I am frequently asked to explain the difference between Absolute Risk, Relative Risk, Absolute Risk Reduction and Relative Risk Reduction. So here goes.....
Reading the newspaper this morning I was interested to see the headline:
"Among women who took tamoxifen for ten years, 25 per cent fewer had recurrences of breast cancer and 23 per cent fewer died, compared to those who took the drug for just five years."
"Drug can HALVE risk of breast cancer returning: Patients taking tamoxifen for 10 years instead of five 'better protected and less likely to die"
These headlines certainly grab the attention of the reader. Reading further into the articles it becomes apparent that we have a situation which would have actually gone against the guidance from the Association of the British Pharmaceutical Industry regarding advertising and promotion.
This states: "Reference to absolute risk and relative risk. Referring only to relative risk, especially with regard to risk reduction, can make a medicine appear more effective than it actually is. In order to assess the clinical impact of an outcome, the reader also needs to know the absolute risk involved. In that regard relative risk should never be referred to without also referring to the absolute risk. Absolute risk can be referred to in isolation"
So what are absolute risks, relative risks and relative risk reductions. Let me explain by way of a simple example.
Take a two group clinical trial, groups A and B. The outcome we are looking at is disease recurrence, so by the end of the trial the patients are classified as having disease recurrence or not after being on treatment for 2 years.
In Group A: 250 patients out of 404 showed disease recurrence
in Group B: 350 patients out of 402 showed disease recurrence
Absolute Risk can be looked at as the % chance of having disease recurrence in a group. So:
Absolute Risk of Disease Recurrence in A is 250/404 = 61.9%
Absolute Risk of Disease Recurrence in B is 350/402 = 87.1%
Absolute Risk Reduction is simply the difference in these %s, 87.1-61.9 = 25.2%
Relative Risk is the measure that describes the chance of observing disease recurrence in one group COMPARED to the other. It is actually the ratio of Absolute Risks.
In this example the Relative Risk is therefore: 61.9%/87.1% = 0.71
What does this mean? Well one interpretation is that the risk of disease recurrence in group A is only 71% that of group B. This is sometimes a little hard to visualise and therefore the measure that is used is Relative Risk Reduction (RRR). This is a measure of the reduced chance of disease recurrence in group A compared to B. RRR is simple to calculate as it is 1-RR.
In our example RRR = 1-0.71 = 0.29 (or 29%).
This is interpreted as the chance (or risk) of disease recurrence in group A is 29% lower than Group B. Which then leads to the statement of a 29% reduced risk.
If we then looked at a second example with the same disease recurrence measure.
In Group A: 20 patients out of 300 showed disease recurrence
in Group B: 28 patients out of 301 showed disease recurrence
If you work out the Absolute Risks they are A: 20/300 = 6.6%, B: 28/301 = 9.3%
If you work out the Absolute Risk Reduction 9.3-6.6=2.7%
If you work out the Relative Risk this is 6.6/9.3=0.71 which therefore leads to a Relative Risk Reduction of 1-0.71=0.29 (or 29%).
Interestingly that based on the Relative Risk Reduction both of the examples give the same answer, yet when looking at the Absolute Risks (or Absolute Risk Reduction) we see that the results are completely different.
It is now sensible to look back at the ABPI Guidelines and note that they require absolute risks to be presented if relative risks (or risk reductions) are presented. This allows the reader/prescriber/patient to better understand the results. A 29% reduction in relative risk may be a minimal increase in absolute risk benefit to a patient and this can be easily eroded when safety profiles, adverse events, quality of life considerations are taken into account. Whereas a 29% reduction in relative risk with a large benefit in absolute risk may be a much better result.
Going back to the Tamoxifen example. The figure presented is clearly relative and there is no clarification as to what the absolute risks are. I suspect that the we are looking at absolute risk per group in the region of 20% so the absolute risk reduction is around the 5% mark relating to a 25% relative reduction.
I expect that the Tamoxifen examples used a slightly different approach to getting the results rather than my simplistic examples above, e.g. time to event analysis and Hazard Ratios, but the same underlying questions have to be raised when looking at such media reports. Any result presenting a relative risk reduction need to be put into context by presenting the absolute risk to the patient.
Adrian M Parrott
Adrian is the PharmaSchool Subject Expert for Statistics and delivers the "Statistics for Non-Statisticians" Course. The Course has been delivered across the World for a wide variety of Pharma, Healthcare, CRO, Medical Communications and Academic Organisations in locations ranging from UK, US, Europe, India, China, UAE, South Africa, Thailand.