LogicalMANIPULATIVE

Number Needed to Treat Omission

What it is

Advertising or reporting a treatment's benefit in a form — a relative reduction, a “36 percent” — from which the audience cannot recover how many people must be treated for one to benefit, and leaving out the matching number for harm.

How it works

The number needed to treat, introduced by Laupacis, Sackett and Roberts in 1988, is the absolute risk reduction turned into a headcount: if a drug lowers the rate of an event from 3 percent to 2 percent, one percentage point is prevented, and a hundred people must take it for one to be spared. The same trial reported as “a 36 percent reduction” — one is 36 percent less than three, near enough — sounds as if it applies to the person hearing it. Pfizer's 2006-2008 Lipitor advertisements, fronted by the artificial-heart pioneer Robert Jarvik, led with the 36 percent and put the 3-versus-2 in a footnote; the number needed to treat over the trial's three-odd years was about a hundred. The omission is the tactic: the relative figure is the one format from which the headcount cannot be recovered, and the harms — the number needed to harm — are left out because they would sit beside it. Gigerenzer's mammography working shows the other side: of 1,000 women screened for ten years, about 4 die of breast cancer against about 5 unscreened, a number needed to screen near 1,000, alongside roughly 100 false alarms. Both numbers are what a person needs to decide, and neither appears in the leaflet that says “reduces deaths by 20 percent”.

Real-world examples

  • •Pfizer's Lipitor campaign of 2006-2008 advertised a 36 percent reduction in heart-attack risk, with a footnote explaining that in a large study 3 percent of patients on placebo and 2 percent on the drug had a heart attack; the underlying ASCOT-LLA trial implied that about a hundred patients would take the drug for three years for one heart attack to be prevented. The advertisements were withdrawn in 2008 after congressional scrutiny.
  • •Breast-screening invitations in several countries have described a 20 percent (or larger) reduction in breast-cancer deaths without the absolute figures; Gigerenzer and colleagues translated it as roughly one death prevented per 1,000 women screened over ten years, alongside about a hundred false alarms and a number of unnecessary treatments.
  • •Statin marketing to low-risk patients quotes relative reductions drawn from trials in high-risk patients; because the absolute risk is lower in the target group, the number needed to treat is several times larger than in the trial, and the advertisement does not say so.
  • •Schwartz, Woloshin and Welch's drug facts box, tested in 2009, presents benefit and harm as events per 100 people with and without the drug; in trials it improved understanding markedly, which is the measure of what the standard format withholds.

Ethical guidelines

  • ●Report every benefit as events per 100 or per 1,000 people with and without treatment, over a stated time, so the number needed to treat can be read off; add the relative figure if you like, never instead.
  • ●Report the number needed to harm beside the number needed to treat; a benefit without its harm is half a decision.
  • ●When applying trial results to a lower-risk group, say that the number needed to treat rises and by roughly how much.
  • ●Do not put the absolute figures in a footnote and the relative figure in the headline; the layout is the message.

How to defend against it

  • ►Ask the doctor or the advertisement one question: out of 100 people like me, how many are helped by this over how long, and how many are harmed?
  • ►When you see a relative reduction, look for the two absolute rates it came from — usually in the small print — and subtract; one divided by the difference is the number of people treated for one to benefit.
  • ►Ask whether the trial population resembled you; if the trial enrolled sicker people, your number needed to treat is higher than theirs.
  • ►Ask for a drug facts box or an equivalent side-by-side of benefit and harm per 100 people; the format exists and its absence is informative.
  • ►Treat “reduces risk by X percent” in an advertisement as a signal that the absolute figures were unimpressive, and go and find them.

From the Defense Playbook

Ask for Absolute Numbersseconds

When someone quotes a relative change ("cuts your risk by 50 percent", "doubles the danger"), ask what the risk was before and after in plain counts out of the same number of people, because the same fact sounds enormous as a ratio and modest as a difference.

Every playbook entry states how strong its evidence is and when not to use it. Browse the full playbook.

References

  1. Laupacis, A., Sackett, D. L., & Roberts, R. S. (1988). An assessment of clinically useful measures of the consequences of treatment. New England Journal of Medicine, 318(26), 1728-1733
    The introduction of the number needed to treat as the absolute risk reduction expressed as a headcount.
  2. Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients make sense of health statistics. Psychological Science in the Public Interest, 8(2), 53-96
    The mammography working (about 4 versus 5 deaths per 1,000 women over ten years) and the case for absolute formats over relative ones.
  3. Sever, P. S., Dahlöf, B., Poulter, N. R., Wedel, H., Beevers, G., Caulfield, M., et al. (2003). Prevention of coronary and stroke events with atorvastatin in hypertensive patients who have average or lower-than-average cholesterol concentrations, in the Anglo-Scandinavian Cardiac Outcomes Trial — Lipid Lowering Arm (ASCOT-LLA). The Lancet, 361(9364), 1149-1158
    The trial behind the Lipitor 36 percent claim, with the absolute event rates from which the number needed to treat follows.
  4. Schwartz, L. M., Woloshin, S., & Welch, H. G. (2009). Using a drug facts box to communicate drug benefits and harms: Two randomized trials. Annals of Internal Medicine, 150(8), 516-527
    The side-by-side per-100 format and the trial evidence that it improves understanding of benefit and harm.
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