Step 1

Introduction:

Association and causation:

Association:

Consider two variables, say, X and Y. These will be considered to be “associated”, if any of the following is observed:

An increase occurs in the values of X and Y simultaneously;
When an increase occurs in the value of X a decrease occurs in the value of Y;
When an increase occurs in the value of Y a decrease occurs in the value of X.

Note that, this increase-increase or increase-decrease relationship is merely an observation. Such an observation simply suggests that X and Y are somehow related; it does not indicate anything about how they are related.

Causation:

The two variables, X and Y would be considered to have a “cause-and-effect” relationship, if the values of one variable determine the values of the other variable.

Conventionally, we take X as the independent variable and Y as the dependent variable (there is nothing wrong, conceptually if you take the opposite).

There is “causation”, if it is known that X causes Y, and that, the observed values of Y are directly due to the observed values of X.

Step 2

Explanation:

From the above discussion, it can be understood that “association” and “causation” are not the same.

If X causes Y, it would very well imply that the variables are definitely associated or “related”, because, one variable is the cause and the other one is the effect of that cause and this in itself is the association or relation.

However, if we know just about an association between two variables, we simply do not have enough information to conclude anything about causation. For all that we know, the association between the variables may be due to some other factor, which we are not even aware of. It is quite likely that there is a third variable, Z, which causes X in a chain of events, and also causes Y, in a completely separate and independent chain of events. In such a situation, the observed association between X and Y would be because of their individual, and independent cause-and-effect relationship with Y.

In this case, development of a neurological disease is observed among some children who had been given a vaccine. However, nothing is known about the occurrence of the same disease among children who did not receive the new vaccine. So, the rates of occurrence of the neurological disease among the children receiving and not receiving the new flu vaccine are not known, which would help to carry out a comparison. It may be that there was something else common among the children who were given the flu vaccine, that might have caused the disease. Taking these into consideration, it may at most be said that applying the new vaccine and developing the neurological disease are “associated”. It does not mean that the vaccination caused the disease, just because the vaccination took place first and the disease later.

On the other hand, it might also be possible that the children given the new vaccine were representative of several different types of population, and the causes of variations among them were properly controlled for; the occurrence of the neurological disease may have been observed across the vaccinated children of the different populations. If the study was performed in a way to eliminate lurking variables as much as possible, and information is available on the occurrence of the disease among children who were not vaccinated, then it may be possible to conclude if the vaccine really “caused” the disease.

Thus, the two possible statistical explanations for the result are:

Vaccination by the new flu vaccine and occurrence of the neurological disease are associated, and the vaccination does not cause the disease.
The vaccination actually causes the development of the neurological disease.

However, the given information is not enough to determine which of the above two possibilities holds true in this case.

6.some of the children given a new flu vaccine later develop a neurological disease. Parents claim the vaccine caused the disease. What are the two possible statistical explanations for this result?

Public Answer