1 Information Mastery Skills Calculating RR, RRR, ARR and NNTs A. Bornstein, MD, FACC Assistant Professor of Medicine Weil Cornell Medical College New York, NY

2 Consider a Clinical Trial… 200 subjects aged 59 years or older, with previous heart disease and type 2 diabetes randomized to 2 groups:200 subjects aged 59 years or older, with previous heart disease and type 2 diabetes randomized to 2 groups: 1)100 receive experimental treatment (treatment group) 2)100 receive control treatment (standard of care) Follow-up is a mean of 5 yearsFollow-up is a mean of 5 years Endpoint is a composite of all CHD deaths & non-fatal MIsEndpoint is a composite of all CHD deaths & non-fatal MIs

3 Results The treatment is clearly more effective than the control: fewer people suffered CHD-death or non-fatal MIThe treatment is clearly more effective than the control: fewer people suffered CHD-death or non-fatal MI How can we express how much more effective it is?How can we express how much more effective it is? Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 2030 Rate of CHD-deaths or non-fatal MI 0.2 (20%) 0.3 (30%)

4 Relative Risk (RR) or Risk Ratio What is the ratio of the rates of CHD-death or non-fatal MI in the 2 study groups?What is the ratio of the rates of CHD-death or non-fatal MI in the 2 study groups? RR = 20%/30% = 0.67 (or 0.2/0.3 = 0.67)RR = 20%/30% = 0.67 (or 0.2/0.3 = 0.67) Subjects who took the experimental treatment for a mean of 5 years were 0.67 times as likely to die from CHD-related causes or suffer a non-fatal MI as those who took the control.Subjects who took the experimental treatment for a mean of 5 years were 0.67 times as likely to die from CHD-related causes or suffer a non-fatal MI as those who took the control. Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 2030 Rate of CHD-deaths or non-fatal MI 0.2 (20%) 0.3 (30%)

5 Relative Risk Reduction (RRR) By how much has the experimental treatment reduced the risk of CHD-death or non-fatal MI?By how much has the experimental treatment reduced the risk of CHD-death or non-fatal MI? RRR = 1-RR = = 0.33 (or 33%)RRR = 1-RR = = 0.33 (or 33%) or RRR = (difference in event rates)/control event rate = ( )/0.3 = 0.1/0.3 = 0.33 (or 33%) Subjects who took the experimental treatment for a mean of 5 years were 33% less likely to die from CHD-related causes or suffer a non-fatal MI than those who took the control: treatment has reduced the risk by 1/3Subjects who took the experimental treatment for a mean of 5 years were 33% less likely to die from CHD-related causes or suffer a non-fatal MI than those who took the control: treatment has reduced the risk by 1/3 Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 2030 Rate of CHD-deaths or non-fatal MI 0.2 (20%) 0.3 (30%)

6 Absolute Risk Reduction (ARR) or Risk Difference How many fewer subjects in the experimental treatment group suffered CHD-death or non-fatal MI?How many fewer subjects in the experimental treatment group suffered CHD-death or non-fatal MI? ARR = 30% - 20% = 10% (or = 0.1)ARR = 30% - 20% = 10% (or = 0.1) 10% fewer subjects (10/100) who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI than those who took the control.10% fewer subjects (10/100) who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI than those who took the control. Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 2030 Rate of CHD-deaths or non-fatal MI 0.2 (20%) 0.3 (30%)

7 Number Needed to Treat for Benefit (NNT) On average, how many people needed to take the experimental treatment for one to benefit?On average, how many people needed to take the experimental treatment for one to benefit? ARR = 30% - 20% = 10% = 10 in every 100; NNT = 1 in every 100/10 = 10ARR = 30% - 20% = 10% = 10 in every 100; NNT = 1 in every 100/10 = 10 On average, 1 in every 10 subjects who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI, who would have done had they all taken the control.On average, 1 in every 10 subjects who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI, who would have done had they all taken the control. Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 2030 Rate of CHD-deaths or non-fatal MI 0.2 (20%) 0.3 (30%)

