Saturday, July 18, 2009

Flu Math


# 3509


In my last post, one of my readers left the following comment.  Since responding to it would take a good deal of time, and that response would be buried in the comments, I’ve decided to move it to a blog post of its own.


Anonymous said...

Since at present the CFR of H1N1 is low, then barring underlying conditions, a rational parent will say no to this vaccine on the basis that enough others will get it to substantially prevent the spread of the virus. Only when too great a % of parents withhold their kids does the math start to get more complex! Until then why risk an experimental vaccine?



Anonymous raises some interesting questions, and they deserve to be addressed.  


I would point out to start, if all parents are `rational’ as anonymous has defined it, you won’t get enough kids vaccinated to reduce the risk of community spread.  


Since I’m an old poker player from way back, I have a tendency to look mainly at the odds of something good . . . or bad . . . happening based on the choices I make.  


Unlike cards, we can’t always know the exact odds in life, but we can usually approximate them.


I’m going to pluck some numbers out of thin air here, because we have to have some numbers to work with.  I will try, however, to go with the most `reasonable’ numbers I can, despite my admitted bias towards vaccines.


If you feel, in any way, that I’ve unfairly `stacked the deck’ with my assumptions, feel free to plug in your own.

The UK government has estimated that the CFR (Case Fatality Ratio) of this virus is likely to be anywhere from .1% to .35%.   The .1% is roughly the same as seasonal flu . . .or about 1 fatality in 1,000 cases.


To be fair, we’ll go with the lower number.  

And we’re also told that 30% to 50% of the population could be infected this winter – with kids probably seeing the highest infection rate.

Once again, we’ll take the lowest estimate.


If 30% of school age kids get infected, and .1% (or 1 in 1,000) are likely to die, then the odds of dying this winter (if you are a child) are roughly 1 out of 3,300.


It’s a rough approximation, and a `healthy child’ with no comorbid conditions may be as considerably less risk.  Not every parent is blessed with a healthy child, or course,


Frankly, based on what we’ve seen up until today, I still have hopes that the death toll among children will be lower than this.  And so to bend over backwards to make this a fair comparison, I’m going to arbitrarily reduce the CFR by nearly 70%.


Which means that for this little exercise, we’ll call the odds of someone under the age of 18 dying from this flu at roughly just  1 in 10,000


Fair enough?


At this point, it would seem that unless a vaccine were likely to induce death or serious injury in more than 1 in 10,000 cases, you can make a pretty good case for getting the jab . . . .


But of course, vaccines aren’t 100% effective in preventing disease.  A `good’ flu vaccine works about 70% to 90% of the time, but sometimes, the effectiveness is only 50%.


Which means, strictly from an odds standpoint, if I believed that a vaccine was at least 50% effective and unlikely to cause death in more than 1 child out of 20,000 . . .  I (personally) would opt to go with the vaccine.


So . . . how dangerous is this vaccine?   


Right now, we don’t know. But historically, flu vaccines have a pretty good safety record.


The much-maligned swine flu shots of 1976 produced roughly 500 serious adverse reactions, and was blamed for 25 deaths.


A dismal toll, but not quite as bad as it sounds when you consider that 40 million people received the shot. Had the pandemic arrived as predicted, those deaths would have been considered `acceptable losses’.

The odds of having a serious reaction were about 1 in 80,000.


And the odds of dying from the vaccine were only about 1 in 1.6 million. 


In other words, based on the 1976 experience, if you vaccinated all 80 million kids in the US with a vaccine with exactly the same level of adverse reactions as the 1976 vaccine you’d see about 1,000 serious side effects and 50 deaths.


Left unchecked, and using the numbers from above, deaths from the virus among those 80 million American kids would be roughly 8,000  (80 Million/10,000). 

And that’s probably a low-ball figure.


If a vaccine were only 50% effective, and was delivered early enough, you might reduce that number in half. 


To only 4,000 pediatric deaths.

So you’d save roughly 4,000 lives while risking (from the vaccine) 50 lives.  That makes the risks from the flu 80 times greater than from the shot.


Yes, it’s a numbers game, and those odds are no doubt cold-comfort to anyone whose kid  is unlucky enough to see an adverse effect from the vaccine.


But sometimes, the best you can do is go with the odds and pray you don’t get a bad beat. 


(I once bet the farm on 4 aces and lost to a straight flush.  Believe me, I never saw that coming.)


It would seem to me that a vaccine would have to be a whole lot more dangerous than we saw in 1976, or this flu virus a whole lot less dangerous than we currently believe, for it to make sense to avoid the vaccine.


Now . . . are either possible?   Sure. 


And I don’t know what the incidence of side effects from this vaccine will be, nor do I know the eventual CFR of this virus. Either or both could be higher or lower.


The numbers I’ve used are illustrative and (I hope) reasonable, but certainly not writ in stone.  


I would invite Everyone to plug their own numbers into all of this, based on their perceptions of the threat posed by the virus and the dangers of the vaccine


It’s easy enough to do.


And then, rationally, base their decisions on that.


Zachary said...

Also, contrary to the commenter's suggestion, we won't have enough vaccine to reach anything close to herd immunity for a long time. If everything goes right, administering the vaccine to school kids might reduce spread, but there will still be a lot of infections and deaths.

Warwick D said...

"a `healthy child’ with no comorbid conditions may be as considerably less risk ... I’m going to arbitrarily reduce the CFR by nearly 70%. "

What risk do you suppose the virus poses to someone with HIV then? Suppose that 1 in 200 has HIV.
The CFR for HIV sufferers would have to be only 1 in 5 to explain an overall 1 in 1000 just on its own. Then there are all the other high risk groups to consider. Your 70% reduction then looks pretty arbitrary indeed - and not big enough.

It's not surprising that the observed CFR for swine flu is much lower than the 0.1% for flu, as you note elsewhere: most of the flu deaths are geriatric, the same people not dying of swine flu. Similar concepts.
(I also notice that deaths from flu in the UK are orders of magnitude lower (per cap) than in the USA. Why? Probably because we don't have as many people living in trailers with no heating/healthcare. You can call it a death from flu, I'd call it a death from poverty...)

The current policy in the UK is that even though we have enough vaccine, they are waiting to see what happens to the high risk groups being vaccinated first, and waiting to see how the virus develops too, before it is released to the general population.

I personally think that is pretty sensible.

The GBS risks from the vaccine may be small, but then again the risks from the virus - to a healthy person - are presently not as great as you're suggesting here.

FLA_MEDIC said...

Warwick D,

Your point is well taken about the ultimate CFR for healthy children.
I don't think we know the answer to that yet.

But I'll grant that it may be lower than most scientists feared when I wrote this piece several months ago.

The numbers I used (1 in 1,000 CFR) was the LOWER range of the UK Govt's estimates at the time.

Not mine.

I then reduced that by 2/3rds ( quite arbitrarily) to 1 death in 3,000 infections.

3 months later, is that low enough? Perhaps not.

But we now have 3 months more experience with this virus since then.

That's why I invited people to plug in their own numbers. To use whatever is reasonable for them.

If you feel that 1 death in 10,000 or 1 in 20,000 or even 1 in 30,000 is more realistic, then that is the number you should use.

The CFR, as you've noted, varies from one region to the next.

But even at those rates the risk of death (1 in 1.6 million) from the 1976 vaccine was considerably lower.

Of course, this just compares deaths. It gets more complicated comparing non-fatal events.

I'd submit that the liberal dispensing of antivirals in the UK may have more than a little to do with the lower CFR, but I suppose that's something for epidemiologists and historians to thrash out when this is all over.