A key step in implementing the GRADE (Grading of Recommendations Assessment, Development and Evaluation) system is the estimation of a risk difference based on estimates of the baseline risk and the relative risk estimated from different sources. In this paper we describe a simple and effective method to calculate confidence intervals (CIs) for the risk difference for this situation. Whenever an independent source is available to estimate the baseline risk for the population to which the effect estimates should be applied, this source should be used and CIs for the absolute risk difference should be calculated taking all sources of uncertainty into account.

Availability of high-quality estimates of the absolute difference in effectiveness between alternative treatment options is crucial to the application of evidence-based healthcare to populations of patients and corresponding decisions. One framework for assessing confidence in estimates of the effect of alternative management strategies on patient-relevant outcomes within the Grading of Recommendations Assessment, Development and Evaluation (GRADE) system

Often, the best available evidence for the absolute difference in effectiveness between a treatment under consideration and a standard regime does not come from a single study, but from two totally separate sources. Sometimes, an estimate of the relative risk (RR) of the outcome of interest between the two treatment options is available from a meta-analysis combining evidence from several randomised trials. Owing to the larger sample size available, this will in general have greater precision than an RR derived from a single study. In most contexts, estimates of relative effect of a therapy are more consistent across different baseline risks than absolute effect estimates.

To convert an RR into an absolute RD, we also require an estimate of the baseline risk (BR), the rate of occurrence of the event of interest when the standard treatment is used. The absolute RD is then calculated from the BR and RR using the formula RD = BR×(RR−1).

In most applications, the RR is below 1, representing a reduction in risk due to the intervention. The calculated RD is then negative. Sometimes, the RR may be greater than 1, representing an increase in risk due to the intervention. The calculated RD is then positive.

Spencer

All the quantities we concerned to estimate, such as the BR, the RR or the RD, are derived from series of patients of finite size. A CI is normally used to display the resulting uncertainty of such an estimate. CIs convey information about magnitude and precision of effect simultaneously, keeping these two aspects of measurement closely linked.

Confidence limits for the RD may be calculated from those for the BR and RR by a procedure called Method of Variance Estimates Recovery (MOVER). This is a general approach that may be used to calculate CIs for sums and differences of two independently estimated quantities. MOVER may be extended to apply to products or ratios, but greater care is required. Neither an approach using logarithms of BR and (RR−1)

While it is simple to calculate the RD from the BR and RR, the formulae to derive confidence limits for the RD from those of the BR and RR are quite complicated.

The calculations in the spreadsheet start with estimates of the BR and RR and the corresponding CIs. The RD together with its CI is then derived from these figures. If 95% CIs are used for the BR and RR, the resulting CI for the RD is also a 95% CI. The spreadsheet is designed to be a highly user-friendly resource, though needless to say, great care is needed with the negative numbers used to represent benefits.

Spencer

We could equally well construct a CI representing the uncertainty of the BR only, −0.088 to −0.007 here.

Absolute risk reduction (expressed as events prevented per 1000 women) for effect of low-dose, low-molecular-weight heparin on venous thrombolic events, from Bates

Arzola and Wieczorek

Absolute risk difference (in %) for effect of low-dose bupivacaine on spinal anaesthesia efficacy, from Arzola and Wieczorek.

Whenever the BR and RR are derived from separate studies and thus are estimated independently, the calculations described here, based on MOVER-R, lead to an appropriate CI for the RD which correctly allows for the degree of imprecision of both the BR and RR. As in

In many applications, the RR is taken from a meta-analysis. However, the method described here must not be used when the BR and RR are derived from exactly the same series of individuals, because the assumption that they are statistically independent is violated. In the situation of a single study, the RD should be calculated directly from the data, as the proportion of patients experiencing the event of interest in the intervention group minus the corresponding proportion for the control group. A CI for this RD is calculated using the second block of the spreadsheet

For example, Rascol

In the context of a meta-analysis in which it makes sense to use RD as the effect measure, the RD should be estimated in each study and then pooled using meta-analysis methods. One meta-analysis situation in which no clear solution has yet been established is where the RD should not be used as an effect measure due to heterogeneity, but the relative effect measure, the RR can be pooled adequately and the BR is taken to be the median or some other summary measure derived from the observed absolute risks of the control group across the

In summary, a simple and effective method to calculate CIs for the RD from independent estimates of the baseline risk and the RR is available. This method improves the currently used methods within the GRADE system, because both sources of uncertainty, namely the estimation of the RR as well as that of the BR are taken into account.

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