BEWARE OF UNINFORMED WARNINGS ABOUT RISK

Perhaps you are reading this column while sitting at the kitchen
table, or in a booth at the local diner, or bouncing along in a bus.
Wherever you may be, you are at risk. Right now -- at this very
instant -- there is a chance that a large rock will blaze down from
the sky and smash you to a thousand unrecognizable bits.

Most people are not terribly concerned by this mortal threat for the
very sensible reason that while the risk is real, it is tiny. Very, very tiny.

But what if we were to open the newspaper tomorrow and read that
scientists had concluded the number of asteroids smacking the Earth
is 200 per cent higher than previously believed? Just like that, the
chance of being crushed while watering the delphiniums would triple.

A 200-per-cent increase in the danger. Triple the risk. Would it be
rational to respond to this news by carrying a cast-iron umbrella and
replacing the delphiniums with a backyard bomb shelter? Of course
not. Three times zero is zero. And a tripling of an itty-bitty risk
produces a slightly larger itty-bitty risk. The delphiniums can stay.

At this point, the reader may think a flying rock has hit Gardner's
head. This is so obvious. Why is he telling us this?

Because sometimes it is not so obvious. Take a look at any newspaper
or news broadcast. Journalists, activists and politicians routinely
warn the public about increases in relative risk without saying
anything about the absolute risk. And people just as often get the
impression that the danger is greater than it actually is.

Case in point: A paper published in the British medical journal The
Lancet last week found that users of marijuana have "an increase in
risk of psychosis of about 40 per cent" compared to those who had
never used marijuana. The most frequent users were at 50 per cent to
200 per cent greater risk.

There are many things to note about this study.

First, it's not new. It's a meta-study of existing work that supports
earlier conclusions.

Second, as the authors were careful to note, the study does not prove
marijuana causes schizophrenia and other forms of psychosis. It shows
they are associated. The researchers tried to control for various
factors but they can't rule out the possibility that something else
may be at work.

But let's assume that The Lancet paper really does show that
marijuana causes psychosis. And let's assume the increased risk
really is as high as 200 per cent. What does that mean? Nothing.
Rather, it means nothing by itself.

If the lifetime risk of being crushed by an asteroid were to triple,
we would ignore it because the original risk is so tiny. But a
tripling of the lifetime risk of getting cancer is serious because
the existing risk is big. So to make sense of the increased risk of
psychosis, we have to know what the existing risk of psychosis is.
Without that, these stats are scary but meaningless.

And yet, many journalists did not provide that key piece of
information, while others buried it as if it were a trivial detail.
Even an editorial that accompanied the paper in The Lancet only
mentioned the relative risk.

An Agence France-Presse story that appeared in the Ottawa Citizen did
modestly better: "The report stresses that the risk of schizophrenia
and other chronic psychotic disorders, even in people who use
cannabis regularly, is statistically low, with a less than one-in-33
possibility in the course of a lifetime."

That's not a lot of information, but it's enough to work out the
basic numbers: According to this paper, someone who never uses
marijuana faces a lifetime risk of around one per cent; a light
user's risk is about 1.4 per cent; and a regular user's risk is
between 1.5 and three per cent.

These are significant numbers, but they're not nearly as scary as the
numbers that got the headlines. And as far as I can tell, not one
news story anywhere in the world reported them in full. And that, I'm
sorry to say, is all too typical.

Last year, a study found, in the words of one newspaper article, that
women who use the Ortho Evra birth-control patch "were twice as
likely to have blood clots in their legs or lungs than those who used
oral contraceptives."

Twice the risk: In newspapers across North America, that was the only
information readers got. It sounds big. No doubt some women found it
quite frightening.

An Associated Press story provided the missing piece of the puzzle:
"The risk of clots in women using either the patch or pill is small.
Even if it doubled for those on the patch, perhaps just six women out
of 10,000 would develop clots in any given year." The AP story was
carried widely across North America but many newspapers that ran it,
including The New York Times, actually cut that crucial sentence.

We face lots of risks in life, including the risk of getting bad
information about risk. Reader beware.