8 What if the Baseline Risk is Lower? RR = 2%/3% = 0.67RR = 2%/3% = 0.67 RRR = = 0.33 or 33%RRR = = 0.33 or 33% ARR = 3% - 2% = 1%ARR = 3% - 2% = 1% NNT = 100/1% = 100NNT = 100/1% = 100 On average, 1 in every 100 subjects who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI, who would have done so had they all taken the control.On average, 1 in every 100 subjects who took the experimental treatment for a mean of 5 years did not die from CHD-related causes or suffer a non-fatal MI, who would have done so had they all taken the control. Treatment group Control group Number of subjects Number of CHD-deaths or non-fatal MI 23 Rate of CHD-deaths or non-fatal MI 0.02 (2%) 0.03 (3%)

9 Apples were $3.00 a bag; now only $2.00 a bag Let’s try to show this with a shopping analogy 1)Amount saved is $1.00 per bag (Original rate – new rate) 2)Saving is 1/3 or 33%; (original rate – new rate)/original rate; i.e., 3-2 = 1; 1/3 = one third; 1/3 x 100 = 33%

10 Would you go out and buy apples if the saving was ONLY described as “ONE THIRD OFF”? Apples were $30.00 a bag; now $20.00 a bag 1)Saving is $10.00 a bag 2)Saving is STILL one third Apples were $30.00 a bag; now only $20.00 a bag 1)Amount saved is $10.00 per bag (Original rate – new rate) 2)Saving is 1/3 or 33%; (original rate – new rate/original rate; i.e., 3-2 = 1; 1/3 = one third; 1/3 x 100 = 33% Lets try to show this with a shopping analogy

11 Harms can be Expressed in the Same Way Relative risk RR = 3%/2% = 1.5Relative risk RR = 3%/2% = 1.5 Relative risk increase (RRI) = = 0.5 or 50%Relative risk increase (RRI) = = 0.5 or 50% or RRI = (difference in event rates)/control event rate = ( )/0.02 = 0.01/0.02 = 0.5 (or 50%) Absolute risk increase or risk difference (RD) = 3%-2% = 1%Absolute risk increase or risk difference (RD) = 3%-2% = 1% Number needed to harm (NNH) = 100/1% = 100Number needed to harm (NNH) = 100/1% = 100 The experimental treatment increased risk of major bleeds by 50%. On average, 1 in every 100 subjects who took it for a mean of 5 years suffered a major bleed which they would not have done had they all taken the control.The experimental treatment increased risk of major bleeds by 50%. On average, 1 in every 100 subjects who took it for a mean of 5 years suffered a major bleed which they would not have done had they all taken the control. Treatment group Control group Number of subjects Number of major bleeds 32 Rate of major bleeds 0.03 (3%) 0.02 (2%)

12 Weighing Risks and Benefits In both groups, the experimental treatment reduced the risk of CHD death or non-fatal MI by 33% but increased the risk of major bleeds by 50%In both groups, the experimental treatment reduced the risk of CHD death or non-fatal MI by 33% but increased the risk of major bleeds by 50% On average, 1 in 10 of the higher-risk subjects benefited but 1 in 100 were harmedOn average, 1 in 10 of the higher-risk subjects benefited but 1 in 100 were harmed –For every 100 treated, 10 benefited and 1 was harmed On average, 1 in 100 of the lower-risk subjects benefited but 1 in 100 were harmedOn average, 1 in 100 of the lower-risk subjects benefited but 1 in 100 were harmed –For every 100 treated, 1 benefited and 1 was harmed

13 In pictures

14 In pictures

15 In pictures

16 In pictures

17 In pictures

18 In pictures

19 Examples! 1)COPD exacerbation rates: 5% (treatment) vs. 6% (control) 2)Rate of upper GI perforations, obstructions or bleeds: 3% (treatment) vs. 5% (control) 3)Stroke or TIA: 21% (treatment) vs. 35% (control) 4)Proportion of patients reporting “good” or “excellent” improvement in osteoarthritis symptoms: 40% (treatment) vs. 30% (control)

20 Summary RR, RRR, ARR and NNT are easy to calculateRR, RRR, ARR and NNT are easy to calculate RR & RRR or relative risk & relative risk reduction are constantRR & RRR or relative risk & relative risk reduction are constant –They tend to look impressive, but on their own they can be misleading NNTs give the benefit in Absolute Risk Reduction populationNNTs give the benefit in Absolute Risk Reduction population –The lower the baseline risk, the lower the absolute benefits (and the greater the NNT) for any given relative risk reduction All the above applies to harms as well as benefitsAll the above applies to harms as well as benefits We need to use absolute and relative terms consistentlyWe need to use absolute and relative terms consistently