CRITICAL NUMBERS LIVING WITH RISK At the end

CRITICAL NUMBERS LIVING WITH RISK

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

• 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

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

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.

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? ”

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 16 -80 times more frequent for Baycol as compared to any other statin

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: www. news. bayer. com/news. nsf/ID/010219

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…

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.

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.

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 develop disease a b Number who do not develop disease c d 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)

Example 2 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 Felt better Placebo 12 3 Did not feel better not develop disease 3 Total 17 15 ‘Risk’ of improvement on magnesium ‘Risk’ of improvement on placebo 14 = 12/ 15 = 0. 80 = 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

Clinical problem For our example if we imagine 1, 000 prescriptions for Baycol Other statins Number who die from rhabdomyolysis Number alive or die 2 999 998 1 9 999 of other causes Total 1 000 ‘Risk’ of dying on Baycol ‘Risk’ of dying on other statins 10 000 = 2 / 1 000 = 1 / 10 000 Relative risk of dying from rhabdomyolysis for the Baycol patients compared to other patients on statins = (2/1 000) / (1/10 000) = 20. 5 i. e. Patient on Baycol is 20 times more likely to die from rhabdomyolysis compared to patient on other statins

The clinical problem So this quote: “The FDA reports that the rate of fatal rhabdomyolysis is 16 -80 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?

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.

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

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 50 th of this i. e. 4 per 100 000 prescriptions

Issues with RR – defining success Success Failure Treatment A Treatment B 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

Issues with RR – defining success Success Failure Treatment A Treatment B 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

• 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

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 1 000 This is 0. 000002 In patients using other statins the absolute risk (of dying from rhabdomyolysis – and not something else) was 1 in 10 000 This is 0. 0000001 The ARE is 0. 000002 – 0. 0000001 = 0. 0000019

0. 0000019 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 0. 0000019 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

Example From the previous example of comparing magnesium therapy and placebo: Magnesium Placebo Felt better 12 3 Did not feel better not develop disease 3 Total 17 15 14 ‘Risk’ of improvement on magnesium = 12/ 15 = 0. 80 ‘Risk’ of improvement on placebo = 3/ 14 = 0. 18 Absolute risk reduction = 0. 80 - 0. 18 = 0. 62

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.

Example From the previous example of comparing magnesium therapy and placebo: Magnesium Felt better Placebo 12 3 Did not feel better 3 Total 17 15 14 ‘Risk’ of improvement on magnesium ‘Risk’ of improvement on placebo = 12/ 15 = 0. 80 = 3/ 14 = 0. 18 Absolute risk reduction Number needed to treat (to benefit) = 0. 80 - 0. 18 = 0. 62 = 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

0. 0000019 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/ 0. 0000019 = 526 315 So to cause one additional death from rhabdomyolysis with Baycol we would need to make out over half a million prescriptions for Baycol

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10 0. 1100 0. 0100 0. 10 11 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10 0. 1100 0. 0100 0. 10 11 10 0. 1500 0. 0500 0. 10 3 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10 0. 1100 0. 0100 0. 10 11 10 0. 1500 0. 0500 0. 10 3 10 0. 2000 0. 10 2 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10 0. 1100 0. 0100 0. 10 11 10 0. 1500 0. 0500 0. 10 3 10 0. 2000 0. 10 2 10 0. 3500 0. 2500 0. 10 1. 4 10

Issues with NNT – always consider all the risks PA PB PB-PA PB/PA NNT 0. 1001 0. 0001 0. 10 1001 10 0. 1010 0. 0010 0. 10 101 10 0. 1100 0. 0100 0. 10 11 10 0. 1500 0. 0500 0. 10 3 10 0. 2000 0. 10 2 10 0. 3500 0. 2500 0. 10 1. 4 10 0. 6000 0. 5000 0. 10 1. 2 10

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 nonoccurrence. 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)}

Odds and Odds Ratio (2) Exposed Number with disease Number without disease Total Not exposed a c b d 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

Example From the previous example of comparing magnesium therapy and placebo: Magnesium Felt better Placebo 12 3 Did not feel better not develop disease 3 Total 17 15 Odds of improvement on magnesium Odds of improvement on placebo 14 = 0. 80/(1 -0. 80) = 4. 0 = 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

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

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 formal statistical analyses

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?

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

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

Should now know about: • 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