1. CRITICAL NUMBERS LIVING WITH RISK

2. At the end of session, should know about:
Measures of risk
Different ways to describe risk
At the end of session, should be able to:
Explain:
Risk
Relative risk
Odds and odds ratios
Absolute risk reduction and risk excess
Number needed to treat
Understand that odds ratios are sometimes used to describe risk
Be familiar with the concept of risk ladders
Demonstrate awareness that presenting the same risk in different ways may affect how patients (and doctors) perceive risk

3. There is now a ‘language of risk’ for doctors
You need to be educated about risk and understand what is meant by different measures of risk
You will need to be able to communicate the concept of risk effectively to patients

4. Terminology
There are several terms used to describe ‘risk’ : risk / probability / chance
These are the same, but each has an implied meaning e.g. we talk about the chance of winning the lottery, not the risk of winning, but what we really mean is the probability of winning

5. Risk
The risk of an event is the probability that an event will occur within a stated time period (P). This is sometimes referred to as the absolute risk.
Examples
The risk of developing anaemia during pregnancy for a particular group of pregnant women would be the number of women who develop anaemia during pregnancy divided by the total number of pregnant women in the group.
The risk of a further stroke occurring in the year following an initial stroke would be the number who have another stroke within a year divided by the total number of stroke patients being followed up.

6. The Scenario
“Our doctor is worried by an article he has read in a journal that seems to suggest that a drug he has been prescribing is dangerous. What is the risk?”

7. The clinical problem Details of the fax…..
“This fax is to inform you of the withdrawal yesterday of Cerivastatin (Baycol/ Lipobay) by Bayer. You will be receiving more information directly from Bayer in the near future”
Bayer has announced the withdrawal of all dosages of the preparation with immediate effect
The FDA reports that the rate of fatal rhabdomyolysis is times more frequent for Baycol as compared to any other statin

8. The clinical problem
“The reason for this voluntary action lies in increasing reports of side effects involving muscular weakness (rhabdomyolysis), especially in patients who have been treated concurrently with the active substance gemfibrozil despite a contraindication and warnings contained in the product information.”
Quote taken from the Bayer website:

9. About statins
Cerivastatin was one of the more commonly used anti-cholesterol drugs
Many trials showed a link between high cholesterol and increased risk of heart attacks
Lowering cholesterol can lower the risk of heart attacks…

10. Absolute Risk
The risk of an event is the probability that an event will occur within a stated time period (P). This is sometimes referred to as the absolute risk.

11. Relative Risk (RR)
Ratio of risk in exposed group to risk in not exposed group (Pexposed / Punexposed)
Pregnancy example
Relative risk of anaemia for pregnant women compared to non-pregnant women of a similar age = risk of developing anaemia for pregnant women divided by the risk of developing anaemia for non-pregnant women of a similar age.
Stroke example
Relative risk of further stroke for patients who have had a stroke compared to patients who have not had a stroke = risk of a stroke within one year post stroke divided by the risk of having a stroke in a year for a similar group of patients who have not had a stroke.

12. Example 1
A group of subjects are followed up over time. Some are exposed to a hazard, some are not. In both groups some will develop a disease (an event), some will not.
Exposed Not exposed
Number who a b
develop disease
Number who do c d
not develop disease
Total a+c b+d
Risk of developing disease for exposed = a / a+c
Risk of developing disease for unexposed = b / b+d
Relative risk of developing disease for the exposed compared to the unexposed = {a /(a+c)}/ {b /(b+d)}
= a(b+d) / b(a+c)

13. Example 2 ‘Risk’ of improvement on magnesium = 12/ 15 = 0.80
Below are the results of a clinical trial examining whether patients with chronic fatigue syndrome (CFS) improved six weeks after treatment with intramuscular magnesium. The group who received the magnesium were compared to a group who received a placebo and outcome was feeling better.
Magnesium Placebo
Felt better
Did not feel better
not develop disease
Total
‘Risk’ of improvement on magnesium = 12/ 15 = 0.80
‘Risk’ of improvement on placebo = 3/ 14 = 0.18
Relative risk = 0.80/0.18 = 4.5
(of improvement on magnesium therapy compared to placebo)
Thus patients on magnesium therapy are 4 times more likely to feel better on magnesium rather than placebo

14. Clinical problem
For our example if we imagine 1,000,000 prescriptions for Baycol
Baycol Other statins
Number who die from
rhabdomyolysis
Number alive or die
of other causes
Total
‘Risk’ of dying on Baycol = 2 /
‘Risk’ of dying on other statins = 1 /
Relative risk of dying from rhabdomyolysis for the Baycol patients compared to other patients on statins
= (2/ ) / (1/ ) = 20.5
i.e. Patient on Baycol is 20 times more likely to die from rhabdomyolysis compared to patient on other statins

15. The clinical problem So this quote:
“The FDA reports that the rate of fatal rhabdomyolysis is times more frequent for Baycol as compared to any other statin.”
is referring to a relative risk comparing Baycol to
other similar drugs.
But why is it written as a range?

