Information Mastery Skills

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Information Mastery Skills

• Calculating RR, RRR, ARR and NNTs

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Consider a clinical trial

• 200 subjects aged 59 years or older, with
  previous heart disease and type 2 diabetes
  randomised to two groups
• 100 receive the experimental treatment
• 100 receive the control treatment
• Follow-up is a mean of 5 years
• Endpoint is a composite of all of the CHD deaths
  and non-fatal MIs

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Results

• The 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?

4
Relative risk (RR) or risk ratio

• What is the ratio of the rates of CHD-death or
  non-fatal MI in the two study groups?
• 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.

5
Relative risk reduction (RRR)

• By how much has the experimental treatment
  reduced the risk of CHD-death or non-fatal MI?
• RRR 1-RR 1-0.66 0.33 (or 33)
• or
• RRR (difference in event rates)/control event
  rate
• (0.3-0.2)/ 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 the treatment
  has reduced the risk by one third.

6
Absolute risk reduction (ARR) or risk difference

• How many fewer subjects in the experimental
  treatment group suffered CHD-death or non-fatal
  MI?
• ARR 30 - 20 10 (or 0.3 - 0.2 0.1)
• 10 fewer subjects (10 in every 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.

7
Number needed to treat for benefit (NNT)

• On average, how many people needed to take the
  experimental treatment for one to benefit?
• ARR 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.

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What if the baseline risk is lower?

• RR 2/3 0.67
• RRR 1-0.67 0.33 or 33
• ARR 3-2 1
• NNT 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 had they all
  taken the control.

9
Lets try to show this with a shopping analogy

• Apples were 3 a bag, now only 2 a bag
• Amount saved is 1 per bag (Original rate new
  rate).
• Saving is one third or 33. (original rate new
  rate / original rate i.e. 3-2 1, 1/3 one
  third, 1/3 x 100 33

10
Lets try to show this with a shopping analogy

• Apples were 3 a bag, now only 2 a bag
• Amount saved is 1 per bag (Original rate new
  rate).
• Saving is one third or 33. (original rate new
  rate / original rate i.e. 3-2 1, 1/3 one
  third, 1/3 x 100 33

• Apples 30p a bag, now 20p a bag
• Saving is 10p a bag
• Saving is STILL one third

Would you go out and buy apples if the saving was
ONLY described as ONE THIRD OFF?
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We can express harms in the same ways

• Relative risk RR 3/2 1.5
• Relative risk increase (RRI) 1.5-1 0.5 or 50
• or
• RRI (difference in event rates)/control event
  rate
• (0.03-0.02)/0.02 0.01/0.02 0.5 (or 50)
• Absolute risk increase or risk difference (RD)
  3-2 1
• Number needed to harm (NNH) 100/1 100
• The experimental treatment increased the 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.

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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
• On 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 harmed
• For every 100 treated, 1 benefited and 1 was
  harmed

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In pictures
www.nntonline.net
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In pictures
www.nntonline.net
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In pictures
www.nntonline.net
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In pictures
www.nntonline.net
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In pictures
www.nntonline.net
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In pictures
www.nntonline.net
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Now try these!

• COPD exacerbation rates 5 (treatment) vs. 6
  (control)
• Rate of upper GI perforations, obstructions or
  bleeds 3 (treatment) vs. 5 (control)
• Stroke or TIA 21 (treatment) vs. 35 (control)
• Proportion of patients reporting good or
  excellent improvement in osteoarthritis
  symptoms 40 (treatment) vs. 30 (control)

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Summary

• RR, RRR, ARR and NNT are easy to calculate
• Relative risk and relative risk reduction are
  constant
• They tend to look impressive, but on their own
  they can be misleading
• Absolute risk reduction and NNTs give the benefit
  in the 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
  benefits
• We need to use absolute and relative terms
  consistently