In the context of statistical analysis of randomised controlled trials, explain the following terms:

a) Risk ratio

b) Number needed to treat

c) P-value

d) Confidence intervals

## College Answer

**a) Risk ratio **

A risk ratio is simply a ratio of risk, for example, [risk of mortality in the intervention group] / [risk of mortality in the control group].

It indicates the relative likelihood or experiencing the outcome if the patient received the intervention compared with the outcome if they received the control therapy.

**b) Odds ratio **

Odds ratio is the odds of an event occurring in one group to the odds of it occurring in another

**c) Number needed to treat (NNT)**

Number of patients that need to be treated for one patient to benefit compared with a control not receiving the treatment

1/(Absolute Risk Reduction)

Used to measure the effectiveness of a health-care intervention, the higher the NNT the less effective the treatment

**d) P-value **

A p-value indicates the probability that the observed result or something more extreme occurred by chance. It might be referred to as the probability that the null hypothesis has been rejected when it is true.

**e) Confidence intervals **

The confidence intervals indicate the level of certainty that the true value for the parameter of interest lies between the reported limits.

For example:

The 95% confidence intervals for a value indicate a range where, with repeated sampling and analysis, these intervals would include the true value 95% of the time

## Discussion

This is a straighforward question about the definitions of basic everyday statistics terms.

Judging by the relatively high pass rate, over two thirds of us already have a fair grasp of this.

Additionally, please note the model answer to the odds ratio question. Clearly we are not expected to demonstrate a genius-level understanding of these concepts. In fact, there is no odds ratio mentioned in the college question, and the very existance of it is inferred from the fact that there is an odds ratio answer.

Anyway, it never hurts to revise the basics.

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

In brief:

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

**Odds ratio:** The odds of an outcome in one group / odds of that outcome in another group.

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

**p-value** in a research study is the probability of obtaining the same (or more extreme) study result assuming that the null hypothesis was true. It is the probability that the null hypothesis was incorrectly rejected. As a single-value assessment of error rate, the p-value has its opponents.

**Confidence interval:** CI gives a range of results and the percentage chance that the same experimental design would produce results within this range if the experiment were repeated. Thus, a CI of 95% means that in 95% of repeated experiments the results would fall within the specified range.

The CI is a pain in the arse to calculate for the mathematic-averse *Homo vulgaris*. A good impression of the difficulty involved can form if one reads one of these two BMJ articles.

### References

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.

Szumilas, Magdalena. "Explaining odds ratios." *Journal of the Canadian Academy of Child and Adolescent Psychiatry* 19.3 (2010): 227.

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.

Goodman, Steven N. "Toward evidence-based medical statistics. 1: The P value fallacy." *Annals of internal medicine* 130.12 (1999): 995-1004.

Morris, Julie A., and Martin J. Gardner. "Statistics in Medicine: Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates." *British medical journal (Clinical research ed.)* 296.6632 (1988): 1313.

Campbell, Michael J., and Martin J. Gardner. "Statistics in Medicine: Calculating confidence intervals for some non-parametric analyses." *British medical journal (Clinical research ed.)* 296.6634 (1988): 1454.