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Statistics — the devil is in the details

Math is hard. And if you think math is hard, don't even think of wading into the minefield of causal relations.
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Math is hard. And if you think math is hard, don't even think of wading into the minefield of causal relations. If you do, ponder this query: Assess the probability of a person in, say, their mid-20s, skiing or boarding down Whistler Mountain, not wearing a helmet, eating a bacon sandwich, and suffering either a fatal head injury or developing colorectal cancer.

If you scanned recent newspapers or spent any time on social media, you may be inclined to say the probability is pretty high of one, possibly both of those fates befalling our hypothetical skier/boarder. The obvious conclusion is to slap a helmet on them — a mandatory one at that — and take away their bacon before they become yet another cancer victim.

Yet, if you pull back the curtain a bit and take a hard look at the wizard(s) conjuring those scary reports and conclusions, you just might draw different conclusions. Of course, to do so requires some digging, a little math and critical reading skills that may keep you from enjoying the next cute kitten video to pop into your social media feed. But what the heck, I've got nothing better to do for the next several hundred words.

Sixteen-year-old Brazilian exchange student Luca Cesar was snowboarding with friends on Grouse Mountain on Nov. 29, 2013. It was a Friday, around 7 p.m. Luca became separated from his friends. While there are lights on Grouse, it was dark out and there was thick fog and sleet. There were also trees and cliffs. Luca collided with a tree, according to Tim Jones from North Shore Rescue. His body was found at the rocky bottom of a nine-metre ledge. According to coroner Timothy Wiles' report, he died of severe injuries caused by blunt force head trauma.

Only two things are certain in this case: death and head injury. No one knows how fast Luca was going. No one, including the coroner, knows whether a helmet would have changed the outcome.

Despite this vacuum of knowledge, Mr. Wiles' report says, "... it is clear that traumatic brain injuries continue to pose a significant risk to skiers and snowboarders." Conjuring the power of statistics, he calls for mandatory helmets for anyone skiing or snowboarding at B.C. ski hills.

What constitutes a significant risk? The numbers are alarming, though perhaps not in the way you might think. In a six year period, 2007–13, there were 136 "winter activity" deaths. Of those, 27 per cent occurred while the decedents were skiing or boarding. I'll do the arithmetic for you; that's just under 37 deaths... in a six-year period.

Of those 37, we aren't told how many were skiing and how many were snowboarding but for the sake of illustration, let's assume it was 50 per cent each, 18.5 deaths from skiing, the same from snowboarding. Drilling down a final level, 26 per cent of the skiing deaths and 20 per cent of snowboard deaths were caused by head injuries. Quick, how many is that? Don't panic, I'll tell you. That's 4.8 and 3.7 deaths, respectively.

Over six years, fewer than five skiers were killed due to head injury. Fewer than four snowboarders. Oh, and there is no indications if any of them were wearing helmets. A quick look around most ski areas these days indicate there are quite a few folks who do. It's hard to imagine none of the poor souls who died of head injuries were wearing them.

With in excess of two million skier days per year at Whistler Blackcomb alone, it is difficult — even paying respectful homage to the sanctity of life — to consider eight or nine deaths in a six-year period statistically significant. Please note the word statistically. More people died driving to and from Whistler in the same period.

So it leaves us wondering how, exactly, Mr. Wiles believes it is "clear" that (a) traumatic brain injuries continue to pose a significant risk, and (b) to what extent mandatory helmets will ameliorate that risk.

What we're not wondering about at all is the impact on participation in skiing and riding such a law would have. It would be another impediment to anyone who heads to their local ski hill a couple of times a year.

For the record, I wear a helmet. It was my choice. I believe it should remain my choice... and yours.

Bacon, on the other hand, now there's a killer. The International Agency for Research on Cancer (IARC) released its study of studies irrefutably linking processed meats and red meat to cancer. They've concluded processed meats — bacon, ham, salami, meats also classified as delicious — are a definite cause of cancer, Group 1 carcinogens. Less deadly is red meat in general; your steak, roast, chop is a probable cause of cancer, a Group 2a carcinogen.

When widely reported last week, pork bellies tanked on commodity markets. In countries with strict gun controls, strongarm crimes were suddenly being committed by desperados wielding deadly salamis. And folks everywhere began to worry that their breakfast bacon or ham sandwich would do them in before their time.

After all, the IARC reviewed 800 studies!

Yet, buried in their report — you can read it here www.thelancet.com/journals/lanonc/article/PIIS1470-2045%2815%2900444-1/fulltext — was this. "The largest body of epidemiological data concerned colorectal cancer. Data on the association of red meat consumption with colorectal cancer were available from 14 cohort studies. Positive associations were seen with high versus low consumption of red meat in half of those studies... Of the 15 informative case-control studies considered, seven reported positive associations of colorectal cancer with high versus low consumption of red meat. Positive associations of colorectal cancer with consumption of processed meat were reported in 12 of the 18 cohort studies... Supporting evidence came from six of nine informative case-control studies. A meta-analysis of colorectal cancer in ten cohort studies reported a statistically significant dose–response relationship, with a 17% increased risk per 100 g per day of red meat and an 18% increase per 50 g per day of processed meat."

Two-thirds of cohort studies and case-control studies out of a total of 27, provided supporting evidence. Kinda blunts the impact of that 800-study review, doesn't it?

The takeaway from the IARC report is not that bacon will give you cancer. It reports a causal link, not a volumetric one. It doesn't tell you how much cancer processed meat will cause. I've already bored you with enough math for one column. Dig a bit for yourself and you'll discover the quantum of colorectal cancer eating what most of us would consider massive amounts of processed meat causes is only slightly larger than the number of deaths helmets might save.

On the other hand, stress and worry will definitely kill you. So be mindful, but stop worrying.