Showing posts with label maths. Show all posts
Showing posts with label maths. Show all posts

Tuesday, August 28, 2018

Trying to link ward-level hand hygiene compliance and healthcare-associated infections


I've spent 15 years studying hand hygiene, so I obviously think it is critical to safe healthcare delivery. As I mentioned in my prior post on hand hygiene and HAI, sometimes these posts are difficult to write. The difficulty stems from the inertia required to confront dogma, while simultaneously bracing for the inevitable criticism. And of course, I could be completely wrong. Often times, dogma is correct.

But as I've gazed out of my office in the old Singapore CDC (soon to be replaced by a shiny new NCID), I've had moments to consider various causal diagrams linking hand hygiene to various outcomes, like CLABSI. (see below or source) If you carefully examine (click to expand) this or other causal models you see that hand hygiene is there, but it is only one of many possible causes of CLABSI. So, strictly speaking hand hygiene is in the causal pathway to CLABSI development. That's the dogma and it's true, to a point.


But let's move on to my contention: ward-level or ICU-level hand hygiene compliance changes can't be linked to reductions in HAI. For example, no amount of raising hand hygiene from 0% to 100% can be associated with reductions in HAI, such as CLABSI. It's just not mathematically possible. Sure, some study might show such an association, but I wouldn't believe it.

So to borrow a strategy used often by fellow blogger Mike, I'll use math(s).

Most facilities monitor hand hygiene compliance with direct observation. On the ward level, we reported that less than 30 opportunities/ward/month are collected. That was in 2012, so let's say things are much better and we observe 100 opportunities. This actually doesn't matter - you could observe 10,000 per month with an automated system, but let's stick with 100 opportunities.

Now, let's estimate how many opportunities are related to HH moment #2 (before aseptic procedure). Most estimates that I've seen are close to 10%. And how many of HH moment #2 involve directly manipulating a central venous catheter - let's go with 2%. You can estimate a lower or higher rate depending on ward acuity, but I'm going to stick with 2% since the vast majority involve peripheral lines. So, 2% of 10% is 0.2% or 0.002.

So, how many months of 100 observations/month are required before we witness one opportunity where the HCW touches a CVC? Answer: 5 months.

Now over those 5 months, let's assume we have observed a hand hygiene compliance of 50%, so 250/500. Let's also assume the worst and say that HCW were 0% complaint with CVC-related moment #2 in those 5 months. Now, let's assume they were 100% compliant over the next 5 months after we targeted a hand hygiene education program to moment #2. Our compliance would increase to 251/500 or 50.2%. Any other increases in hand hygiene would not be in the causal pathway for CLABSI, so even if compliance shot up to 80%, we would only care about the 0.2% increase.  In fact, this highlights why it's difficult to link ward-level hand hygiene compliance to reduced CLABSI, since most of the increase does not involve CVC-related moment #2. It's almost all noise.

And if you still want to install the automated monitoring system, you can multiply the numerator and denominator by 100, and still have 25000/50000 (50%) with an increase to 25100/50000 (50.2%). And if your hand hygiene education was super successful and compliance increased to 80% (40000/50000), it would still be true that only 100 of the 15000 additional compliant opportunities would be CVC related. 100/15000 is 0.67%. Thus, CVC related hand hygiene opportunities are a needle in a haystack.

I encourage you to check my math, choose different rates or numbers and correct me in the comments below or on Twitter. Sadly, it's hard to link ward (or ICU) level hand hygiene compliance to ward-level CLABSI rates. But as I've said before, keep washing your hands and monitoring hand hygiene compliance in your hospital. No one wants a CRE outbreak.


Sunday, December 20, 2015

Influenza Vaccine Mandate Math


Last week, I described five steps individual hospitals, systems and society should take when implementing compulsory influenza vaccination of healthcare workers. One component of many influenza vaccine policies is mandatory surgical masks for healthcare workers who refuse or otherwise cannot receive the vaccine. Does masking unvaccinated healthcare workers even make sense? Or rather, who is more likely to spread influenza in hospitals - an unmasked, vaccinated healthcare worker or an unvaccinated, masked healthcare worker? Let's look at the numbers.

Let's assume influenza vaccine is 50% effective. In 2014-15, overall effectiveness was 19% while in 2012-13 and 2013-14 it was 49% and 51%, respectively. I'll give the vaccine a mulligan last year since during the prior decade, vaccines were far more effective. Let's further assume with vaccine mandates, 90% of healthcare workers receive the vaccine and 10% do not.

If 90% receive a vaccine that is 50% effective, we will have 45% of healthcare workers in our hospital protected and 45% unprotected. The tricky thing is that we won't know who is protected or unprotected. And what if the 45% vaccinated but non-immune healthcare workers assume they are immune and work while sick? You can imagine them saying - "I'm sick, but it's not influenza because I was vaccinated, so I'll do my ICU shift." Any mandatory vaccination policy should consider that scenario or it's possible that the mandate could make hospitals less safe. But what of the 10% required to wear masks? I suspect they'd be more likely to stay home if sick, but even if they don't they'll be wearing a mask!

Finally, if I had a choice between being cared for by a vaccinated, unmasked healthcare worker or a masked, unvaccinated healthcare worker, I'd chose the mask. That is, until we implement influenza prevention bundles that focus on presenteeism.

Note: Mike wrote a fantastic quantitative post (in 2010!!) comparing a vaccine mandate to a presenteeism reduction policy. His conclusion: "Reducing presenteeism by 1 percentage point (from 70% to 69%) would have the same impact as increasing vaccination from 70% to 98%." It's too bad not many read the blog back in 2010...

OSHA! OSHA! OSHA!

  In many parts of the country, as rates of COVID-19 are declining and vaccination coverage is increasing (albeit with substantial variati...