HAI and aliens: The Drake equation in epidemiology

In a 1961, Frank Drake introduced the following equation for the number N of civilizations in our galaxy with which radio-communication might be possible,

N = R x F_p x N_e x F_l x F_i x F_c x L

As described by the SETI institute,

• R is the average rate of star formation in the galaxy, 
• F_p is the fraction of those stars that have planets, 
• N_e is the average number of planets that can potentially support life per star that has planets, 
• F_l is the fraction of planets that could support life that actually develop life at some point, 
• F_i is the fraction of planets with life that actually go on to develop intelligent life (civilizations), 
• F_c is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space, and 
• L is the length of time for which such civilizations release detectable signals into space. 

Drake's purpose in writing this equation was to facilitate discussion at a meeting. Its importance is not the numerical prediction of communicative civilizations in the galaxy (note there are 7 factors in the equation and errors in each term will combine to make any calculation wildly uncertain) but rather in the framing of issues related to the search for alien life. That said, the equation tells a story. Assuming that these are the relevant factors, then if any the terms are zero, N is zero and we are likely to be alone. If none of them are zero, then even if they are exceedingly small, there is a chance that there is life somewhere in the galaxy. Moreover, it's unlikely that any of these terms are zero, given the huge size of the galaxy. In epidemiological terms, then, the equation helps to frame our thinking about the potential prevalence of life in the Milky Way galaxy.

Given that NASA opined recently that we're likely to have strong indications of life beyond Earth within a decade, it made me wonder about Drake-like equations in medicine and epidemiology. As a toy example, suppose that we write the number of patients contracting hospital-acquired infections (HAIs) yearly in the US as the product of several factors, say

N = N_{hospital visits} x P_contact x P_{develop disease} x P_{disease reported}

where

• N_{hospital visits} is the number of patients visiting hospitals annually,
• P_contact is the probability that a patient comes into contact with infectious material (e.g., via environmental contamination or an infectious patient or HCW)
• P_{develop disease} is the probability of developing disease if infected, and 
• P_{disease reported} is the probability that an infection is recognized and reported.

According to the CDC, there are 35.1M hospital discharges annually in the US, so N_{hosp visits}~35M. Now suppose that P_contact and P_{develop disease} are both low, say 1% , and that we have excellent surveillance so that P_{disease reported} ~1. If that could be true, then we would expect to see 3,500 HAI per year. We should be so lucky. Being more realistic, however, might yield a 10% change of coming into contact to infection, P_contact~0.1, and a higher probability of contracting disease if infected, say 50%, so that P_{develop disease} ~ 0.5. In that case we get N=1.75M HAI annually, which is close to the CDC estimate of 1.7M.

How could this be decreased? The number of hospital visits, N, is unlikely to decrease drastically, so that's not really a control variable. Perhaps we could develop interventions to decrease P_contact and P_{develop disease}. Obviously there is tremendous focus on reducing P_contact through handwashing, alcohol based had rubs, contact precautions, better environmental cleaning, etc already. If P_contact could be reduced by a factor of 10, from 0.1 to 0.01 -- seemingly a tall order -- N could be dropped to 175K. That may not be possible, but suppose we could achieve a factor of 2 improvement so that P_contact ~ 0.05. If we could combine that with a similar decrease in P_{develop disease} by, say, better use of antimicrobials, then N could in turn fall from 1.7M to 438K. Thus, combination strategies could have great impact.

This is simply a back of the envelop calculation: the equation above is but an approximation and the estimates are completely arbitrary. Moreover, parameters will vary from facility to facility and even between patient populations (imagine how P_{develop disease} is likely to vary between transplant versus general surgery patients). That said, this toy model illustrates a simple point: Breaking a problem down into smaller pieces can be helpful in thinking about it.

While this way of thinking is not alien (pun intended) to biostatistics and epidemiology, and clearly has limitations, I think it's helpful for framing issues in one's mind. In addition to clearly laying out assumptions in whatever is being contemplated (in this case, HAI), toy model approaches can suggest what may be needed in order to get a better answer.

(image source: Wikipedia)

Nowhere is it written that dangerous pathogens must have high basic reproduction ratios

As discussed previously, there are lessons aplenty to learn from the ongoing Ebola outbreak in West Africa. One simple lesson is this: Even with a low basic reproduction ratio (symbolized mathematically as R₀), a pathogen can still spread widely under the right conditions.

Current estimates of the basic reproduction number for this Ebola outbreak are roughly in the range of 1.3-2.5. That's pretty modest when compared with other notorious agents. Estimates of R₀ for smallpox outbreaks, for example, were typically 4-10 and those for cholera epidemics can be in the range of 3-12. Measles outbreaks can have R₀ values of up to 18.

R₀ itself is sometimes thought of as a surrogate for "epidemic potential". Certainly, and by definition, pathogens with high R₀ spread quickly, whereas pathogens with lower R₀ don't. Does this mean that pathogens possessing relatively low values of R₀ have lower potential to harm public health?

Certainly not. In fact, pandemic influenza viruses, for example, often fall in the range 1.5-2.0. Pathogens associated with lower values of R₀ can spread widely if control efforts are not effective. In the case of pandemic influenza, control measures include vaccination and handwashing. In the current Ebola situation, due to a range of social, economic, and political factors, it has been difficult to implement widespread, effective control measures. The infection has thus spread and will likely continue do so in the region.

