Tuesday, 19 February 2013

Day 116: Let me draw you a picture

Having watched epidemiologists present their findings to audiences whose math skills do not match their interest in the subject, I was a little concerned that today's appearance by Jack Siemiatycki at the Montreal tobacco trials might serve to confuse as much as enlighten.

Perhaps I took too seriously the suggestions of (JTI-Macdonald lawyers) Kevin LaRoche and Guy Pratte that the content would be too challenging even for their intellectual powers. If they felt they "could not master" the content, what hope would there be for the rest of us?

I was wrong to have any such apprehension.

Facing the prospect of handful of industry experts trying to throw up dust around Mr. Siemiatycki's conclusions, André Lespérance took the wise course of unbundling the report of his renowned expert witness, and allowing him to demystify it.

As it turned out, the key conclusions of Mr. Siemiatycki's expert report (Exhibit 1426.1) were not discussed today, at least not in terms of the numbers he finally arrived at.  (He concludes that there were 110,000 Quebec residents in the class period whose "who suffered from one of the four diseases and who would have had probability of causation greater than 50% that the cause was cigarettes smoking.")

Instead, what was presented was how he arrived at this conclusion, and why any other approach should bring the court to a similar finding.


The risk of this approach could have been the glazing of eyes and later confusion. It was the manner of presentation chosen by the plaintiffs, however, that made the exercise simple, clear and compelling.

A few weeks back André Lespérance had suggested allowing Mr. Siemiatycki to illustrate his ideas using Powerpoint. The idea had been shot down, including by Justice Riordan, who said it was "looking for trouble" to bring new material to court in this way because of the objections it would trigger.

So the plaintiffs ingeniously hit upon another technology - the iPad app "Paper". Despite a few technical rough spots, this had the apparent spontaneity of a back-of-the-envelope sketch, while leaving a document for the court record. Better yet, the opposing lawyers seemed happy with the idea, or at least unprepared to challenge it.

Continuing Education

iPad at his fingertips, Mr.Siemiatycki resumed his gently-paced tutorial from the day before, when the concept of relative risk had been presented. He began today by explaining how to estimate the amount of disease that can be attributed to risk exposure (attributable fraction).

He related the concept to the job at hand: "You have in front of you a certain number of cases [of cancer] that have occurred in Quebec and the natural question is 'what fraction of these would not have occurred but for smoking?' – it is the Attributable Fraction among the Population that answers that question." 
He showed how to estimate the amount of cancer among all smokers and former smokers that could be attributed to smoking by measuring the area/number of people that lay above the normal risk that existed for smokers and non-smokers alike. The Attributable Fraction (AF) area is shown with black diagonal lines.

He also showed an alternative way of viewing it if smokers were divided into categories of risks  depending on how long or how much they had smoked. This area (shown with yellow diagonal lines) hinted at what was to come next. (I added the  typed descriptions of smoking patterns because these were only given orally).

The second concept he presented today was the probability of causation. "When a person is selected at random ...  he is sick, and he is a smoker and we know nothing else about him. how can we guess at the probability that his disease was caused by smoking?" he asked rhetorically before providing his answer. "The best approach is to look at the attributable fraction [and determine] what is the probability that he will be chosen from above the dotted line or below the dotted line [that separates the normal risk from the additional risk]." 

Again he used the iPad to illustrate an equation by which the probability of causation could be calculated. He described it as the additional risk divided by the whole risk, or PC=(RR-1)/RR.

By way of example, the probability of causation if the relative risk were 10 would be (10-1)/10, or 90%. The probability of causation if the relative risk were 2 would be (2-1)/2 or 50%.

Up to this point, he said, he had presented  "conventional" ideas within epidemiology. The the next concept, however, was one of his own characterization.

Legally Attributable Fraction 

He said he had wanted to apply the legal concept of balance of probabilities to the epidemiological notion of probability of causation. "The way I thought about the problem was this “cut point” where something is more likely than not ...greater than 50% probability."

He gave this quantity a name - the Legally Attributable Fraction (LAF). There was clearly some discomfort in the court with  the term 'legal' being bandied about by a scientist (Simon Potter registered an objection and Justice Riordan found alternative ways of expressing it), but the construct continued to be used by the witness throughout the day.

Mr. Siemiatycki explained that in a group where the probability of causation was less than 50%, none of the disease would be considered a "legally attributed fraction." In a population where  the probability of causation was higher than 50%, however, everyone would be included.

On Exhibit 1427.3, with a hypothetical probability of causation drawn underneath categories of smokers with increasing levels of cigarette exposure, he drew the LAF in red lines (all those with the probability of causation over 50%). The proportion of disease that would be not be considered to be legally attributable was drawn in grey lines (probability of causation less than 50%).

Every former student of calculus will be familiar with his next move -- translating the discrete steps into a continuous sloped line that represented the dose response risk. The more you smoke, the greater the risk - not in discrete lumps but in a smooth continuous way. Based on his review of several studies, he calculated that the slope of this dose-response line was .34, and that every additional pack year increased the relative risk of lung cancer by .34.

He defined a "Critical point [C] where the probability of causation hits 50%," and pointed out that mathematically "that corresponds to the level where the relative risk is equal to 2."  This is the amount of cigarette consumption at which a cancer patient can be thought, on a balance of probabilities, to have had his or her cancer caused by smoking.

The next building block in this exercise was to determine how many cigarettes someone would have to smoke for the relative risk to be equal to 2. His meta-analysis had suggested that for lung cancer, this would be 4 pack-years for men and 3 pack-years for women. (For larynx cancer, throat cancer and COPD/emphysema it was slightly higher, at about 5 pack-years).

No mathematical mystery. No fancy footwork. No voodoo. Just simple ideas, simply presented.

The bigger picture

At this point the lecture broke for lunch, and when the session resumed in the afternoon, André Lespérance moved to questions that involved somewhat more detailed explanations, and which laid the foundation for Mr. Siemiatycki's final explanations of why it is that even if the values underlying his calculation were adjusted somewhat, the general conclusions would not change greatly. In some detail, he showed how his calculations understated the number of cancers caused by smoking.

Mr. Semiatycki's professional life usually focuses on risks other than smoking, but nonetheless he recognzies tobacco use as a predominant risk for disease in Quebec. It is the double-whammy of a higher risk combined with greater population exposure that has put tobacco in a class of its own. "There is really no comparison in the magnitude of the impact they can have. One [tobacco] is enormous and the others [occupational and environmental exposure] beside it are small." 

The defence teams sit it out.

There were very few objections voiced today by any of the three defence teams.

Guy Pratte had been given the lead with this witness, and at one moment he tried to object to the introduction of term "legally acceptable fraction" that had not been used in Mr. Siemiatycki's 2009 report but which had, apparently, been used in the more recent version which has not been filed with the court.

Justice Riordan seemed satisfied that the elements of the idea were in the 2009 report and allowed the new concept to be discussed. This sounded like a significant set-back for the defence, particularly in light of the prominent role that this argument had taken in their sabre-rattling last week and yesterday.

We will find out tomorrow, when Jack Siemiatycki will be cross-examined. I think the risk that he might be allowed to use an iPad to illustrate his points is relatively small.

The cross-examination of Jack Siemiatycki is scheduled for tomorrow and Thursday.