Chance and inevitability

In an op-ed in today's issue of the Los Angeles Times, Michael Shermer wrote about the rush "to find the deep underlying causes of shocking events", with reference to the shooting in Tucson, Arizona and the recent mass bird deaths.

Shermer made some good points, but parts of his argument were flawed. For example, he cited statistics from the National Institute of Mental Health to argue that unbalanced people are not uncommon, and

Given these statistics, events such as the shooting in Tucson are bound to happen, no matter how nicely politicians talk to one another on the campaign trail or in Congress, no matter how extreme tea party slogans are about killing government programs, and no matter how stiff or loose gun control laws are in this or that state. By chance — and nothing more — there will always be people who do the unthinkable.

In other words, he is pointing out what he sees as an inevitability, and then attributing it to chance. But an inevitability is the opposite of chance: it is a systematic pattern. And a systematic pattern is precisely what we can hope to change. I tend to agree with Shermer that "there will always be people who do the unthinkable." But surely we ought to do what we can to make such occurrences as rare as possible, and to reduce the harms as much as we can.

Shermer finishes his piece as follows:

... as often as not, events in life turn on chance, randomness and statistical probabilities that are largely beyond our control. So calls for "an end to all overt and implied appeals to violence in American politics" — such as that just issued by MoveOn.org — may make us feel better, but they will do nothing to alter the inevitability of such one-off events in the future.

By definition "one-off events" are unpredictable and idiosyncratic. And yet Shermer says they are inevitable. The apparent confusion here is between statistical probabilities that can be used to make fairly certain predictions, and the virtual impossibility of prediction at the micro level. For example, age- and sex-specific incidence rates of different types of cancer are carefully tabulated by the CDC, and we can use these rates to predict the number of people who will be diagnosed with cancer this year. But we can't predict well who those people will be. There are, however, patterns. We learned that smoking causes lung cancer (and heart disease, and emphysema, ....) and through reduced smoking rates we have seen reductions in mortality [pdf]. Perhaps we do have some control after all.

The Fort Chipewyan cancer cluster

Fort Chipewyan (often called Fort Chip) is a town of 1200 in northern Alberta. In 2006, a local physician reported 6 suspected cases of a rare form of cancer, cholangiocarcinoma, as well as elevated rates of other cancers. What made this particularly alarming is that Fort Chipewyan is located downstream from the huge Athabasca oil sands development and there is also uranium mining and pulp and paper industry in the area. Yesterday, Alberta Health Services released a report on Cancer Incidence in Fort Chipewyan, Alberta 1995-2006 [pdf].

It turns out that only two of the six suspected cases were in fact cholangiocarcinoma. However overall cancer rates do seem to be elevated. The report concludes that:

In particular, increases of observed over expected were found for biliary tract cancers as a group and cancers of the blood and lymphatic system. These increases were based on a small number of cases and could be due to chance or increased detection. The possibility that the increased rate is due to increased risk in the community, however, cannot be ruled out.

To be precise, during the period 1995-2006 there were 51 cases of cancer, where 38.9 were expected based on the population and age-distribution of the town. Thus the incidence is 31% higher than expected, which can be expressed as an "indirect standardized incidence ratio" (ISIR) of 1.31. A 95% confidence interval for the ISIR goes from 0.98 to 1.72. Because this confidence interval (barely) includes 1, we cannot reject the hypothesis that this is simply a chance finding. The report, however, notes that this:

... is a two-sided equal tail test that does not discriminate whether the aim was to examine an ISIR that is greater than 1 (Observed>Expected), or an ISIR that is less than 1 (Observed<Expected)

As an alternative, the report presents the results of simulations. The red bar below shows where the observed 51 cases lie relative to a Poisson distribution with mean 38.9. (The Poisson distribution is the simplest assumption for event counts. Note that its mean and variance are equal.)


The caption notes that the "percentage of the simulated counts greater or equal to the observed count is 3.5%". This is equivalent to a one-sided test, which rejects (at the 5% level) the hypothesis that this is a chance finding. (Generally speaking, two-sided tests are preferred because they are more conservative and do not presuppose a direction of deviation.)

As noted above, two specific types of cancer are of particular concern. Eight cases of cancer of the blood or lymphatic system were observed compared to the expected 3.4, an ISIR of 2.37 with a 95% confidence interval of 1.02 to 4.68. Three cases of cancer of the biliary tract (cholangiocarcinoma is part of this category) were observed compared to the expected 0.7, an ISIR of 4.48 with a 95% confidence interval of 0.92 to 13.08.

There are always limitations

The report notes that:

• The small population size of Fort Chipewyan limits the ability to interpret results. In larger populations, one additional case does not have the same impact.
  
• The increased rates observed were all based on a small number of cases.
  
• The First Nations in Fort Chipewyan may have unique characteristics that are different from other First Nations communities in Alberta; this cannot be accounted for in the current analysis.
  
• This study was not able to account for the effect of migration on the cancer rate calculation.
  
• The study was not designed to determine whether living in Fort Chipewyan elevated cancer risk.
  
• The study was not designed to determine the cause of any of the cancers experienced in Fort Chipewyan.
  

Cluster distruster?

In Cancer as an Environmental Disease, edited by Polyxeni Nicolopoulou-Stamati et al., A. Novogradec and S. Harris Ali note (p.25) that:

The value of studying cancer clusters has been questioned by those who contend that little has been gained in terms of acquiring etiological understanding ... Such critiques commonly cite the issue of 'pre-selection bias' or the 'bulls-eye problem'.

But they go on to say that:

... clusters at the very least should signal the possibility that there may be a common source or mechanism for carcinogenesis amongst members of the cluster.

There is a lot more that could be said about the particular situation at Fort Chipewyan (including evidence of environmental contamination and its sources), about the strengths and weaknesses [pdf] of the study, about epidemiological methodology for investigating cancer clusters, and about the history of other cancer clusters around the world. My sense is that the answers may not be straightforward.

Update 09Feb2009: Here are two interesting blog posts on the subject, one from Ken Chapman and the other from Metis Bare Facts. Also note that the U.S. National Cancer Institute and Centers for Disease Control and Prevention both have good pages on cancer clusters.