**In the context of clinical trials, define the following terms:**

**a) Relative risk**

**b) Absolute risk**

**c) Number needed to treat**

**d) Power of the study**

## College Answer

A number of potential definitions exist. One example for each is listed below:

**R****elative risk**: the difference in event rates between 2 groups expressed as proportion of the event rate in the untreated group.

**A****b****solute risk**: this is the actual event rate in the treatment or the placebo group.

**N****u****mb****er Needed to Treat**: The NNT is the number of patients to whom a clinician would need to administer a particular treatment for 1 patient to receive benefit from it. It is calculated as 100 divided by the absolute risk reduction when expressed as a percentage or

1 divided by the absolute risk reduction when expressed as a proportion.

**P****o****w****er of the study**: The probability that a study will produce a significant difference at a given significance level is called the power of the study. It will depend on the difference between the populations compared, the sample size and the significance level chosen.

## Discussion

Some of this ground is covered in Question 23 from the second paper of 2011. It also asks about risk ratio and NNT.

Here is a link to my summary of basic terms in EBM.

**Risk ratio:** risk in treatment group / risk in control or placebo group

**Absolute risk:** Risk of event in a group (any group). Essentially, it is the incidence rate.

**NNT:** Numbers needed to treat; 1/ absolute risk reduction.

**Power of a study:** The power of a statistical test is the probability that it correctly rejects the null hypothesis, when the null hypothesis is false. This is the chance that a study is able to discern a treatment effect, if there is an actual treatment effect. It is influenced by the level of statistical significance one expects, the sample size, the variance within the studied population, and the magnitude of the effect size.

### References

Cohen, Jacob. "Statistical power analysis." *Current directions in psychological science* 1.3 (1992): 98-101.

Cook, Richard J., and David L. Sackett. "The number needed to treat: a clinically useful measure of treatment effect." *Bmj* 310.6977 (1995): 452-454.

Viera, Anthony J. "Odds ratios and risk ratios: what's the difference and why does it matter?." *Southern medical journal* 101.7 (2008): 730-734.

Malenka, David J., et al. "The framing effect of relative and absolute risk."*Journal of General Internal Medicine* 8.10 (1993): 543-548.

Gail, Mitchell H., and Ruth M. Pfeiffer. "On criteria for evaluating models of absolute risk." *Biostatistics* 6.2 (2005): 227-239.