ORs and RRs are informative when summarizing case-control and cohort studies. However, when an investigator conducts a clinical trial, it is important to enumerate the effects of the intervention being studied. Patients and clinicians alike want to know when the benefits of an intervention outweigh the harms. One way to express the effects of the intervention is in terms of the RRR: the relative difference in the rate of an event (i.e., death, hospitalization, etc.) between the intervention and the nonintervention group. RRR is calculated by dividing the difference between rate of an event in the intervention group and nonintervention group by the rate of the event in the nonintervention group. For example, in a hypothetical trial, if an event occurs in 40% of the nonintervention group and in 20% of the intervention group, the RRR from the intervention is 0.50, or 50% (calculated as 40% minus 20%, divided by 40%). Another measure of the benefit or harm of an intervention is the ARR. This is the absolute difference in the rate of an event between the intervention and nonintervention group. To calculate ARR, the event rate in the intervention group is subtracted from the event rate in the nonintervention group. In the hypothetical trial above, the ARR would be 20%.11,14,15
Because the rate of an event in the nonintervention group serves as the denominator for calculating RRR, the RRR will always be greater than the ARR. And, as the event rate becomes smaller, the difference between the relative and ARR will widen, making the RRR appear more dramatic.14 However, RRR should be interpreted with caution. Because it is a relative measure, it does not take into account the base-line event rate in the control group. Therefore, when the event is very rare or very common, RRR will dramatically overestimate or underestimate, respectively, the true effects of the intervention. Contrarily, ARR does account for the event rate in the nonintervention group at baseline and, thus, provides a more clinically practical measure of the effect of the intervention.15 Hence, the ARR is often referred to as the attributable risk of an intervention.
Although both RRR and ARR are ways to understand the benefits of an intervention, they are not easily applied to individual patients. Instead, clinicians can employ a measure known as the number needed to treat (NNT) to better enumerate these effects in a clinically useful way. The NNT is defined as the number of patients that need to receive a treatment in order to prevent one patient from experiencing an adverse outcome over a specified period of time (the study period).16 It is calculated as the inverse of the ARR (1/ARR) and the smaller the NNT, the more effective the treatment. In the hypothetical trial above, the ARR was 20%. Therefore the NNT would be five, which is to say that five patients would need to receive the treatment to avoid one adverse outcome. However, the NNT can also be applied to individual patients: In the example, an individual patient has a one in five chance of benefitting from the treatment.14
In January, 2006, Vesikari, et al. published a study examining the safety and efficacy of a live pentavalent human-bovine reassortant vaccine against rotavirus gastroenteritis.17 This study was a double-blind, placebo-controlled, randomized trial involving more than 69,000 children in 11 countries. Healthy infants between 6 and 12 weeks of age were randomized to receive three doses of oral vaccine or placebo. All subjects were followed for the development of acute gastroenteritis requiring hospitalization or emergency department care, as well as the development of complications such as intussusception.
In this study, 57,134 children were involved in an analysis of health care service use attributed to rotavirus gastroenteritis. For our discussion, we will look simply at the efficacy of the vaccine in reducing hospitalizations resulting from acute rotavirus gastroenteritis. Among the infants who received the vaccine, 6 of 28,646 developed acute rotavirus gastroenteritis requiring hospitalization for 14 days or more following receipt of the last dose of the vaccine. In the placebo group, 138 of 28,488 infants were hospitalized. Children in the vaccine group had an RR of 0.043 for developing rotavirus gastroenteritis requiring hospitalization (calculated as 6/28,646 divided by 138/28,488), meaning that vaccinated children had 4.3% of the risk of being hospitalized as a result of rotavirus gastroenteritis compared to unvaccinated children. The RRR from vaccination was 95.7% (calculated as 138/28,488 minus 6/28,646 divided by 138/28,488), while because of the low incidence of hospitalization overall, the ARR from vaccination was just 0.46% (calculated as 138/28,488 minus 6/28,646 times 100). However, the NNT of 216 (calculated as 1 divided by the difference of 138/28,488 and 6/28,646, or 0.0046) means that vaccination of 216 children prevented 1 case of acute rotavirus gastroenteritis requiring hospitalization over the first year of life.
An NNT of 216 may seem high to some readers. However, one needs to take into account the prevalence of disease, as well as the risk-benefit ratio of the intervention. Rotavirus infection affects more than 100 million children annually worldwide and is the leading cause of deaths resulting from acute gastroenteritis.18 Even in the United States, rotavirus gastroenteritis is responsible for more than 60,000 hospitalizations per year.19 Therefore, given the cost associated with hospitalization (parental missed days of work, health care costs, etc.), the significant morbidity and mortality associated with severe rotavirus gastroenteritis, the incidence of this disease worldwide, and the relative safety and efficacy of this vaccine, widespread vaccination has a considerable potential benefit.