The World Turned Upside Down: The Second Low-Carbohydrate Revolution (33 page)

The probability of an event happening
is simply:

Probability = number of particular
events / total number
of events.

Probability in many medical tests is
called risk. So,

Probability, or "risk" of getting a
"6" with a fair die is
⅙
.

If you have two groups, for example,
meat eaters and
vegetarians and you want to compare their risk, you report relative
risk or
(RR):

RR = risk (meat group) / risk
(vegetarians).

It is important to realize that when
you calculate RR, you
have lost the information as to how much the risk was to begin with. If
they
tell you the RR of a disease, you don't know whether it is a rare
disease or
one that everybody has.

A problem in a medical experiment may
be deciding when the
experiment is over and a related measure is the hazard which is the
same as the
probability but measured over a fixed time intervals, that is, a rate.

Hazard is more complicated and
technical, but it doesn't
hurt to consider hazard as the same as probability. When you compare
two groups,
you report the HR. The interpretation is like the RR, relative
probability of
occurrence.

In some cases, rather than the
probability, the odds might
be reported. Odds are slightly different from probability.

Odds = (number of ways of
winning)/(number of ways
not
winning).

Odds of getting a "6" with a fair die
is 1/5. You would
usually say that the odds are "1 to 5," or "5 to 1 against." As
the probability gets smaller, the odds and the probability become
closer
together and in conversation are used similarly..

The probability of getting the ace of
spades from fair deck
= 1/52 = 0.0192.
Odds of getting the ace of spades = 1/51 = 0.0196

Odds ratio (OR) is what it says, the
ratio of the odds of
two different events. Again, you don't know whether the odds were good
or bad
only their relation to each other. An OR of 1 means that there is no
difference
in the likelihood of two events. It is sometimes said "50-50" or "equal
odds."

Bottom line: in reading a scientific
paper, you can take RR,
HR and OR as roughly the same, telling you the comparison between how
likely
two events are to occur. The big caveat: you have to make sure you know
what
the individual probabilities are. The problem described in a narrative:

You are in Las Vegas. There are two
black-jack tables and,
for some reason (different number of decks or something), they have
different probabilities
of paying out. The probability of winning at Table One is 1 in 100
hands, or
0.01 or 1 %. At Table Two, the probability of winning is 1 in 80 or
about 1.27%.
The ratio of the probabilities is 1.27/1.0 = 1.27. (A ratio of 1 would
mean
that there is no difference between the tables). Right off, something
is wrong:
you lost a lot of information. One gambling table is definitely better
than the
other but the odds aren't particularly good at either table. But you
had to
know that in advance; you can't tell from the probability ratio because
the
information about the real payoff is lost. Suppose, however, that you
did get a
glimpse at the real info and you could find out what the absolute odds
are at
the different tables: 1 % at Table One, 1.27 % at Table Two. Does that
help?
Well, it depends on who you are. For the guy who is sitting at the
black-jack
table when you go up to sleep in your room at the hotel and who is
still there
when you come down for the breakfast buffet, things are going to be
much better
off at the second table. He will play hundreds of hands and the better
odds
ratio of 1.27 is likely to pay off. Suppose, however, that you are
somebody who
will take the advice of my cousin, the statistician, who says to just
go and
play one hand for the fun of it, just to see if the universe loves you
(that's
what gamblers are really trying to find out). You're going to play the
hand and
then, win or lose, you are going to do something else. Does it matter
which
table you play at? Obviously it doesn't. The odds ratio doesn't tell
you
anything useful because your chances of winning are pretty slim either
way. Put
another way, if you buy two lottery tickets instead of one, your
chances of
winning are doubled, but does that make you want to play?

Tell me the difference
in absolute risk

Going over to the original red meat
paper (skip to the next
paragraph if you just want the conclusion), there are a number of
different
"models" (reworking of the data) and there are mind-numbing tables
giving you
the different hazard ratios. Using the worst case HR between high and
low red
meat intakes for men, we get HR = 1.48 or, as they like to report in
the media
48 % higher risk of dying from all causes. Sounds bad. But wait, what
is the
absolute difference in risk? Well, the paper says that the whole group
of 322,
263 men was divided into five sub-groups (quintiles) of 322, 263/5 =
64, 453
people. The people who don't eat much red meat had 6437 deaths or 10.0
%. The
big meat eaters must have had 14.8 % deaths. That's an absolute
difference of 5
% and it's the very worst conclusion correcting for some variables. The
authors, however, corrected for other things that might have
contributed to the
outcome. Correcting for all variables, the difference for men goes down
to 3 %.

Bottom line: There is an absolute
difference in risk of
about 3 %. How much would you change your life for that benefit? And
remember,
this is for big changes, like 6 or 7 times as much meat. So, what is a
meaningful HR? For comparison, the HR for smoking
vs
not smoking and lung disease was about
20. For smoking heavily, the HR was about 30.
Going back to
Bradford Hill
's criteria: "First upon my list I
would put the strength of the association," again, the effect size.
Relative
risk does not have meaning by itself. You must know the changes in
absolute
risk.

Another way of looking at the data is
the number needed to
treat (NNT), which is the reciprocal of the absolute risk or 20-30
people that
you would have to treat to save one life. That's not great but it's
something.
Or is it?

What about public
health? good news or not?

