[alancalverd]

Apologies for a long post, but it's something I've had in mind for some years and seems very appropriate right now.

It is doubly unfortunate that epidemiologists have chosen the symbol R to denote the “effective reproduction number” of an infective agent, and politicians have seized upon R as an indication of viral virulence, or their “success” in controlling a pandemic.

For anyone unacquainted with the terminology, R is the average number of persons infected by a single carrier of a disease. That sentence will have triggered a “caution” response in numerate readers, and a howl of derision from anyone who has travelled in a crowded train. If the specific infectivity of a virus is constant, R is obviously dependent on the behavior of the carriers, not the virus: R_COVID = 0 for a hermit in a desert, maybe 20 for someone who sneezes his way around the London Circle Line at 8 am. 

As shown by experiment, there is no scientific justification for relaxing social distancing or quarantine rules when R decreases: doing so merely allows it to increase again.  And R is an average of the entire population exposed by all recent behaviors including total isolation: it does not indicate the likelihood of any individual becoming infected at a particular time and place.  R is an effect, not a cause or a decision parameter.

Why doubly unfortunate? Because some years ago I proposed a risk index R as a means of communicating risk to the public, and the present COVID pandemic demands a simple, efficient parameter that can be used for public information and emergency planning. So in deference to the World Health Organisation, I’d like to relaunch the risk index with the Cyrillic symbol Я (pronounced Ya).

Define Я = 10 + log₁₀ P where P is the probability of an event.

If the event is inevitable, P = 1 and Я = 10

If the event is so unlikely that no living human will see it,  Я < 0.1

The logarithmic scale is actually familiar to the public and consistent with our intuitive appreciation of risk. Winds of Beaufort force below 4 are of no consequence. Force 5 is inconvenient, 6 is mildly hazardous and 10 is “seldom experienced inland” with trees uprooted and major structural damage. Likewise the Richter earthquake scale: up to 4 is of scientific interest, 5 – 6 causes recoverable damage and anything above 8 is a disaster.

In everyday life we consider Я ≤ 5 “worth it” for the fun or benefit. The UK annual risk index for death in a road accident is about 5, but deep sea fishing with an annual Я_DEATH approaching 7 is a dangerous profession in northern waters.

My original interest was in efficiently communicating the risk of diagnostic x-rays. The natural incidence of cancer gives Я_{<DEATH|CANCER>}  ≈ 9.4 (no apologies to this audience for Dirac notation, and I’m sure Joe Public will get the idea pretty quickly).  Against this, we have Я ≤ 4 for a dental x-ray (negligible – could save you pain and infection, and safer than driving to the clinic) and 7 for a repeated abdominal CT (worth the risk to avert a greater one).

In a pandemic, I think honest public information demands activity-specific values of Я_<Y|X> , the risk index of an individual contracting Y whilst doing X. Early in the UK outbreak I cancelled a biannual jazz concert on the estimated Я_<COVID|GIG> of 8.4 (unacceptable, however good the band) given the likely size and packing density of the audience and the probable local incidence of infection.  I take no pleasure in being right in this instance – by the original date, two members of the prospective audience of 100 were indeed infectious, one becoming very seriously ill a few days later.

It should be possible to estimate and publish general Я values for, say, working in an office, a ventilated factory, or an outdoor team, and travelling to work by bus or train.  You can subtract an appropriate value for each type of face mask. Those of a social science bent might study crowd behavior in theatres, pubs etc and on beaches, and estimate appropriate Я values that would be far more meaningful and specific than the current global R that allegedly “informs” political decisions. Individuals can then make properly informed choices about their work and leisure. 

[Bored chemist]

That sentence will have triggered a “caution” response in numerate readers, and a howl of derision from anyone who has travelled in a crowded train.

I suspect that just generated a sigh from any passing epidemiologists.

Epidemiology deals with populations, not individuals so there isn't an "R" for a man on a train.
There may be an "R" for "men on trains".

there is no scientific justification for relaxing social distancing or quarantine rules when R decreases: doing so merely allows it to increase again.

That's the exact reason for justification of the policy
They totally screwed up, but that's not the epidemiology's fault.
The politicians just didn't listen to them.

