Weighing the Evidence: Relatives, Absolutes, and the Number Needed to Treat

Abstract

Interpretation of “significant” research findings can be challenging. Outcome differences can be reported in relative or absolute terms. Belshe et al reported that children who received live attenuated influenza vaccine had a 3.9% risk of influenza during the subsequent season, while children who received inactivated influenza vaccine had an 8.6% risk. This difference in influenza rates can be expressed as the absolute risk reduction (ARR), also known as risk difference, which is simply the arithmetic difference between the outcome rates in the treatment and comparison groups (ARR = 8.6% – 3.9% = 4.7%).The same difference in rates can be expressed as the relative risk reduction (RRR), which is the ARR divided by the risk in the comparison group (RRR = 4.7% ÷ 8.6% = 0.55 or 55%).Relative measures, including RRR, relative risk, and odds ratios, are helpful in understanding the etiology of disease or the efficacy of interventions. The finding that live vaccine is associated with an influenza rate that is 55% lower than the rate following inactivated vaccine helps establish that live vaccine “works” better than inactivated vaccine – ie, that it actually protects better against influenza.Large relative effects, however, do not always translate into important clinical effects.The clinical or public health importance of disease-causing exposures or effective treatments may be better appreciated from absolute measures. The 55% relative decrease in influenza rates with live vaccine translates into a 4.7% absolute decrease (ie, among vaccinated children, 4.7% fewer will have influenza if live vaccine replaces inactivated vaccine).The ARR can be converted into a very useful quantity called the number needed to treat (NNT), which is the number of patients one would need to treat with an intervention in order to realize one improved outcome. The NNT is simply the reciprocal of the ARR, rounded up to the next whole number (NNT = 100% ÷ 4.7% = 21.3). Thus, one would have to vaccinate 22 children with live vaccine rather than inactivated vaccine in order to prevent one additional case of influenza.In an analogous way, the number needed to harm (NNH) compares adverse effects of different treatments. Belshe et al noted that among children less than 24 months of age, medically significant wheezing occurred within six weeks of the first vaccine dose in 3.2% of those receiving live vaccine compared with 2.0% of those receiving inactivated vaccine. Thus, the absolute risk increase or risk difference is 1.2%. The NNH can be calculated as 100% ÷ 1.2% = 83.3. Thus, for every 84 children in this age group vaccinated with live vaccine rather than inactivated vaccine, one additional child will have medically significant wheezing.By considering the absolute effect of an intervention and the NNT (along with the NNH for any significant adverse effects), one can make a better-informed decision as to whether a new treatment should be applied in practice.