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## The difference between association, correlation and causation

• Study design & methods

Association. Correlation. Causation. Do you know the difference?

It is easy to confuse association and correlation. In every-day language, association and correlation are used as synonyms. However, association is not a technical term, and merely means that there is some sort of general relationship between two variables. Correlation, on the other hand, is a statistical measure which determines the co-relationship or association between two variables. The correlation coefficient is the measure used for the strength of the association. In order to establish a causative relationship, several criteria must be fulfilled, as discussed in this article.

## Association versus correlation

It is important to understand that association is a non-technical term. Correlation is measured by a correlation coefficient, and requires that there is an association between two variables, but association does not imply correlation.

## The correlation coefficient

The correlation coefficient is a numerical value that refers to the extent to which two variables move together in an increasing or decreasing trend. Correlations can be linear or non-linear. For quantitative and ordinal data, there are two primary measures of correlation: Pearson's correlation (r), which measures linear trends, and Spearman's (rank) correlation (s), which measures increasing and decreasing trends that are not necessarily linear, but can be U-shaped or J-shaped. Pearson's correlation assumes that both variables are normally distributed, whereas Spearman's (rank) correlation is non-parametric.

## Association does not mean causation

Causation requires that there is an association between two variables, but association does not necessarily imply causation. Association between two factors can occur both with and without a causal relationship. If we conduct a study and observe that individuals that invest heavily in sports gear have reduced risk of developing heart failure, we cannot conclude that buying sport gear protects against cardiovascular disease (causal relationship). A hypothesis would be that people buying sports gear are physically active, a known protective factor. Physical activity is here a confounding variable and the common cause to both investments in sports gear and reduced risk of developing heart failure.

## Causation in epidemiological studies

In epidemiologic research, the aspects of an association between two variables that guide a conclusion of cause and effect, have been particularly well studied. Historically, the association between smoking and lung cancer spurred the seminal paper by Sir Austin Bradford Hill that proposed a series of nine aspects (often called “criteria”) that should be considered before a conclusion of causation is drawn:

1. Strength of association can be demonstrated by valid statistical tests

2. Consistency - the association has been demonstrated repeatedly in independent studies

3. Specificity - the association is limited to precise exposures and outcomes

4. Temporality - the outcome follows the exposure

5. Biological gradient - dose-response relationship

6. Plausibility - the causal relationship is not inconsistent with the current understanding of biological mechanisms even though it may be new or unexpected

7. Coherence - proposed causal relationship fits with the other generally known facts of the conditions being studied

8. Experimental evidence - interventional studies or laboratory experiments support a conclusion of causation

9. Analogy - similar causal relationships have been identified previously

These nine aspects are important inputs to both study design and to the scientific process in general. In most cases there is a long process from identifying and describing a disease or condition to generating a hypothesis, test it in both experimental conditions and in clinical trials and to finally repeat the findings by independent research groups under different conditions. However, Hill´s criteria guides both how to evaluate various study designs and how to evaluate the strength of the conclusions in scientific reports. Temporality is a good example, as prospective studies are generally much more convincing compared to retrospective study designs. The strength of association demonstrated by valid statistical tests and methods supported by biological dose-response relationships, are also important factors to consider.

## Statistically significance vs clinically significance in medical research

An important criterion for drawing conclusions in medical research is that the observed relationship between variables is statistically significant. However, in clinical studies results may be statistically significant, but the findings may still be biologically irrelevant. If the sample size is high, even weak correlations can be statistically significant. Often there are multiple factors that contribute to the outcome, and the parameter being studied is just one determinant. In interventional studies, the magnitude of the treatment effect is usually the most relevant measure. Thus, it is important to keep in mind that clinical significance reflects the biological impact and potential consequence for clinical practice, whereas statistical significance only indicates the reliability of the results.

Standardized study designs and widely accepted statistical tests and procedures with established cut-off values offers a framework for evaluating the statistical significance. The clinical significance, however, is a more multifactorial judgment where many factors play in; examples are strength, consistency and longevity of the treatment effect, adverse events and tolerability, whether the treatment has a noticeable and meaningful subjective impact on the patients´ lives, cost-effectiveness, and ease of implementation.