You pretty much can't get R down to zero.
Some damned rat will get sneezed on then eaten by a cat which then gets petted by a kid.
But you don't need to get it to zero, you need to get it below 1

So, any social distancing or whatever, measures that reduce it much further than "below 1" are arguably excessive.
And it becomes a cost benefit analysis; in principle, one of the easy ones because the units in both cases are "dead people".
Draconian measures in an attempt to get R from 0.1 to 0.01 would reduce the availability of doctors to treat other conditions.
The net death toll would rise. (As well as Trashing the economy)

Boris' experiment hasn't really shown this, because none (except possibly early versions) of his "lockdown" brought R significantly below 1.
You can't blame R for that failing (I imagine Boris will try).

Why doubly unfortunate? Because some years ago I proposed a risk index R as a means of communicating risk to the public,

"some years ago "
How many years ago? The reproduction number has been in use (at least) since the 50s
Did they choose the wrong letter, or did you?

It's also fair to say that it's used for plenty of other things without confusion.



"I proposed a risk index R as a means of communicating risk to the public".
To whom?

The logarithmic scale is actually familiar to the public and consistent with our intuitive appreciation of risk. Winds of Beaufort force below 4 are of no consequence. Force 5 is inconvenient, 6 is mildly hazardous and 10 is

People memorise the "what damage happens at what number" precisely because they can't deal with a logarithmic scale.

I'm willing to bet that 90% of the general population don't understand pH or dB scales.

I'd suggest you read up on another risk scale- which I (and others) think is more readily understood.
https://en.wikipedia.org/wiki/Micromort
And the related
https://en.wikipedia.org/wiki/Microlife

[alancalverd]

Quote from: alancalverd on Today at 15:46:07
That sentence will have triggered a “caution” response in numerate readers, and a howl of derision from anyone who has travelled in a crowded train.
I suspect that just generated a sigh from any passing epidemiologists.

It shouldn't have - it's their definition!

The problem is that idiot politicians parade it (and some gullible punters accept it) as a measure of  progress in "defeating" the disease. My whole point is that  your decision whether to go to work on a bus should not be influenced by a global statistic of everybody doing everything, which includes suicidal Republicans and anti-vaxers holding crowded hate-ins, but something specific to your choice of action and environment.

[Bored chemist]

It shouldn't have - it's their definition!

No Alan.

That sentence will have triggered a “caution” response in numerate readers, and a howl of derision from anyone who has travelled in a crowded train.

Is what you said.

My whole point is that  your decision whether to go to work on a bus

there isn't an "R" for a man on a train.

... or a bus.

So, your decision to get on the bus can't be dependent on R for getting on a bus.

But the government's decision to, for example, only allow people onto busses if they have masks, is dependent on the R.

There may be an "R" for "men on trains".

You seem more determined than the politicians to ignore what R is about.

[alancalverd]

But the government's decision to, for example, only allow people onto busses if they have masks, is dependent on the R.

I think you (or more likely the government) are confusing cause and effect. Wearing masks alters R.

The decision of an individual to  get on a bus should be driven by  Я, a measure of the risk to the individual of that particular activity.

[set fair]

The problem is that idiot politicians...

We all know the one about the computer geek whose car won't start, all out, wait five minutes then get in one at a time and see if it starts. It didn't work, but hey, maybe it will with covid.

[Bored chemist]

Quote from: Bored chemist on 03/08/2020 18:48:32
But the government's decision to, for example, only allow people onto busses if they have masks, is dependent on the R.
I think you (or more likely the government) are confusing cause and effect. Wearing masks alters R.

The govt is probably confused, but that's not the issue here.
R depends on many things.
The important thing for a competent government to do is to keep R below 1 (The current UK govt isn't competent)

If you reduce it by one action- closing the schools- then you can use the leeway generated to do other things like allow people on busses provided they wear masks and still keep R below 1.
If some other effect- a hot day and all the covidiots streaming to parks and beaches for example- raises R then  the govt should  take other actions to reduce it.

So, it works both ways. R affects policy and policy affects R.

The decision of an individual to  get on a bus should be driven by  Я, a measure of the risk to the individual of that particular activity.

Which plainly depends on the same things that R is affected by.

If you are stealing the bus, and don't plan to let anyone else on board, the  Я is more or less independent of R- but that's because R is only defined for populations.
Otherwise  Я depends on stuff like the govt mandating masks.