Correlation does not imply Causation

I just know, or Do I?

Mike Hartmann in a Ted Talk, titled, Unpacking the biases that shape our belief (https://www.youtube.com/watch?v=dU7Mhne4CzU) wherein he shares the following statistics:


One person reads the following headline:

77% of cases in whooping cough outbreaks were fully vaccinated!

Another person reads another headline as under:

Unvaccinated children had five-fold risk of getting pertussis!

And Mike read the following:

Pertussis outbreak in elementary high school with high vaccination rate


After reading these headlines, you as a reader may come to the conclusion that vaccines are not effective"


So let’s review the facts:

1. There were 208 school students and of which 195 were fully vaccinated against pertussis.
2. 35 cases of outbreak occurred.
3. 27 out of 35 elementary school students were in the fully vaccinated group and 8 in the not vaccinated group.

In other words while 14% of students vaccinated were effected, almost 62% of those unvaccinated were effected.

We all fall trap to intrinsic bias, that confirms our own beliefs of, “I just know!”
It is the interrogation of data that can free us from such bias. To start with, we must be willing to examine and review our own bias.

One way to review this is through Causal graphs. Causal graphs allow for us to talk about causal pathways both in an intuitive and pictorial way.

Lets first start with translating normal English to Causal Graphs or DAG (directed acyclic graph).

One needs to note that Causation and Association are different. When we find a correlation we say its is an association. However, when the variable (exposure) has an influence on the outcome, its is said to be causal. Is smoking ‘pot’ and having troubled relationship during teenage, an association or a causation?
And if one jumps of a cliff, would that be the cause of injury?

Let's review the following 4 cases:

(i). A----→ Y Cause and Effect

In figure I, A causes Y. The arrow from A to Y indicates this as a symbol.

        ------------------------------------->
(ii). L (parent)----→  A (child)       Y (grandchild) Common Causes

In figure ii, you could have common causes for Y occurring.

For example,
• Firstly you have data that L (smoking) causing Yellow Fingers (A), but there is no evidence that Yellow Fingers causes Cancer (Y).
• You may also have causation where Smoking (L) causes Y (Cancer)

            ------------------>
(iii).    A          Y ---→L Conditioning on Common Effect

In figure iii, there is a collider L, is an effect by two common causes, Y and A.

For example:

(L) Mortality can be caused both by Y (say Kidney Disease) or A (Age)
Of course, we can say Age causes Mortality too.

Age is therefore a common cause of KD and Mortality.

iv. Chance
Something happen by chance and there is no causality.

How do we start to eliminate bias?

We start with recognising Confounding. Confounding is the bias due to the presence of common cause and the outcome. For example, we may infer, that Yellow fingers caused by smoking leads to Lung Cancer!

Confounding can be detected when it must meet three criteria’s:

1. Must have an association with the outcome
2. Must be associated with the exposure
3. Must not be in the causal path of from exposure to outcome

While smoking may lead to lung cancer, there maybe an association with Coffee drinking and smoking, but Coffee drinking is not causal to lung cancer.

Judea Pearls Rules :

1. Two variables are d-separated* if all paths between them are blocked
2. Two variables are marginally or unconditionally independent if they are d-separated without conditioning.
3. If however, the collider is ‘conditioned’ a back entry is possible.

* d-separated is a relationship between three disjoint set of vertices in a directed graph.

As you explore data, you will soon recognise, associations, causal and confounding issues.

In conclusion to establish a causal relationship, one has to assess Consistency, Strength, Specificity, temporal relationship and coherence of the association.