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Risk . Extension Article by Dr Tim Kenny http:// www.patient.co.uk /print/4875. A bat and a ball cost $1.10. If the bat costs $1 more than the ball, how much is the ball?. A bat and a ball cost $1.10. If the bat costs $1 more than the ball, how much is the ball? 5c.

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Risk

Extension

Article by Dr Tim Kenny

http://www.patient.co.uk/print/4875





  • We have the same problem with risk. the ball, how much is the ball?

  • Many reports in the media about the benefits of treatments present risk results as relative risk reductions rather than absolute risk reductions.

  • This often makes the treatments seem better than they actually are.



Absolute risk
Absolute risk the ball, how much is the ball?

  • Absolute risk of a disease is your risk of developing the disease over a time period.


Relative risk
Relative risk the ball, how much is the ball?

  • Relative risk is used to compare the risk in two different groups of people.


Example
Example the ball, how much is the ball?

  • Say the absolute risk of developing a disease is 4 in 100 in non-smokers.

  • Say the relative risk of the disease is increased by 50% in smokers.

  • The 50% relates to the 4 - so the absolute increase in the risk is 50% of 4, which is 2. So, the absolute risk of smokers developing this disease is 6 in 100.


An example when talking about treatments
An example when talking about treatments the ball, how much is the ball?

  • Say men have a 2 in 20 risk of developing a certain disease by the time they reach the age of 60.

  • Then, say research shows that a new treatment reduces the relative risk of getting this disease by 50%.

  • The 50% is the relative risk reduction, and is referring to the effect on the 2. 50% of 2 is 1. So this means that the absolute risk is reduced from from 2 in 20, to 1 in 20


Number needed to treat
Number needed to treat the ball, how much is the ball?

  • A figure which is often quoted in medical research is the number needed to treat (NNT). This is the number of people who need to take the treatment for one person to benefit from the treatment.


  • For example, say a pharmaceutical company reported that medicine X reduced the relative risk of developing a certain disease by 25%.

  • If the absolute risk of developing the disease was 4 in 100 then this 25% reduction in relative risk would reduce the absolute risk to 3 in 100.


  • But this can be looked at another way. If 100 people do not take the medicine, then 4 in those 100 people will get the disease.

  • If 100 people do take the medicine, then only 3 in those 100 people will get the disease.

  • Therefore, 100 people need to take the treatment for one person to benefit and not get the disease. So, in this example, the NNT is 100.



  • Say the absolute risk of developing complications from a certain disease is 4 in 20.

  • Say a medicine reduces the relative risk of getting these complications by 50%.

  • This reduces the absolute risk from 4 in 20, to 2 in 20.

  • In percentage terms, 4 in 20 is 20%, and, 2 in 20 is 10%. Therefore, the reduction in absolute risk in taking this medicine is from 20% to 10% - a reduction of 10 percentage points. The NNT would be 100 divided by 10. That is, 10 people would need to take the medicine for one to benefit.


Helping to decide about taking a treatment
Helping to decide about taking a treatment certain disease is 4 in 20.

  • The decision on whether to take a treatment needs to balance various things, such as:

  • What is the absolute risk of getting the disease to start with?

  • How serious is the disease anyway?

  • How much is the absolute risk reduced with treatment?

  • The risks or side-effects in taking the treatment.

  • How much does the treatment cost? Is it worth it to an individual if the individual is paying, or is it worth it to the country if the government is paying?


Example1
Example: certain disease is 4 in 20.

  • Say your absolute risk of developing a certain disease is 4 in 1,000.

  • If a treatment reduces the relative risk by 50%, it means the 4 is reduced by 50%.

  • Therefore, the treatment reduces the absolute risk from 4 in 1,000 to 2 in 1,000. Not really much in absolute terms.



  • Say there was a 1 in 100 risk of developing serious side-effects from treatment. You are then not likely to want the treatment, as the risk from serious side-effects is higher than the risk from the disease.

  • If there were no risk from the treatment, you might consider the treatment worthwhile.


