On Magical Powers, Mathematics and the Effects of Air Pollution on our Health

I recently had the pleasure of giving a talk entitled “What does magic have in common with research on the health effects of air pollution?” at an adult education centre in Barcelona (CFA Bon Pastor). It was an enjoyable event organised to disseminate scientific information, in this case to explain why people like me who work in the field of environmental epidemiology spend most of our time estimating risks. And to explain how risks are essentially probabilities and that probability is a branch of mathematics.

People like me that work in the field of environmental epidemiology spend most of our time estimating risks

We started the session with a number of games that illustrate certain characteristics of the scientific mind. The first was an exercise, used in primary schools, that involved colouring the beads of a necklace following the instruction: "Continue to colour in the white beads following the same pattern".

Figure 1: Colour in the white beads following the pattern.

After discussing the solutions proposed by different people, we came to the conclusion that there are an infinite number of possible solutions that could be said to represent “a pattern”. Moral: In science, as in life, there are very few problems that have only one solution. It is a good idea to take nothing for granted, to set aside your preconceptions and to rely on reasoning.

Figure 2: There are innumerable ways to colour the beads on a necklace "following the same pattern". Each one of these examples follows a pattern.

In the course of two other games, I then demonstrated my (supposed) magical powers. In the first of these, I did a series of mathematical calculations in my head much more quickly than the others in the room, who used calculators. In the second activity, I read their minds, guessing the animal and the name of the country they were thinking of. Moral: Things that appear magical and illogical can often be explained by science (in this case I used the mathematical concept of the digital root).

If we assemble 23 people at random, the probability that at least two of them will share a birthday is over 50%, and this probability shoots up to 99% in a group of 57 people!

Then we went on to an illustration of how calculating probabilities to estimate risks can be a very useful technique when we have to make decisions. For example, we saw that if we assemble 23 people at random, the probability that at least two of them will share a birthday is over 50%, and that this probability shoots up to 99% in a group of 57 people!

Figure 3. Probability that at least two people in the group will have their birthday on the same day.

Another example. Candidates taking an examination to get a job as a secondary school teacher in Spain must write on one topic from a list of five that the examiners choose on the day by a random draw from a predefined list of 71 topics. How many of the 71 topics do I have to prepare to make it very likely that I will be able to write about at least one of the 5 topics chosen by the examiners on the day? It might surprise you to find out that I only need to prepare 19 of the 71 topics to achieve an 80%  probability. And if I prepare 26 topics, that figure rises to 90%. Moral: Knowing how to estimate risks can reduce levels of anxiety, stress, fear and lack of confidence.

Figure 4. Probability that at least one topic that I have prepared will be among the 5 selected in the random draw.

At this stage the group was prepared to hear more about how we work in the field of epidemiology, a branch of medicine that deals with assessing health risks when a population is exposed to a potential risk factor. For example, imagine the following conversation:

- A study says that if you smoke you have a lower life expectancy than if you don’t.

- I don't believe those studies because my grandfather has smoked since he was 16 and he is 93.

Now let us return for a moment to the game of shared birthdays. In total, there were 35 people in the room at the event. According to what we saw in Figure 3, the probability of finding at least two people in the group with birthdays on the same day was 80%. However, that was not the case on that day. Moral: Probability does not predict what will happen in a specific case but rather predicts what will happen when we look at many cases. In that hypothetical conversation, the first person is referring to an experiment "done many times", in other words to an average value (life expectancy). The second person, on the other hand, refers to a specific case (his grandfather). Epidemiology, derived from the Greek epi (upon) + demos (people) + logos (word, treatise) is not about specific people but rather deals with the population as a whole.

To take just one example of risk comparison, let us look at a study on the short-term effects of urban air pollution on the health of the city’s inhabitants

To take just one example of risk comparison, let us look at a study on the short-term effects of urban air pollution on the health of the city’s inhabitants. The first modern study of this type analysed a period of severe air pollution that occurred in London in 1952—an event called the Great Smog (smog was a new term coined by combining the words "smoke" and "fog").

Great Smog. London, 1952.

The peak in pollution during the Great Smog was accompanied by a peak in mortality. Moreover, a kind of delayed effect can be seen in that the peak in deaths is displaced to the right of the peak in pollution:

Figure 5: Relationship between air pollution and mortality during the Great Smog in London (1952). Source: Johns Hopkins Bloomberg School of Public Health. Creative Commons BY-NC-SA.

Today, in studies of this type, we analyse much longer periods (years instead of days). The figure below comes from a recent study undertaken by ISGlobal to analyse the short-term health impacts of air pollution in Barcelona.

Figure 6: Total daily mortality and levels of fine particulate matter (PM_2.5) in the atmosphere (Barcelona 2013 and 2014).

Now, unlike what we saw in Figure 5, the relationship between the peaks is not obvious. In such cases, we use statistical models to estimate the mortality risk for different hypothetical air pollution scenarios. In practice, the risk is usually estimated for two different scenarios: the observed scenario (that is, using the actual levels of pollution recorded) and a hypothetical reference scenario considered to be “safe” (for example, one in which the daily pollution levels remain below the safety threshold recommended by the World Health Organisation (WHO)). Without going into technical details, the statistical models used in these studies are sufficiently sophisticated to take into account other variables that can affect mortality, such as ambient temperature, the day of the week, the level of soy allergen produced by the Port of Barcelona, the number of cases of influenza in the city, and possible transient trends in mortality.

So, risk estimates are useful not only for deciding how much to bet on the chance that two people in a group will share a birthday or knowing how many topics I have to study to pass an exam. It also serves to show that if the levels of fine particulate matter (PM_2.5: particles with a diameter not exceeding 2.5 microns) in Barcelona remained within the limits recommended by the WHO, then we could avoid 160 deaths due to cardiovascular causes (3.6%) and 280,000 (1.3%) visits to a primary care centre due to short-term effects (6 days), every year. By the way, remember, those results are subject to a certain margin of error because statistics does wonders but it is not magic.