treatment.  Paula Braveman provided some figures in her keynote that indicate that the mortality and incidence rates of many infectious diseases drastically reduced before effective medical interventions were introduced.  I had heard this before, but a picture is worth a 1000 words.  I tracked down a few of the images online (see below).   Public health initiatives such as housing, ventilation, improved sewage systems, and education improved health outcomes much more than medical interventions that were later introduced.  This reflects the fact that there are many good proxies for public health that reflect infrastructure, networks, and transportation, all of which are things that we like to evaluate in operations research models.

It strikes me that any operations research models that reflect public health would fit in well with community-based OR initiative.  Those who do research in this area might be interested in a new Springer volume.  The call for papers is pasted below (I could not find a link).  Note that I am not affiliated with this effort.

“Community-based operations research” (CBOR) is defined as the collection of analytical methods applied to problem domains in which interests of underrepresented, underserved, or vulnerable populations in localized jurisdictions, formal or informal, receive special emphasis, and for which solutions to problems of core concern for daily living must be identified and implemented so as to jointly optimize economic efficiency, social equity, and administrative burdens. This domain was first discussed in a chapter in Tutorials in Operations Research 2007 – OR Tools and Applications: Glimpses of Future Technologies (INFORMS 2007) by Johnson and Smilowitz and subsequently in an article that appeared in the February 2008 issue of OR/MS Today.

As community-oriented operations research, as defined here, is central to the mission of the Section on OR/MS Applied to Public Programs, Service and Needs, submissions from SPPSN members will be especially welcome.

Chapters in this volume can describe current results for a specific research problem, a literature review, or a discussion of the nature of CBOR within the operations research/management science discipline.

Proposals for submissions to this volume should be not more than one page in length, describe the nature of the submission, and clarify if the submission is likely to be based on current or on-going research, a new research project, or synthesize previous findings. Submissions will be peer-reviewed. The deadline for submission proposals is October 16, 2009. The deadline for chapter submissions is February 1, 2010; final drafts of chapter submissions will be sent to the publisher on August 1, 2010.

Manuscript proposals, as well as inquiries regarding further details, should be sent to:  Michael P. Johnson, Ph.D, Department of Public Policy and Public Affairs, University of Massachusetts Boston, Boston, MA 02125-3393

Link to yesterday’s post about the conference.

Mortality rates from infectious disease in the USMortality rate of whooping cough

Mortality rate of measles

Mortality caused by scarlet fever in England and Wales (re-drawn from T Mc Keown, 1976)

I am enjoying the Virginia Health Equity Conference.  It’s hard not to believe that operations research can be used to improve public health.

I particularly enjoyed Dr. Howard Frumkin’s keynote about public health and the built environment. His talk was particularly inspiring for operations researcher. We spend almost all of our time in built environments (home, school, work, transportation, parks), and there is an enormous body of research that suggests that our environment is a strong predictor of our health. Our built environment is the result of a series of decisions, some of which can be the result of good operations research and mathematical modeling. A good built environment offers a wide portfolio of public health benefits. Dr. Frumkin listed several opportunities for operations research modeling to improve our built environment (and in turn, public health), including:
• Investigating where to locate schools (perhaps using decision analysis),
• Improving school bus routes that are also safe (Safe Routes), including walking school bus routes (using network design),
• Improving and analyzing transportation networks in urban sprawl regions, which are plagued with low connectivity and low population density (this leads to a host of problems such as reliance on vehicles, low rates of physical exercise, poor access to emergency medical vehicles, etc.).
• Locating trees and green space in urban areas to “cover” poor neighborhoods.

Dr. Frumkin stressed that many of these decisions are generally not made by public health people (perhaps some can be made by operations researchers).

I apologize for being offline for the past month. Between illnesses, weddings, and the start of the school year, I cut back on blogging and twitter. I finally feel like I’m back into the swing of things.

I am looking forward to the Virginia Health Equity Conference later this week. Although the conference will mainly be attended by medicine and public health people, I hope to blog about health care during the conference. So keep an eye on the blog.  You can follow the conference twitter feed here.

I have been closely following the national debate surrounding health care and health insurance. Although it seems like the issue is mainly a macro-economics issue, I really do think that OR has a lot to offer, particularly in predicting the costs and benefits of treatment and care. But I see so much misinformation (sometimes well-meaning people with the wrong information, and sometimes more sinister ulterior motives) that I easily get discouraged about having a rational, quantitative discussion using OR methodologies.

Last week, I tried discussing some of the health care issues in my class (probability and statistics for engineers). After introducing Bayes rule, I illustrated why it implies that preventive medicine costs so much, in general. I think the discussion backfired. David Brooks explains it better [podcast link here]–when I try, I come off sounding like a an insensitive monster that wants to deny people health care. Really, I just want good numbers to support the debate so we can make good decisions. I’m not sure what the answer is, because I have no idea what the facts are yet. I hope OR is instrumental in providing the facts.

Underage college students drink. A lot. OR may be able to help.

Ben Fitzpatrick at Loyola Marymount University gave a talk here on Friday about modeling college student drinking habits using mathematical tools. It was entitled “Ecological Systems Modeling of College Drinking,” and it was one of the most engaging talks I have seen in awhile.

Forty-two percent of college students confess to binge drinking, which correlates highly with several forms of violence. Individual interventions are not very successful at curbing drinking problems, but community policies on the aggregate level show promise. Can mathematical modeling be used to predict whether changing the drinking age is a good idea? The premise is that college campuses are relatively homogenous (compared to metropolitan areas), so the resulting model may be useful for policy-making.

Fitzpatrick applied statistical models, dynamical systems, and differential equations that compartmentalized the college population into several groups. His approach uses the fact that people overestimate how frequently their peers engage in risky behaviors (e.g., smoking, drinking). The higher this misperception, the more likely students are to engage in binge drinking. The Social Norms Marketing Research Project provided him with four years of data from 32 schools to estimate misperception. Linear regression was used to estimate some of the parameters needed for Fitzpatrick’s model, and it worked fairly well (R^2 > 0.99 for several parameters).

One model incorporated social interactions (e.g., peer pressure) and social norms/perceptions using a network model (similar to the SIR model used by epidemiologists) to estimate how social interactions could increase or decrease drinking problems. His simulations showed that as drinking misperceptions grow, more students engage in binge drinking (called heavy episodic drinking). I found this particularly interesting, since VCU is always distributing anti-drinking propaganda in the bathrooms (called the Stall Seat Journal, I kid you not), which in essence attempts to reduce misperceptions. Apparently, this is a good strategy for battling underage drinking.

When the drinking age goes down, the “wetness” level in campus goes up, since there are more legal ways to get alcohol. But the Amethyst hypothesis is that misperception goes down when the drinking level goes down (and wetness goes up), since it is easier to directly observe peer drinking activities. Fitzpatrick’s model suggests that results are more sensitive to alcohol availability than to misperception.

This seems to be an important first step in the debate about the drinking age. Before I commit to a policy position, I’d like to see more of these mathematical models to predict what would happen if the drinking age changed. Interestingly, research shows that binge drinking almost completely disappears after college. Maybe we should be trying to get students to finish their degrees in 4 years or less, rather than allowing them to take five or six years to finish?

John McCardle (of the Amethyst initiative and President Emeritus of Middlebury U) appeared on the Colbert Report (3/19/09) to talk about why the current drinking age of 21 is not working. Link.