16. Points to consider
As with many estimated quantities it is possible to calculate a confidence interval for relative risk.
For the Baycol example the 95% confidence interval for the relative risk is (16-80). This means that though we estimate that patients are 20 times more likely to die of rhabdomyolysis on Baycol than other statins, it is possible that this relative risk could be as low as 16 times or as high as 80 times, with 95% certainty.

17. Points to consider What does a relative risk of 1 mean?
That there is no difference in risk in the two groups.
For our magnesium example, if the relative risk was 1, it would mean that patients are as likely to feel better on magnesium as on placebo
If there was no difference between the groups the confidence interval would include 1

18. The clinical problem In the same report, the FDA said
“The reporting rate for fatal rhabdomyolysis with Baycol monotherapy (1.9 deaths per million prescriptions) was 10 to 50 times higher than for other statins”
So we’re talking about a risk of 1.9 deaths per
MILLION PRESCRIPTIONS…
Other statins have a risk of a 50th of this i.e. 4 per prescriptions

19. Issues with RR – defining success
Treatment A
Treatment B
Success
Failure
0.96
0.04
0.99
0.01
If the outcome of interest is success then RR=0.96/0.99=0.97
Always consider all the risks

20. Issues with RR – defining success
Treatment A
Treatment B
Success
Failure
0.96
0.04
0.99
0.01
If the outcome of interest is success then RR=0.96/0.99=0.97
If the outcome of interest is failure then RR=0.04/0.01=4
Always consider all the risks

21. There are several ways of comparing risk
So far we have talked about absolute and relative risk i.e. the risk of an event occurring in one group relative to the risk of it occurring in another
When considering a particular ‘risk’ it is important to know whether relative or absolute risk is being presented as this influences the way in which it is interpreted

22. Absolute Risk Difference
It is the absolute additional risk of an event due to an exposure. Risk in exposed group minus risk in unexposed (or differently exposed group).
Absolute risk reduction (ARR) = Pexposed - Punexposed
If the absolute risk is increased by an exposure we sometimes use the term Absolute risk excess (ARE)
So the absolute risk (of dying from Rhabdomyolysis) in patients on Baycol was 2 in
This is
In patients using other statins the absolute risk (of dying from rhabdomyolysis – and not something else) was 1 in
This is
The ARE is – =

23.
Since this is such a small number and hard to deal with we would often multiply this by a larger number (say a million) and present it as X per million
In this case is the same as saying
An absolute risk excess of 1.9 deaths per million (Prescriptions of statins) for Baycol compared to other statins
Thus in absolute terms this risk is very small

24. Example
From the previous example of comparing magnesium therapy and placebo:
Magnesium Placebo
Felt better
Did not feel better
not develop disease
Total
‘Risk’ of improvement on magnesium = 12/ 15 = 0.80
‘Risk’ of improvement on placebo = 3/ 14 = 0.18
Absolute risk reduction = = 0.62

25. Number Needed to Treat (to benefit) / Number Needed (to Treat) to Harm
This is the additional number of people you would need to give a new treatment to in order to cure one extra person compared to the old treatment.
Alternatively for a harmful exposure, the number needed to treat becomes the number needed to harm and it is the additional number of individuals who need to be exposed to the risk in order to have one extra person develop the disease, compared to the unexposed group.
Number needed to treat =1 / ARR
Number needed to harm =1 / ARR, ignoring negative sign.

26. Example
From the previous example of comparing magnesium therapy and placebo:
Magnesium Placebo
Felt better
Did not feel better
Total
‘Risk’ of improvement on magnesium = 12/ 15 = 0.80
‘Risk’ of improvement on placebo = 3/ 14 = 0.18
Absolute risk reduction = = 0.62
Number needed to treat (to benefit) = 1 / 0.62 = 1.61 ~2
Thus on average one would have to give magnesium to 2 patients in order to expect one extra patient (compared to placebo) to feel better

27.
An absolute risk excess of 1.9 deaths per million (Prescriptions of statins) for Baycol compared to other statins
The number needed to treat to harm would be
1/ =
So to cause one additional death from rhabdomyolysis with Baycol we would need to make out over half a million prescriptions for Baycol

28. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10

29. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101

30. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101
0.1100
0.0100 11

31. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101
0.1100
0.0100 11
0.1500
0.0500 3

32. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101
0.1100
0.0100 11
0.1500
0.0500 3
0.2000
0.1000 2

33. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101
0.1100
0.0100 11
0.1500
0.0500 3
0.2000
0.1000 2
0.3500
0.2500
1.4

34. Issues with NNT – always consider all the risksPA PB
PB-PA
PB/PA
NNT
0.1001
0.0001
0.10
1001 10
0.1010
0.0010
101
0.1100
0.0100 11
0.1500
0.0500 3
0.2000
0.1000 2
0.3500
0.2500
1.4
0.6000
0.5000
1.2

35. Odds and Odds Ratio (1) ODDS
The odds of an event is the ratio of the probability of occurrence of the event to the probability of non-occurrence. P
(1 - P)
ODDS RATIO (OR)
Ratio of odds for exposed group to the odds for not exposed group.
{Pexposed / (1 - Pexposed)}
{Punexposed / (1 - Punexposed)}

36. Odds and Odds Ratio (2)
Exposed
Not exposed
Number with disease
Number without disease a c b d
Total
a+c
b+d
Odds of developing disease for exposed = {a/(a+c)} / {c/(a+c)} = a/c
Odds of developing disease for not exposed = {b/(b+d)} / {d/(b+d)} = b/d
Odds ratio of developing disease for the exposed compared to the unexposed = {a/c} / {b/d} = ad / bc

37. Example
From the previous example of comparing magnesium therapy and placebo:
Magnesium Placebo
Felt better
Did not feel better
not develop disease
Total
Odds of improvement on magnesium = 0.80/(1-0.80) = 4.0
Odds of improvement on placebo = 0.18/(1-0.18) = 0.21
Odds ratio = 4.0 / 0.21 = 19.0
(of magnesium compared to placebo)
Thus, for those who improved, they were 19 times more likely to be in the magnesium group than the placebo group (95% CI: 3.2 to 110.3).
Compare with relative risk

38. Relative Risk and Odds Ratio
The odds ratio can be interpreted as a relative risk when an event is rare and the two are often quoted interchangeably
This is because when the event is rare (b+d)→ d and (a+c)→c.
Relative risk = a(b+d) / b(a+c)
Odds ratio = ad / bc

39. Relative Risk and Odds Ratio
For case-control studies it is not possible to calculate the RR and thus the odds ratio is used.
For cross-sectional and cohort studies both can be derived and if it is not clear which is the causal variable and which is the outcome should use the odds ratio as it is symmetrical, in that it gives the same answer if the causal and outcome variables are swapped.
Odds ratio have mathematical properties which makes them more often quoted for formal statistical analyses

40. The clinical problem
Although Baycol seemed to be more ‘risky’ than other statins it doesn’t seem very risky!
How does a risk of 1 in 500,000 compare with other risks?

41. Calman Chart (BMJ, 1996): Risk per year
Term used Risk range Example Actual risk
High >1:100 Transmission to susceptible 1:1 to 1:2
household contacts of measles*
Moderate 1:100-1:1000 Death because of smoking 10
cigarettes per day 1:200
Low 1: :10,000 Death from road accident 1:8,000
Very low 1:10,000-1:100,000 Death from leukaemia 1:12,000
Death from accident at home 1:26,000
Minimal 1:100,000- 1:1,000,000 Death from rail accident 1:500,000
Negligible <1:1,000,000 Death from lightening strike 1:10,000,000
Death from radiation from 1:10,000,000
nuclear power station
* risk of transmission after contact (not death per year)

42. Calman Chart (BMJ, 1996): Risk per year
Term used Risk range Example Actual risk
High >1:100 Transmission to susceptible 1:1 to 1:2
household contacts of measles*
Moderate 1:100-1:1000 Death because of smoking 10
cigarettes per day 1:200
Low 1: :10,000 Death from road accident 1:8,000
Very low 1:10,000-1:100,000 Death from leukaemia 1:12,000
Death from accident at home 1:26,000
Minimal 1:100,000- 1:1,000,000 Death from rail accident 1:500,000
Negligible <1:1,000,000 Death from lightening strike 1:10,000,000
Death from radiation from 1:10,000,000
nuclear power station
it probably won’t be you!
* risk of transmission after contact (not death per year)
Baycol

43. Should now know about: Should now be able to: Measures of risk
Different ways to describe risk
Should now be able to:
Explain:
Risk
Relative risk
Odds and odds ratios
Absolute risk reduction and risk excess
Number needed to treat
Understand that odds ratios are sometimes used to describe risk
Be familiar with the concept of risk ladders
Demonstrate awareness that presenting the same risk in different ways may affect how patients (and doctors) perceive risk