Does this have implications for other infections? It absolutely does. One could imagine some theoretical pathogen, for example, that is spread predominantly by hands (call it "pathogen X") and that is not killed by alcohol based hand rub (ABHR). Then, in circumstances where ABHRs are used in place of handwashing, one might imagine that pathogen X could, over time, become widely prevalent, even if it does not possess a high R₀. Pathogen X might be similar to Clostridium difficile; one estimate of R₀ for C. difficile is in the range 0.5-1.5.

For this reason, we should not think only in terms of R₀ for classifying pathogens as dangerous or not. While high R₀ pathogens spread quickly, leaving little time to react and take action, Ebola in West Africa this year demonstrates that a pathogen possessing a more modest R₀ can result in a dangerous public health situation. 

There's a story, which is possibly apocryphal, that Enrico Fermi once remarked that nowhere is it written that the laws of physics must be linear. I think there's an analogue that should be kept in mind in infectious disease epidemiology: Nowhere is it written that dangerous pathogens must have high R₀.

(image source: ECDC) 

What are we doing to ourselves?

An interesting idea emerged from conversation over dinner with a colleague recently: While it is clear that hand hygiene is foundational for both hospital and community infection prevention, there may be an immunological price to the now all-pervasive focus on hand hygiene in the general population.

Let me explain. Hygiene is one of the pillars of public health and infection prevention, though we still struggle to practice what we know globally. Semmelweis showed us the need for clean hands in the clinical environment, and the notion of ridding hands of germs has evolved since then. Today, alcohol based hand rubs (ABHRs) are prominent in daily life. People rub their hands with "hand sanitizer" before eating out, after riding the bus, after using the restroom, and even at their desks throughout the day. What could possibly go wrong with such an awareness of hand hygiene?

Potentially, nothing. The importance of hand hygiene is undisputed and indisputable in infection prevention. That said, I often see people using ABHR very frequently throughout the day and it makes me wonder if such use of ABHR is eroding not only the transient flora of our hands, but also the resident flora. What is on our hands ultimately ends up challenging the immune system, via oral ingestion, absorption through rubbing the eyes, or inoculation via scrapes and cuts on the hands and fingers. Constantly challenging the immune system with a diversity of biologic agents gives rise to broad immunity.

Might we be eroding the frequency and diversity of that challenge, and thus the strength and diversity of the immunological protection, with such pervasive use of ABHR? This general notion, that cleanliness might have deleterious, unintended community-level consequences, is not new. It's been discussed within the context of polio, for example, and there is speculation about inverse relationships between cleanliness and asthma.

I'll close by noting that ABHR is but one of the several tools society currently employs to kill the spectrum of microbes in our immediate environment. There are also antimicrobial wipes and antimicrobial soaps. The weapons of mass microbial destruction are many and proliferating. They obviously have their place in the clinic but, regarding their sometimes near-obsessive use in the community, are they helping or hurting us in the long run?

(image source: David Hartley)

Hand washing, rubbing, and posters

Every now and then one sees something that is obviously well intentioned and potentially even effective, but that is problematic nonetheless. A case in point is the poster shown at the right, proclaiming that "Alcohol-based handrubs kill bacteria more effectively than soap and water." Certainly they do, but that's not the point of handwashing with plain soap and water.

The purpose of handwashing with plain soap is to mechanically remove foreign material and microorganisms from the surface of the skin. It is not to kill microbes. Plain soaps have minimal, if any, antimicrobial activity. The purpose of alcohol-based handrubs (ABHRs) is to reduce the microbial burden on the skin to a safe level through the antimicrobial action of alcohol. Because handrubs do not remove organic material, they are not a substitute for washing visibly soiled hands. Moreover, ABHRs don't kill spore forming microorganisms such as Clostridium difficile or certain other pathogens of public health importance. Handwashing with soap and water is needed to remove such contamination. Antimicrobial soap combines the cleaning action of regular soap with antiseptic activity. 

These and related issues, such as when the different approaches are best used, are well covered by Manfred Rotter in chapter 91 of the 4th edition (2012) of the expansive text Hospital Epidemiology and Infection Control. Additional information can be found in the WHO guidelines on hand hygiene in healthcare and at a related CDC website. 

In the case of the poster above, it is available at a URL that is part of an interactive education module on hand hygiene for professional HCWs. The training itself, consistent with the poster, advises (on slide #19) that plain soaps are "good" at killing bacteria whereas ABHRs are "best" and antimicrobial soaps fall in between. I can't find evidence that plain soap kills bacteria or any other pathogen. Rather, plain soap removes pathogens by acting as a surfactant or detergent, and this seems to be well established in the literature. Perhaps "Remember to wash your hands -- Soap removes germs!" or "Alcohol-based hand rubs are often an effective alternative to soap for making your hands safe!" would have been more evidence-based, defensible, and constructive messages for a poster.

More importantly, if the overarching objective of hand hygiene -- preventing transmission of microorganisms via the hands -- is to be achieved, an awareness of the issues involved in the various approaches is needed. Knowing when to wash versus rub, and why, seems relevant to communicate widely.

(image source: CDC)