As described by the SETI institute,N = R x F_{p}x N_{e}x F_{l}x F_{i}x F_{c}x L

- 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.

N = Nwhere_{hospital visits}x P_{contact}x P_{develop disease}x P_{disease reported}

- 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.

_{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.

_{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.

_{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.

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