Okay. The odds are not very good.
Many people would say
that, sure, for a single person, red meat might not make a difference
but if
the population reduced meat by half, we would save thousands of lives.
At this
point, before you and your family take part in a big experiment to save
health
statistics in the country, you have to apply Principles 2 and 3. You
have to
ask how strong the relations are. To understand how good the data is
you must
look for things that would
not
be expected to have a correlation. "There was an increased risk
associated with
death from injuries and sudden death with higher consumption of red
meat in men
but not in women" which sounds like we are dealing with a good deal of
randomness.

More important, what is the
risk
in
reducing
meat intake. The data don't really tell you that. Unlike cigarettes,
where
there is little reason to believe that anybody's lungs really benefit
from cigarette
smoke, we know that there are many benefits to protein especially if it
replaces carbohydrate in the diet, especially for the elderly,
especially for
all kinds of people. So with odds ratios around one – remember that an
odds
ratio of one means that there is no difference between no red meat and
lots of
red meat – you are almost as likely to
benefit
from adding red meat as you are reducing
it. Technically, it
is called a two-tailed distribution, that is, things can change in both
directions. The odds still favor things getting worse but it really is
a risk
in both directions. You are at the gaming tables. You don't get your
chips
back. If you bet on reducing red meat and it does not reduce your risk,
it may
increase your risk.

The fine print. The
smoking gun.

What's written above is approximately
what I wrote as a
blogpost. In turning it into this chapter, I went back to the original
paper to
check the calculations. I had used the numbers for men since it was a
worst
case (and it still has the problems that I described) but in
re-calculating
things, I looked at the numbers for women. The data are shown below:

The population was again broken up
into five groups or
quintiles. The lower numbered quintiles are for the lowest consumption
of red
meat. Looking at all cause mortality, there were 5,314 deaths and when
you go
up to quintile 05, highest red meat consumption there are 3,752 deaths.
What?
The more red meat, the lower the death rate? Isn't that the opposite of
the
conclusion of the paper? And the next line has relative risk which now
goes the
other way: higher risk with higher meat consumption. What's going on?
As near
as one can guess, "correcting" for the confounders changed the
direction. The
confounders are listed in the legend to the figure. For the "basic
model," the
data were corrected for race and total energy intake and risk went up.
Why? We
can't tell if we can't see what the effect was.

A useful way to look at this data is
from the standpoint of
conditional probability. We ask: what is the probability of dying in
this
experiment if you are a big meat-eater. The answer is simply the number
of
people who both died during the experiment and were big meat-eaters
(Q5)
divided by the number in Q5 = 3752/(223,390/5) = 0.0839 or about
8%.  If you
are
not
a big
meat-eater, your risk is (5314 +
5081+ 4734 + 4395)/(0.8 x 223, 390) = 0.109 or about 11%. 

This paper tested the hypothesis that
red meat is associated
with all cause mortality. The data showed that it wasn't. That's what
it
showed. It wasn't unless you drag in  other factors,
education, marital status,
family history of cancer body mass index, smoking history using smoking
status
(never, former, current), time since quitting for former smokers,
physical
activity, alcohol intake, vitamin supplement user, fruit consumption
and
vegetable consumption have to be added in to make it true. What makes
anybody
think that red meat among these other ten inputs is the key variable?
Wouldn't
it be better to find out which of these had the biggest effect? Maybe
we're
looking at the effect of smoking (known risk) corrected by all the
others.

What I offer here is a professional
scientist's view and I
try to make my description dispassionate and not insulting but what is
this but
flim-flam?

What about red meat?

Red meat isn't a chemical. What is it
about the red meat?
The meat? The red? To be fair to the authors, they also studied white
meat
which was mostly beneficial. But what about potatoes? Cupcakes?
Breakfast
cereal? Are these completely neutral? If we ran these through the same
computer, what would we see? Unspoken, in everybody's mind is saturated
fat,
that Rasputin of nutritional risk factors who will come after you
despite
enough bullets in its body to have killed several scientific theories.
Maybe it
wasn't the red meat
per se
but the way it was procured. Maybe it's ritual slaughter that conferred
eternal
life (or lack of it) on the consumer – nothing is as harrowing as the
Isaac
Bashevis Singer stories equating meat eating with other sins of the
flesh.
Finally, there is the elephant in the room: carbohydrate. Basic
biochemistry
suggests that a roast beef sandwich may have a different effect than
roast beef
in a lettuce wrap.

Summary

Rules for dealing with the scientific
literature:

1. Do
   the results make sense? Biology comes before statistics. Experience
   comes
   before statistics.
   
2. Is
   there a big effect. Are we talking about meaningful, that is, large
   numbers?
   
3. What
   was measured? If the effect is not large, then the data have to be very
   reliable. If the data have big potential error, then the conclusion
   must be
   substantial.
   

In nutrition, as in other fields,
recommendations are often
tinged by the personal preferences of those dishing them out. In
combination
with the dogmatic state of government and private recommendations, it
takes
some work to know if you are reading a meaningful study. The points in
this
chapter are that you have the right to ask for and the author has the
obligation to provide clear explanations. The practical application of
Hill's
criteria is that results should make sense in terms of magnitude and
what you
know about biology. You should also be very suspicious if only relative
risk is
reported even if just in the Abstract. Remember, Alice has 30 % more
money in
the bank than Bob, but we don't know whether she is rich.