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With apologies to Albert: everything is not relative
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1. Dr David L Streiner, PhD, CPsych
1. Assistant VP, Research Director, Kunin-Lunenfeld Applied Research Unit,
Baycrest Centre for Geriatric Care and Professor, Department of Psychiatry,
University of Toronto; dstreinerklaru-baycrest.on.ca

## Statistics from Altmetric.com

This year marks the 100th anniversary of Einstein’s annus mirabilis, in which he published four papers that transformed the world of physics. One of these earned him the Nobel prize, and another introduced the concept of relativity. With all due respect to his genius, this paper will argue that, at least when it comes to reporting the results of randomised controlled trials (RCTs), relative indices, such as the relative risk (RR) and the odds ratio (OR), tell only half the story, and that half is often wrong. The impetus for this editorial was the CAPRIE trial,1 although the message applies to all trials that use relative indices.

The study found that there was a relative risk reduction (RRR) of 8.7% when patients in the three diagnostic groups (ischaemic stroke, heart attack, and peripheral artery disease) were combined. At first glance, this seems extremely impressive. However, the fact that the p level was a marginally significant 0.043, with over 17 500 patient years in each of the experimental and comparison groups, raises a flag that perhaps something is amiss, and that 8.7% should be looked at more closely. To explore this, let’s imagine a much smaller trial, with only 50 patients in each of the two groups. In the treatment group, 20 patients die; in the control group, 30 die. This is summarised in table 1.

Table 1

Small hypothetical trial

The risk of dying in the treatment group (RT) is 20/50 = 0.40; and in the control group, RC is 30/50 = 0.60. Hence, the RR is RT/RC, or 0.40/0.60 = 0.67. The absolute risk reduction (ARR) is RC−RT, or 0.60−0.40 = 0.20. Finally, the RRR is ARR/RC, which is 0.20/0.60, or 33%. Just looking at those numbers, we would again be very tempted to use the drug as part of our usual practice. Let’s repeat the study now, but with 5000 in each group and the same number of deaths, as in table 2.

Table 2

Larger hypothetical trial

In this case, RT = 20/5,000, or 0.004; RC = 30/5,000, or 0.006; and the ARR = 0.006−0.004 = 0.002. Now for the relative indices: RR = 0.004/0.006 = 0.67 and RRR = 0.002/0.006 = 33%. In this second situation, we have a drug that is virtually useless, yet the relative indices—RR and RRR—are identical to those in the first example. Obviously, we are not getting the full picture. That is why, whenever possible, EBMH also reports the number needed to treat (NNT), which is the reciprocal of the ARR. In example 1, the NNT is 1/0.2, meaning that five people must be treated to avoid one additional death. In the second example, the NNT is 1/0.002, or 500 must be treated to avoid one death. In the meantime, 499 people are exposed to any possible adverse risks of the drug, and they or the healthcare system must absorb the cost. Returning to the CAPRIE trial, the NNT for all events is 200 over two years, and for deaths it is 1165 at a cost of over \$1000 a year in Canada.

The lesson is that “relatively” is fine for physicists, but clinicians also need absolute numbers and NNTs to make sense of trial results.

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