Occasional reflections on Life, the World, and Mathematics

Obesity and cancer


The Guardian has prominently posted a report by Cancer Research UK with a frightening headline:

Obesity to eclipse smoking as biggest cause of cancer in UK women by 2043

That’s pretty sensational. I was intrigued, because the mortality effects of obesity have long intrigued me. It seems like I’ve been hearing claims for decades, loudly trumpeted in the press, that obesity is turning into a health crisis, with the mortality crisis just around the corner. It seems plausible, and yet every time I try to dig into one of these reports, to find out what the estimates are based on, I come up empty. Looking at the data naively, it seems that the shift from BMI 20 to BMI 25 — the threshold of official “overweight” designation — has been associated in the past with a reduction in all-cause mortality. Passing through overweight to “obesity” at BMI 30 raises mortality rates only very slightly. Major increases in mortality seem to be associated with BMI over 35 or 40, but even under current projections those levels remain rare in nearly all populations.

There is a chain of reasoning that goes from obesity to morbid symptoms like high blood pressure and diabetes, to mortality, but this is fairly indirect, and ignores the rapid improvement in treatments for these secondary symptoms, as well as the clear historical association between increasing childhood nutrition and improved longevity. Concerned experts often attribute the reduction in mortality at low levels of “overweight” to errors in study design — such as confusing weight loss due to illness with healthy low weight — which has indeed been a problem and negative health consequences attributable to weight-loss diets tend to be ignored. All in all, it has always seemed to be a murky question, leaving me genuinely puzzled by the quantitative certainty with which catastrophe is predicted. Clearly increasing obesity isn’t helping people’s health — the associated morbidity is a real thing, even if it isn’t shortening people’s lives much — but I’m perplexed by the quantitative claims about mortality.

So, I thought, if obesity is causing cancer, as much as tobacco is, that’s a pretty convincing piece of the mortality story. And then I followed up the citations, and the sand ran through my fingers. Here are some problems:

  1. Just to begin with, the convergence of cancers attributable to smoking with cancers attributable to obesity is almost entirely attributable to the reduction in smoking. “By 2043 smoking may have been reduced to the point that it is no longer the leading cause of cancer in women” seems like a less alarming possible headline. Here’s the plot from the CRUK report:
    Screenshot 2018-09-24 11.48.43
  2. The report entirely conflates the categories “overweight” and “obese”. The formula they cite refers to different levels of exposure, so it is likely they have separated them out in their calculations, but it is not made clear.
  3. The relative risk numbers seem to derive primarily from this paper. There we see a lot of other causes of cancer, such as occupation, alcohol consumption, and exposure to UV radiation, all of which are of similar magnitude to weight. Occupational exposure is about as significant for men as obesity, and more amenable to political control, but is ignored in this report. Again, the real story is that the number of cancers attributable to smoking may be expected to decline over the next quarter century, to something more like the number caused by multiple existing moderate causes.
  4.  Breast cancer makes up a huge part of women’s cancer risk, hence a huge part of the additional risk attributed to overweight, hence presumably makes up the main explanation for why women’s additional risk due to overweight is so much higher than men’s. The study seems to estimate the additional breast cancer risk due to smoking at 0. This seems implausible. No papers are cited on breast cancer risk and smoking, possibly because of the focus on British statistics, but here is a very recent study finding a very substantial increase. And here is a meta-analysis.
  5. The two most common cancers attributable to obesity in women — cancer of the breast and uterus — are among the most survivable, with ten-year survival above 75%. (Survival rates here.) The next two on the list would be bowel and bladder cancer, with ten-year survival above 50%. The cancer caused by smoking, on the other hand, is primarily lung cancer, with ten-year survival around 7%, followed by oesophageal (13%), pancreatic (1%), bowel and bladder. Combining all of these different neoplasms into a risk of “cancer”, and then comparing the risk due to obesity with that due to smoking, is deeply misleading.

UPDATE: My letter to the editor appeared in The Guardian.

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