How we define a problem can influence the solution we come up with. To arrive at the best solution it is crucial to avoid biases, habitual ways of seeing, and unwarranted assumptions about what is important – in other words, to see the problem with “fresh eyes.” It goes without saying that this is difficult to do.
We all tend to focus on certain salient aspects of a problem, and these can obscure other aspects, which may be essential to consider. Experts are not exempt from this tendency, which is particularly in evidence among those who formulate policy.
Artists have long used a variety of techniques to free themselves from the rote and therefore deadening habits that we all fall into. We are so used to the objects around us – the human figure, a chair – that it is difficult not to substitute our idea of the figure or chair for what is actually there. One trick artists use to circumvent these preconceptions is to draw what is NOT the figure, or NOT the chair – what is referred to as the “negative space” surrounding the object.
The most dazzling example of the power of negative space comes from the efforts of analysts during World War II to reduce the enormous losses of aircraft and lives of flight crews that were routine during missions from British airfields over the German industrial heartland.
The main workhorse of the allied air campaign against Germany was the Lancaster four-engine bomber. However, due to its weight and slow speed the bombers suffered very high losses from German night fighters. By one estimate, the chances of a crew reaching the end of a thirty-mission tour was about 25 percent.
An émigré mathematician from Eastern Europe, Abraham Wald, came up with an inspired solution to the problem. Analysts had proposed adding armor to those areas of the aircraft which showed the most damage. What Wald realized was that the damage sustained by the aircraft that returned safely represented areas that were not fatal to the plane’s survival. The fact that there were areas of the returning planes that showed no damage led him to surmise that these were the vulnerable spots that must have led to the loss of the planes to enemy fire. Thus, it was these areas that needed to be reinforced.
In other words, making an inspired leap, Wald posited that there must be a crucial difference in the pattern of damage between those bombers that returned and those that did not.
Wald’s approach to estimating aircraft survivability was used during World War II and by the U.S. Navy and Air Force during the Korean and Vietnam Wars. Today his analysis — which was carried out without computers — is considered a seminal contribution to statistics and specifically to the problem of “missing data.”
Writing about Wald’s work on aircraft survivability in the leading statistics journal in 1984, two statisticians concluded that, “While the field of statistics has grown considerably since the early 1940’s, Wald’s work on this problem is difficult to improve upon… By the sheer power of his intuition, [he] was … able to deal with both structural and inferential questions in a definitive way.”
More broadly, Wald’s analysis provides an example how crucial it is to consider the full range of relevant data, rather than confining oneself to a biased sample (i.e., the planes that returned safely) or to the usual categories.
In the health sciences, where we are trying to understand the causes of complex, multi-factorial chronic diseases, we often tend to focus on what is near-at-hand – the usual suspects – which may actually turn out to play no role or to play only a minor role. This is because, getting to the bottom of what causes brain cancer, lung cancer in people who have never smoked, Alzheimer’s disease, Lou Gerhig’s disease, scleroderma – to name just a few — is difficult and frustratingly slow and faces difficult methodological problems. So it is easier to point to the associations we have, even if these are weak or questionable. In other words, we don’t like to admit that the major portion of the explanation is missing. But this amounts to looking for one’s keys under the lamppost just because that’s where the light is.
It’s surprising that this story is not better known, even among statisticians! It provides a powerful example of how to approach a challenging problem by making room for the unknown – and has the widest application to problems from climate change to identifying the causes of complex, chronic diseases, and many other areas as well.
Geoffrey Kabat is a cancer epidemiologist at the Albert Einstein College of Medicine and author of Hyping Health Risks: Environmental Hazards in Everyday Life and the Science of Epidemiology.