  • If the treatment were very expensive: then you may not be able to afford it and decide to take the risk without treatment;

  • if the government is paying, it might decide not to fund this treatment, as the reduction in absolute risk is not great and many people would need treatment to benefit one person.


Example2
Example: able to afford it and decide to take the risk without treatment;

  • On the other hand, say your absolute risk of developing a disease is 4 in 10 and a treatment reduces the relative risk by 50%. Your absolute risk goes down to 2 in 10 - a big reduction.


  • If it were a minor disease that you are likely to recover from, then you may still take the treatment if there were no risk of side-effects, so as not to be troubled with the disease.

  • If it is a fatal disease, you are likely to definitely want treatment provided the risk of side-effects was much lower than the risk of getting the disease.


  • Treatments for medical conditions are often quoted in the press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. For example, a 75% reduction in relative risk for something that has a 4 in a million absolute risk of happening brings the absolute risk down to 1 in a million.


Stephanie press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Budgett: University of Auckland


Stephanie press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Budgett: University of Auckland


Stephanie press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Budgett: University of Auckland


Stephanie press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Budgett: University of Auckland


Conveying risk
Conveying press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Risk

• Absolute risk

• Baseline risk

• Relative risk

• Risk difference

• Increased risk/Reduced risk

• Odds Ratio

• Number needed to treat

Stephanie Budgett: University of Auckland


Absolute risk1
Absolute press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

The incidence of an event in a particular group

– For example, women in New Zealand have a 0.1 risk of developing breast cancer over their lifetime

– (This risk will vary according to a woman’s age,

family history, lifestyle,…)

Stephanie Budgett: University of Auckland


Baseline risk
Baseline press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

– This is the risk without a specified treatment or

behaviour.

If we want to find out if taking an aspirin helps prevent heart attacks, the baseline risk is…

  • the risk of having a heart attack without taking aspirin.

    If we want to investigate the risk of smoking and

    getting lung cancer, the baseline risk is…

  • the risk of getting lung cancer without smoking

Stephanie Budgett: University of Auckland


Relative risk1
Relative press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

– The ratio of the risks for two groups

e.g. Relative risk of cancer due to smoking

= Risk (prob) of Cancer for a smoker

Risk (prob) Cancer for a nonsmoker

Stephanie Budgett: University of Auckland


Relative risk2
Relative Risk press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

– It is useful to compare the risk of disease (e.g. heart attacks) for those with a certain characteristic (e.g. taking aspirin) to the baseline risk of that disease(e.g. heart attacks in those not taking aspirin).

– It doesn’t usually matter which way round we

calculate the ratio, but relative risks of greater than 1 are easier to interpret than those between 0 and 1.

Stephanie Budgett: University of Auckland


Relative risk of developing breast cancer utts seeing through statistics p224
Relative Risk of Developing Breast Cancer press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. (Utts, Seeing Through Statistics, p224)

Stephanie Budgett: University of Auckland


Relative risk of developing breast cancer utts seeing through statistics p2241
Relative Risk of Developing Breast Cancer press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. (Utts, Seeing Through Statistics, p224)

Stephanie Budgett: University of Auckland


Relative risk3
Relative Risk press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

Stephanie Budgett: University of Auckland


In words
In words press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

The risk of developing breast cancer for women who had their first child at age 25 or older is 1.33 times the risk of developing breast cancer for women who had their first child under the age of 25

Stephanie Budgett: University of Auckland


Or the other way up
OR the other way press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. up

i.e. comparing “under 25” to “over 25”

Relative risk = 0.0143 / 0.0190 = 0.75

The risk of developing breast cancer for women who had their first child under the age of 25 is 0.75 times the risk of developing breast cancer for women who had their first child at the age of 25 or older.

