Obtaining Absolute Risk Reduction (ARR) and Number Needed To Treat (NNT) From Relative Risk (RR) and Odds Ratios (OR) Reported in Systematic Reviews
Estimates of effect in meta-analyses can be expressed as either relative effects or absolute effects. Relative risks (aka risk ratios) and odds ratios are relative measures. Absolute risk reduction (aka risk difference) and number-needed-to-treat are absolute measures. When reviewing meta-analyses, readers will almost always see results (usually mean differences between groups) presented as relative risks or odds ratios. The reason for this is that relative risks are considered to be the most consistent statistic for study results combined from multiple studies. Meta-analysts usually avoid performing meta-analyses using absolute differences for this reason.
Fortunately we are now seeing more meta-analyses reporting both the relative risks along with ARR and NNT. The key point is that meta-analyses almost always use relative effect measures (relative risk or odds ratio) and then (hopefully) re-express the results using absolute effect measures (ARR or NNT).
You may see the term, “assumed control group risk” or “assumed control risk” (ACR). This frequently refers to risk in a control group or subgroup of patients in a meta-analysis, but could also refer to risk in any group (i.e., patients not receiving the study intervention) being compared to an intervention group.
The Cochrane Handbook now recommends that meta-analysts provide a summary table for the main outcome and that the table include the following items—
- The topic, population, intervention and comparison
- The assumed risk and corresponding risk (i.e., those receiving the intervention)
- Relative effect statistic (RR or OR)
When RR is provided, ARR can easily be calculated. Odds ratios deal with odds and not probabilities and, therefore, cannot be converted to ARR with accuracy because odds cannot account for a number within a population—only how many with, for example, as compared to how many without. For more on “odds,” see— http://www.delfini.org/page_Glossary.htm#odds
Example 1: Antihypertensive drug therapy compared to control in elderly (60 years or older) for hypertension in the elderly
Reference: Musini VM, Tejani AM, Bassett K, Wright JM. Pharmacotherapy for hypertension in the elderly. Cochrane Database Syst Rev. 2009 Oct 7;(4):CD000028. Review. PubMed PMID: 19821263.
- Computing ARR and NNT from Relative Risk
When RR is reported in a meta-analysis, determine (this is a judgment) the assumed control risk (ACR)—i.e., the risk in the group being compared to the new intervention—from the control event rate or other data/source
- Formula: ARR=100 X ACR X (1-RR)
Calculating the ARR and NNT from the Musini Meta-analysis
- In the above meta-analysis of 12 RCTs in elderly patients with moderate hypertension, the RR for overall mortality with treatment compared to no treatment over 4.5 years was 0.90.
- The event rate (ACR) in the control group was 116 per 1000 or 0.116
- ARR=100 X .116 X 0.01=1.16%
- Interpretation: The relative risk with treatment compared to usual care is 90% of the control group (in this case the group of elderly patients not receiving treatment for hypertension) which translates into 1 to 2 fewer deaths per 100 treated patients over 4.5 years with treatment. In other words you would need to treat 87 elderly hypertensive people at moderate risk with antihypertensives for 4.5 years to prevent one death.
Computing ARR and NNT from Odds Ratios
In some older meta-analyses you may not be given the assumed (ACR) risk.
Example 2: Oncology Agent
Assume a meta-analysis on an oncology agent reports an estimate of effect (mortality) as an OR of 0.8 over 3 years for a new drug. In order to do the calculation, an ACR is required. Hopefully this information will be provided in the study. If not, the reader will have to obtain the assumed control group risk (ACR) from other studies or another source. Let’s assume that the control risk in this example is 0.3.
Formula for converting OR to ARR: ARR=100 X (ACR-OR X ACR) / (1-ACR+OR X ACR)
- ARR=100 X (0.3-0.8 X 0.3) / (1-0.3 + 0.8 X 0.3)
- In this example:
- ARR=100 X (0.3-0.24) / (1-0.54)
- ARR= 0.06/0.46
- ARR=0.13 or 13%
- Thus the ARR is 13% over 3 years.
- The NNT to benefit one patient over 3 years is 100/13 or 8
Because of the limitations of odds ratios, as described above, it should be noted that when outcomes occur commonly (e.g., >5%), odds ratios may then overestimate the effect of a treatment.
For more information see The Cochrane Handbook, Part 2, Chapter 12.5.4 available at http://www.cochrane-handbook.org/