Thread by @ProfDFrancis

Innocent looking chap, eh? Trustworthy?
Wouldn't con his poor doddery old boss?

"You know you said you would give me anything, if I could teach you Machine Learning?"

"Yes, and you did. What is your 1 wish?"

"22% pay increase."

"Done!"

--- and I certainly have been!

#FOAMED

He didn't fully emphasise that this was 22%, per year, FOREVER.

If his salary is $1000 a year at present, what will it be in 1 year's time?

And after the 20th increment, what will his salary be?

Get a calculator, type

1.22

x

and keep pressing enter, 19 times.

- or -

You can use windows calculator

WTF, no you can't!

OK I found the dropdown at the top. Change it to Scientific.

Cos only scientists pay interest on credit cards

Or suffer from inflation

Obviously.

Type

1.22

Then the "power" button which looks like this

y
x

and then 20

Or go to any modern web browser, and type this into the address bar.

1.22 ^ 20

For example like this.
lmgtfy.com/?q=1.22%5E20

That's what every $1 of starting salary changes to, after 20 years of 22% increments.

Let's call it 50.

So salary ~$50,000.

What would it be after ANOTHER 20 years?

If you were brainwisely lazy and physically energetic, you could go to google again, with 1.22^40.

But fortunately I am brainwisely energetic, and physically lazy, which is why I have high triglycerides and was foolishly thrashing around for a solution that isn't exercise.

Anyway,

If you start with 1

and times it by 1.22, 20 times, and get 50,

Then if you times it by 1.22 ANOTHER 20 times, you will get a result that is 50 times more (than 50).

Which is what/

Now James Howard @DrJHoward makes his subsidiary demand.

"Consistent with my velocitously exuberating status within ORBITA-HQ, I should also have a correspondingly expansitory spatial allocation."

(For he has swallowed a dictionary, too.)

He already has an ultracomputer workstation which occupies about 1% of the institute.

It doesn't seem to unreasonable to grant him another 0.22% of the institute next year.

But in 20 years' time, how much of the institute will be the Howard Dept?

And in 40 years, god save us?

Yes, we would need 25 entire institutions for him to fill with computers, empty coffee cups, and cold pizza.

So obviously, at some stage, the institution would say,

"Whatever ProfDFrancis said, all those years ago, it can't actually be right.

We know he has Papal Infallibility as a Professor of the beloved ORBITA-HQ, but in this case, what he said was impossible."

What is the average of all these rates of growth of plaque, in the placebo arm, of a trial which I shall not name and shall remain anonymous.

(15 + 32 + 1 + 109 + 9 + 11)/6 = 29.5

Or if you like geometric*

(1.15 * 1.32 * 1.01 * 2.09 * 1.09 * 1.11)^(1/6) = 1.25, i.e. +25%

So depending how you look at it, the growth over the 18 months is around 25 to 30%.

I hope you are seeing the problem, now?

A 20% growth rate per year, gives you a growth over 20 years of

1.2^20 = 38

i.e. almost 40 fold

And over 40 years, it will be

THAT is the problem.

If people's coronary plaques really expand at a rate of 20% per year, then almost HOWEVER SMALL they begin, they will completely clog up the arteries in only a few decades.

Everyone will be dropping dead like flies.

So just like James not getting his wish of a ~20% increase in space per year, due to lack of space in the UK's universities, to accommodate him, we know that this can't be correct.

Unless the placebo is harmful.
Or the measurements went a bit wrong somewhere.

But wait!

Advanced topic for brainy statisticians, like @ADAlthousePhD

See down here at the bottom left?

What do the numerical values in the body of the table represent?

And if you want to know how much the mm3 have scaled by, when you know the LOGS of the values at baseline and final are:

LogBaseline LogFInal

How do you calculate the scale factor of the mm3?

Look at these two columns

Of these two columns, which is the ONLY one from which you can calculate the % change in plaque volume?

Yes! Ironic, but the %chg is not at all the percentage chsnge, but something infinitely more ineffable to the human brain and dependent on BOTH the units (mm3 etc) AND the base of the logarithm.

So hopefully they will correct any references to that column, in the paper's text.

For example, in the abstract, obviously these numbers are incorrect and will need to be revised.

Surprising that nobody noticed that in the abstract, plaque volume was DOUBLING in the placebo group.

Remember the rice and the chessboard? Haha

Have a good Thursday!

Postscript __________________________________

Excellent question from wrd2032, whose handle I can't help feeling is related to the word separator being a space (" ") whose value is "20" in hexadecimal and 32 in decimal. I will be very disappointed if this is just a coincidence.

There was no need for that particular complexity of averaging the various supposed growth rates.

Yes I could have just used the "11%".

But of course that 11% is wrong, isn't it?

Heh heh. That whole column is going to be rewritten when the paper is corrected.

In reality the numbers here are LOGs

And there is a base for the logs. Typically this is e (2.71728...) or 10, but in principle could be anything.

(Anything greater than 1, I hurriedly clarify, before @ADAlthousePhD tweet-storms me)

This original version of the paper doesn't specify which log is used.

Obviously this means that almost all the numbers in the paper are useless to other scientists.

I am sure when they correct the paper, they will provide that clarification too.

So if you really want to use the growth rate for total plaque, the correct way to do it, is to observe that the volumes rise in the placebo arm

from Base^4.1

to Base^4.6

At a simplistic level, this is a scale factor of approx Base^0.5.

However they provide a more precise scale factor here

It's not quite Base^0.5, because of rounding.

So let's take Base^0.4, which is kinder to the authors as it is going to be a lower value.

Let's try the two possible bases.

2.71828^0.4 = 1.49, i.e. a 49% increase

10^0.4 = 2.51, i.e. a 151% increase

So again, let's be charitable and assume they were naperian (base 2.71828) logs, so it is 49% increase in 18 months.

Per year, the scale factor is

1.49^(12/18) = 1.30

This makes young James Howard seem rather conservative in his demands!

A 30% annual increase in total plaque would mean:

In 20 years, roughly what % increase?

Hint: lmgtfy.com/?q=1.3%5E20

And in 40 years, an original 100mm3 of plaque becomes what?

Hint: lmgtfy.com/?q=100*1.3%5E4…

How many mm3 in a litre?

Remember 1 litre, i.e. 1 decimetre cubed = 100 mm x 100 mm x 100 mm

(Conversion to Imperial units: 1 quart = 1 pint * 3 7/8 yards + 2 1/16 feet, or something)

Right, so it is 3.6 litres of plaque.

(Conversion to imperial, 45 8/16 pounds-force-per-BTU)

What percentage of a heart, whose volume is (say) 360 ml, will this be?

Just be happy nobody asked me for a conversion of the % into Imperial units too.

I would use the trusty formula

1% = 3/16 of an acre per foot-pound.

Anyway, unless you know people who have their entire bodies turning into a fungating mass of coronary plaque, I wouldn't worry about this paper.

Let's just wait for the correction and then discuss.

Have a good evening! DF

Wait!

Dr Budoff @budoffmd has responded just now!

What base did you do the logarithms to, please @budoffMd?

It is not stated in the paper, as far as we can see.

We need to know this to know how to interpret the log-transformed values in Table 2.