Stephanie Budgett: University of Auckland


Risk difference
Risk press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. difference

– The difference in risk, of lung cancer say, associated

with smoking, is simply

Risk for those exposed (smokers) – Baseline risk (nonsmokers)

Risk for the exposed – Risk for the unexposed

(simple difference between the 2 probabilities)

Seldom used and quoted

– because for small probabilities ratios tend to be much

more stable measures of effect (from population to

population) than differences

Stephanie Budgett: University of Auckland


Risk difference attributable risk
Risk difference (Attributable Risk press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. )

– The difference in risk of breast cancer associated with a woman having her first child at the age of 25 or older (compared with under the age of 25) is:

Risk for those ‘exposed’ (first child > 25)

– Baseline Risk ‘unexposed’ (first child ≤ 25)

= 0.0190 – 0.0143 = 0.0047

Stephanie Budgett: University of Auckland


Increased decreased risk
Increased/Decreased press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

– Sometimes the change in risk is expressed as a

percentage increase (or decrease) instead of a

multiple.

Or

Stephanie Budgett: University of Auckland


Increased risk
Increased press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

The risk of developing breast cancer for women who had

their first child at age 25 or older is 1.33 times that for

those who had their first child under the age of 25.

Thus

Or

In words: There is an increased risk of 33% of developing breast cancer for women who had their first child at age

25 or older compared

Stephanie Budgett: University of Auckland


Decreased risk
Decreased press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. risk

For women who have their first child under the age of 25, the risk of developing breast cancer is 0.75 times that for women who had their first child at age 25 or older.

Thus

or (0.75 - 1.0)100%  -25%

In words:

Thereis a reducedrisk of of developingbreastcancerforwomenwho had their first childunderthe age of 25 comparedtothosewho had their first childat age 25 or older.

Stephanie Budgett: University of Auckland


Odds ratio
Odds press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Ratio

– Very common in technical reporting of risk

– Idea is more complicated than that of “relative risk”

– BUT when we are comparing small probabilities the Relative risk and odds ratio

are numerically almost identical

Stephanie Budgett: University of Auckland


Lots of important forms of statistical press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. analysis naturally produce odds ratios (e.g. logistic regression)

Stephanie Budgett: University of Auckland


Odds of cancer risk for a press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. woman having first child ≥ 25


Breast cancer odds press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

for a woman having first child ≥ 25

for a woman having first child < 25

Odds ratio


Breast cancer odds press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

for a woman having first child ≥ 25

for a woman having first child < 25

Odds ratio


Odds press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

– If the risk of disease is small, the odds ratio and the relative risk will be approximately equal.

– Relative risk is more intuitive, but the odds ratio is easy to deal with statistically.

Stephanie Budgett: University of Auckland


Conveying risk1
Conveying Risk press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

What is the benefit of a cholesterol‐lowering

drug on the risk of coronary heart disease?

“People with high cholesterol can rapidly

reduce…their risk of death by 22% by taking a

widely prescribed drug.”

What does this mean?

Stephanie Budgett: University of Auckland


22 risk reduction
“22% risk reduction press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. ”

Does it mean that out of 100 with high cholesterol, 22 can be prevented from becoming heart attack victims?

NO!

Stephanie Budgett: University of Auckland


Here are some of the results from the trial
Here are some of the results from the trial press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

Stephanie Budgett: University of Auckland


Absolute risk reduction arr
Absolute Risk (Reduction) (ARR): press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk.

“What is the effect of treatment?”

– If we treat 1000 people …. (on average and taking everything at face value) instead 41 dying (as would if untreated) we’d have 32 die a saving of 41‐32 = 9 lives per 1000 people treated

– (0.9%)

Stephanie Budgett: University of Auckland


Stephanie press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. Budgett: University of Auckland


Number needed to treat nnt
Number Needed to Treat (NNT press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. )

– The number of patients that need to be treated to preventone bad outcome.

Stephanie Budgett: University of Auckland


Number needed to treat nnt1
Number needed to treat (NNT) press along the lines ... "New treatment reduces your risk of X disease by 25%". However, although this sounds good, it usually refers to the relative risk. But, the benefit really depends on how common or rare the disease is. A large reduction of relative risk for a rare disease might not mean much reduction in the absolute risk. :

– “How many people do we need to treat to prevent one death?” (on average and taking everything at face value)

9 deaths per 1,000 treated are prevented by the

Drug so on average etc, we need to treat

1000/9 =111 people to prevent one death

Stephanie Budgett: University of Auckland


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