Breast cancer, and probablities, in the news (again)

Angelina Jolie's New York Times editorial on her decision to have bilateral mastectomies when she tested positive for BRCA1 mutations associated with high risk of breast cancer brings up a number of issues.  We have previously commented on the problem of assessing competing risks, in the context of debates about screening, detection, and risk associated with breast cancer.  This is so common, and so serious, a problem that it naturally draws a lot of attention.   Just as naturally, it involves many sorts of probabilities: does a given test detect actual cancer?  Does every cancer need to be detected, or will some go away spontaneously?  And so on.

Under these kinds of conditions, the balance between costs, risks, important detection,  treatment options and the like all involve probabilities.  For example, Jolie writes that she was given an 87% probability of eventually having cancer.  Projecting risks--your net future in regard to this disease--is of vital interest, and because most of the probabilities involved are very inaccurately known, it is even a problem to know whether or to what extent to believe the probability estimates we already have. That is also why the same thing seems to require study over and over and over, without clear results.

In the end, for most women, and their physicians, whether they know it or not, they and their lives and health are highly dependent on the statistical aspects of studies to estimate and assess a wealth of probabilities.  In such cases, there are important, often wildly misunderstood or misapplied statistical approaches, and they often yield probabilities whose accuracy is not high or is even unknown.  Yet the point of statistical and probabilistic analysis is to make decisions about the state of the world.  If that is important, then how we interpret the results is important, but so, to a fundamental extent, is how we come to our results and interpretations in the first place.

This is so serious and widepread an issue in science, that we posted a very fine 2-page primer on statistical design and the basic nature of probabilistic inference that was written for MT by our very knowledgeable colleague, Jim Wood, here in our Department.

And yet, the Jolie story shows that under some circumstances, it is unnecessary and perhaps even wrong to worry about the details.  She decided to undergo double mastectomy as a preventive against breast cancer.  That is, she has decided that in a sense she already had breast cancer in the sense that it was a ticking time bomb in her genome.  Prevention being better than cure, she made that awesomely serious decision.

Jolie discovered that she carried one of the known variants in the BRCA1 gene that confer very high risk of breast (and ovarian) cancer.   She said she was told that the risk she'd get breast cancer was over 85%.  Now, there are actually major uncertainties about even this risk, as different cohorts of women (that is, born in different places or times) have very different risks as estimated by retrospective studies of women known to carry, compared to those known not to carry, such variants.  For some cohorts, the risk by age 60 or so has been estimated at only about half that in other cohorts.

Yet, here it doesn't matter and there is no need to worry about statistical finery or even the specific risk estimate.  Why?  Because under all the established risk scenarios, these mutations confer extremely high, potentially lethal risk.  It matters not at all, at least to most of us, whether a risk is 90% or 50%, if the risk is avoidable and the consequences dire.

Further, the BRCA1 gene function is basically known: it relates to corrections of DNA copying mistakes.  If miscopied DNA is not repaired, the risk is that in some breast cell a mutation will arise that leads the cell to be transformed into a cancer cell, that then proliferates and spreads.  So here we have not just estimates of very high risks, whatever they are, but also a mechanism.  And we have replicated findings in different populations.  So here, that these specific variants are truly risk factors themselves, rather than just being associated with some unmeasured factor, is pretty convincing--convincing enough to bet your life on it.

The nature of epidemiological risks
The cohort dependence of the BRCA1 risk for those with the clear-cut, well-studied variants, raises a very important point, one we've mentioned before.  Risks are expressed in terms of the likelihood of future events.  But how do we know what those are?  The answer is that we generally only know them from the past.  That is, we do retrospective studies, that compare those with or without exposure to a putative risk factor (here, a genetic variant) and see what happened to them.  We estimate how much more happened to those with, compared to those without, exposure to the risk factor.  But how can we predict future risk from such data?  The answer is basically an assumption that might be called uniformitarianism (a term related to the history of geology and that led Darwin to his insight about evolution): we assume that in all relevant ways, the future will be like the past.

That means that we assume that exposure to the same risk factors in the future will have the same effects as exposure did in the past (which we discovered from our sample of cases and controls, etc.).  But this assumes that we measured all the relevant factors in the past and, much more importantly, it assumes that people with the genetic risk factor will be exposed to same other factors in the future to an extent that justifies our uniformitarian extrapolation.

However, even if that were the case, we do not understand the many factors well enough and cannot, even in principle, know what exposures will be like in the future.  We simply do not know what our lifestyles will be like.  So, we have no way to make accurate risk  predictions.  It is, like the parts of the universe beyond which light cannot get here for us to see, literally beyond our reach.

This is why BRCA1 variants are 'lucky', in that whatever happens in regard to future lifestyles, there is no known scenario in which these variants would not also seem to confer very high risk.  The same cannot be said of the vast majority of genetic risk factors that are known today.  For them, risk estimates such as various genome-testing companies, or NIH's drive for 'personalized genomic medicine' are misleading--to an unknown extent.

It needs to be pointed out in this context that there are hundreds of other mutational variants in the BRCA1 gene (and in a handful of others, one of which is BRCA2) that are so rare and or were found only in patients' tumor cells, that we really cannot legitimately attribute causation to them.  Indeed, if they are too rare (as most are) we cannot apply statistical tests to even estimate risk.  All we can do is assume that the gene is relevant and therefore that the variant we find is causal.  Those variants are listed in disease-gene data bases as if they are causal, but that verges on simply being circular: assume a gene is causal and then conclude that the variant in that gene is therefore a cause.  That's bad reasoning.

Again, even here there are environmental (that is, non-genetic) risk factors that are not well established that may make an even larger proportional difference in risk, so that even if these various mutations are in fact causal in some way, that may depend entirely on the environmental context.  If so, that way is highly probabilistic and much farther from certain than the known variants in these genes. Or, some may be exceedingly dangerous, but not statistically demonstrable in the sense of probability that Jim Wood posted about in his excellent primer and discussion yesterday.

In fact, even here one can ask why the same BRCA1 mutations do not cause comparably elevated risks for any and all tissues in the body.  Such associations are generally low and not well established.  So here, the mechanism that seems to be known (DNA repair) should predict--should lead to a prior expectation of--high cancer risk in any tissue in which the gene's expressed.  In a standard 'Bayesian' analysis, the lack of strong effect in other tissues could actually undermine our confidence in our causal expectation for breast cancer itself.  Perhaps explanations for this exist, but we don't know of them.

Unfortunately, for most women there is no pre-smoking gun to guide what here are preventive decisions.  So while it's very unlucky to have inherited such a variant as Jolie did, in a strange sense she was very lucky.  At least she knew.  About 9-10 percent of women in developed countries (that is, where this has been studied) are at risk for breast cancer.  A close friend of ours has just had the same kind of operation as Jolie, but after a tumor was already found, and without carrying the known risk-variants.  Fortunately, although as we noted in our earlier post on this subject (link given above), the story is not entirely rosy, at least there are treatments that can be effective, even after the cancer has already occurred.

Everyone probably knows people who have been affected by breast cancer, and for many it's in their own families.  But unlike those with the clear-cut variants, they must face the kinds of exquisitely difficult decisions, based on very poorly understood, or inaccurate to unknown extent, competing probabilities.  For them, and for most of us in regard to the various disease time bombs silently ticking away inside us, the fine points of statistical analysis really are matters of life and death.  And they are fine points that nobody really understands.....and those who claim to are being misleading.