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)

Semmelweis and hand hygiene

Dr Ignaz Semmelweis was a Hungarian born physician who worked in Vienna in the 1840s. He is popularly credited with the discovery of the importance of handwashing, though perhaps it's more accurate to say that he was among the first to appreciate the importance of hand hygiene, rather than handwashing.  Harbarth (2000) points out that

. . . many scientists have cited Semmelweis' observations, but, amazingly, grossly misleading impressions still arise about Semmelweis and his original idea of antiseptic hand disinfection, often wrongly cited as “handwashing” in the English-language literature. In fact, Semmelweis never promoted handwashing with soap and water; he was opposed to it, since he wrote: “The cadaveric particles clinging to the hands are not entirely removed by the ordinary method of washing the hands with soap.… For that reason, the hands of the examiner must be cleansed with chlorine, not only after handling cadavers, but likewise after examining patients”

Indeed, Semmelweis promoted a policy of using a solution of chlorinated lime (calcium hypochlorite) on the hands between autopsy work and the examination of patients, as opposed to soap.

So, let's celebrate Semmelweis' insights about the importance of the hands in infection prevention rather than associating his name with handwashing alone. He's recently come back on Twitter to help us -- and certainly we need that help. The WHO's World Hand Hygiene Day is May 5. Check out how you can help raise awareness about hand hygiene.

(image source: WHO)

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)