Number needed to screen (and number needed to diagnose)

The number needed to screen is the reciprocal of the absolute risk difference in disease-specific mortality between an invited group and a control group: how many people must be invited to, or must undergo, screening for one death from that disease to be prevented over a stated follow-up. Its companion, the number needed to diagnose, is how many extra cancers must be found to prevent that one death, and is the arithmetic of overdiagnosis. Neither is a property of the test. Both depend on the follow-up length, on the disease risk of the population, on the screening interval and threshold, and on whether the denominator counts men invited or men actually screened.

The European Randomized study of Screening for Prostate Cancer is the reference. At a median 9 years of follow-up in the predefined core age group of 162,243 men aged 55 to 69, the rate ratio for prostate cancer death was 0.80 (95 percent confidence interval 0.65 to 0.98), the absolute risk difference 0.71 deaths per 1,000 men, and 1,410 men had to be screened and 48 additional cases treated to prevent one prostate cancer death. At 16 years, in 162,389 men of the same core group, the rate ratio was 0.80 (0.72 to 0.89), the absolute mortality difference had grown from 0.14 percent at 13 years to 0.18 percent, the number needed to be invited had fallen to 570 from 742 at 13 years, and the number needed to diagnose had fallen to 18 from 26. The direction of travel is the point: the benefit accrues with time while the overdiagnosed cancers are all counted up front, so a number needed to screen quoted without its follow-up is close to meaningless.

Three cautions. First, ERSPC's 1,410 counts men screened and its 570 counts men invited, which are different denominators, and the second is the one that matches how a programme is offered. Second, PLCO reported no significant mortality difference in 76,693 United States men, but screening in its control group rose from 40 percent in the first year to 52 percent in the sixth, so its comparison is organised against opportunistic screening and no number needed to screen can be computed from it. Third, none of these figures came from a modern pathway: the trials randomised a blood test, not magnetic resonance imaging triage followed by targeted biopsy and active surveillance, and both the numerator and the denominator move when the pathway changes. The 2018 United States task force expresses the same quantity the other way up, as about 1.3 prostate cancer deaths and about 3 metastatic cases prevented per 1,000 men screened over about 13 years.