# Measures of Effect Size, Risk and Odds

## Effect size

Question 23 from the second paper of 2008 asked the candidates to define effect size. **Effect size ** is a quantitative reflection of the magnitude of a phenomenon; for example, the magnitude of the positive effects of a drug on the study population.

- In this case, it is the difference in the incidence of an arbitrarily defined outcome between the treatment group and the placebo group.
- Effect size suggests the clinical relevance of an outcome
- The effect size is agreed upon
*a priori*so that a sample size can be calculated (as the study needs to be powered appropriately to detect a given effect size)

## Measures of effect size

### Absolute risk

- Actual event rate in the group (treatment or placebo). Essentially, it is the incidence rate.

### Relative Risk (risk ratio)

**The rate of events in the treatment group, divided by the rate of events in the control group.** The college descrives it as "the difference in event rates between 2 groups expressed as proportion of the event rate in the untreated group". Essentially, it is a likelihood ratio: how much more likely is the outcome to occur in the treatment group as opposed to the control group?

### Odds ratio

**The Odds Ratio represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.**

Its not the same as the relative risk reduction.

Consider a treatment trial. The odds are calculated when the number of treated patients with the outcome is divided by the number of treated patients without the outcome. The result is the "odds" of having that outcome. Then, the number of control patients withe the outcome is divided by the number of patients without the outcome.

Now, you have two sets of odds: the odds of developing the outcome with the treatment, and the odds of developing it without the treatment. The odds ratio is one set of odds divided by the other.

An OR =1 suggests there is no association.

If the CI for an OR includes 1, then the OR is not significant (i.e. there might not be an association).

Odds ratio ended up appearing in Question 2 from the second Primary Exam paper of 2008, and therefore a more extensive discussion of OR and risk is carried out in the CICM Primary statistics summaries.

### Relative risk reduction

**RRR= absolute risk reduction divided by the control group risk.**

Or, one can calculate it by subtracting relative risk (RR) from 1.

Thus, RRR = (1-RR)

### Absolute risk reduction

**This is the difference between the baseline population risk and the treatment risk.**

It is an effective way of demonstrating a treatment effect.

ARR = incidence in exposed - incidence in unexposed

### Attributable risk

This is a measure of the absolute effect of the risk of those exposed compared to unexposed.

AR = Incidence(exposed) – Incidence(unexposed)

### Numbers needed to treat or harm

One must use the absolute, rather than the relative, values here. NNT is the inverse of absolute risk reduction.

Lets say the absolute risk reduction is 10%. Thus, NNT = 1/0.1, or 10.

## References

Barratt, Alexandra, et al. "Tips for learners of evidence-based medicine: 1. Relative risk reduction, absolute risk reduction and number needed to treat." *Canadian Medical Association Journal* 171.4 (2004): 353-358.