The Patient Was…

Many, if not most, things in the world are connected in some way to something else. A truly independent event or phenomenon is rare. The apparent independence of some events probably reflects our inability to recognize their connection or relationship to some other circumstance.

The manner in which things are connected to one another is important to our understanding of the world around us and to our ability to influence the effects and outcomes of these relationships. Among the major different types of connections between and among entities are causation, association, and correlation.

The easiest of these types of relationships to understand is probably causation. Simply put, one thing causes the other. If we say that A causes B, we easily grasp the idea. If I punch you in the nose and your nose bleeds, we can correctly conclude that the punch caused the bleeding. But even an idea as simple as cause and effect has nuances that are vital to our full understanding of the concept.

If A causes B, does it always do so, or are there other circumstances that affect the relationship? Can A by itself cause B? In other words, is A alone a “sufficient” cause of B or is something else required? Can B occur without A, or is A a “necessary” cause of B?

If we apply these questions to the example of the punch in the nose, it should be obvious that the punch does not always cause a nosebleed. Maybe the punch is too light. Maybe you are moving away, and the punch isn’t as forceful when it lands. Maybe you’ve stuffed cotton in your nose in anticipation of a punch, so your nose doesn’t bleed. (Kirk Douglas does this in a movie when he knows he is going to be beaten up by some sheriff’s deputies in a western movie.)

Is a punch in the nose a necessary cause of a nosebleed? Of course not. You could slip and fall on your face and develop a nosebleed. You could even blow your nose too hard, and it might bleed. So, many things can cause a nosebleed besides a punch.

We can thus see that even in a cause-and-effect relationship, there are nuances that come into play. The cause can be “sufficient,” that is, it can create the effect by itself. If it is not “sufficient,” then something else is also required for the effect to occur. The cause may or may not be “necessary.” If it is, then that cause must be present if the effect is to occur; but if it is not “necessary,” then other things can also cause the effect.

Think, then, of the combinations that might be present. A cause could be sufficient but not necessary, meaning it can create the effect by itself, but other things could also cause the effect. The cause could be sufficient and necessary, meaning it can cause the effect by itself, and it must be present if the effect is to occur, regardless of what other contributing causes there may be. A cause could be not sufficient, meaning it cannot cause the effect by itself. If it is not sufficient but is necessary, then some other cause must also be present. And if a cause is neither sufficient nor necessary, then other things can create the effect without its presence or influence.

These considerations are not just semantics, because if effects or outcomes are to be created or negated, it is essential to understand the causation of the outcomes to be affected or manipulated.

Another type of connection between things is “association.” The term is a more general one and can refer to various types of relationships between and among two or more entities. The relationship could be cause-and-effect but is not necessarily so. Association just implies some statistical dependence between two or more things. The dependence could be due to a common cause, or it could even be coincidental.

Note that there can be “positive” and “negative” associations between things. A positive association means that as the statistical values of one thing increase, the values of the other increase. And when the values of one entity decrease, the values of the other do as well. The relationship is more directional than numerical, but there is a discernible dependence of one thing on the other.

Yet another type of connection between things is “Correlation.” Whereas  “Association” is a rather general term indicating some dependence between things, “Correlation” refers to a more numerical and statistical relationship. It defines the strength and direction of two variables. If things are perfectly correlated, they change by the same numerical or statistical values. If correlation is less than perfect, the degree of numerical and statistical closeness can be defined mathematically by what are called correlation coefficients.

Correlation, like association, does not necessarily imply causation. Things may move in the same direction and by the same amount due to chance or coincidence. An example on the Science News website highlights an almost perfect correlation between the consumption of margarine among Americans and the divorce rate in Maine over ten years. Another example, recalled from my medical school Statistics course, showed a very close correlation between the incidence of Tuberculosis cases in India and the production of cars in Detroit. Clearly, there is no rational explanation for these statistical correlations other than coincidence.

Correlation, like Association, can be positive or negative. If two numerical, statistical relationships move upward and downward in synchronized fashion, the correlation is said to be “positive.” If, on the other hand, they move by similar numerical and statistical amounts but in opposite directions, one moving up while the other moves down, then the correlation is described as “negative.”

If a punch in the nose, as described earlier, seems too extreme a scenario, let’s look at fever as another example. Fever is something we have all encountered and, while it can be a cause of certain things, it is much more often an effect. Many things can cause a fever: infections, inflammation, drug reactions, malignancies, and more. When physicians find fever in a patient, they look for a cause. They know that fever is associated with many things, but they must look elsewhere for the reason or reasons behind it. Since fever accompanies many conditions, it represents an association with those illnesses. In many instances, the degree of fever matches the severity of the illness. As the illness worsens, fever goes up; as the disease resolves, fever comes down. If the rise and fall of the fever with the severity of the illness match one another closely, then fever can represent a correlation with the disease. It can be used as one measure of success or failure in treatment. But treating the fever alone will not cure the underlying condition, because fever is not the cause.

One other term, “Confounding,” deserves brief mention. Confounding refers to the distortion of the apparent relationship between two things by a third, extraneous factor. It can create the appearance of a relationship between things when one might not actually exist. An example is a study done some years ago that concluded that coffee drinking was a cause of lung cancer. The data showed that coffee drinkers had a higher incidence of lung cancer than did people who did not drink coffee. This was somewhat alarming until another analysis revealed that many coffee drinkers were heavy cigarette smokers. A relook at the original data, examining the results only in coffee drinkers who did not smoke, showed no relationship between coffee and lung cancer. Smoking was a “confounder” in the original dataset.

The point of all this is that these different terms for the relationships and connections between things are not just semantic differences. They are basic to our understanding of the world we live in, and they underpin the efforts we may make to change that world. Think about the importance of understanding cause-and-effect, and its nuances, and the wasted time and expense if we address the wrong issues in trying to effect an outcome. Consider associations and correlations, and the ways in which they contribute to our attempts at mastery of our environment. And beware of confounders in examining apparent relationships.

There are connections and relationships in so much of what we experience in our lives.  Understanding the nature of these interactions is essential to our understanding and control of our world.