Reading Jeff’s explanation of risk calculation below was like taking the *Ice Bucket Challenge*. My views on that phenomenon are published **HERE**. This article is very helpful in understanding the nuances and adding perspective to statistical analyses like those published on coffee drinking below. Ultimately one needs to understand the actual biochemical mechanism that explains the benefits of coffee and any other drugs used to treat disease to verify their statistical merits. Until then, I will continue to take my timed-release gram of vitamin C in the morning and pick up a large Dunkin Donuts coffee on my way to work. John Leavitt

From Jeff Gordon, M.D.

Relative Risk is not the same as an actual increase or a decrease in risk.

The Absolute Risk is the risk of developing a disease (such as cancer) over a defined period of time.

The Relative Risk is the risk difference when comparing two groups of people, for example people who smoke cigarettes and people who do not smoke cigarettes. The Hazard Ratio expresses this relative risk difference, but by a different number mechanism.

Let’s say that the risk of developing lung cancer is 80% higher in people who smoke than in people who do not smoke. This means the Relative Risk is an 80% increase. The Hazard Ratio states this as being 1.8. A Hazard Ratio of 1 means the difference between the two groups (smokers and non-smokers) is zero. Numbers higher than 1 mean increased risk. Numbers lower than 1 mean decreased risk. So, 1.8 means the smoking group has an 80% increase of getting lung cancer than does the non-smoking group.

First, this does not mean that the risk of getting lung cancer in the non-smoking group is 0. It just means the risk of getting lung cancer if you smoke is higher than if you do not smoke.

Second, the 80% risk increase may sound like a lot when looking superficially at the number “80%”. But, what is the Absolute Risk increase?

Let’s say the risk in non-smokers of getting lung cancer is 1 in 100,000. For smokers, this risk is increased by 80%, so the risk goes from 1 in 100,000 to 1.8 in 100,000. The absolute difference of 0.8 is very small. If the population were 300 million, then a 1 out of 100,000 risk increasing to a 1.8 out of 100,000 risk would translate into 3,000 cases of lung cancer increasing to 5,400 cases of lung (an increase of just 2,400 cases).

That puts things in perspective.

But, what if the Relative Risk increase is 800%? The Absolute Risk increases from 1 in 100,000 (for non-smokers) to 8 in 100,000 (for smokers). If the population were 300 million, then a 1 out of 100,000 risk increasing to a 8 out of 100,000 risk would translate into 3,000 cases of lung cancer increasing to 24,000 cases of lung (an absolute increase of 21,000 cases).

Even as the Relative Risk goes up, the Absolute Risk increase in this example is not staggeringly high because the baseline risk is not high.

But, what if the risk of getting lung cancer in a non-smoker is 1 out of 100? If the Relative Risk increase is 80% for non-smokers, then given a population of 300 million, as in the example above, then the cases of lung cancer go from 300,000 up to 540,000. This is an absolute increase of 240,000 cases. The increase in total cases goes up more due to the higher baseline Absolute Risk.

If the Relative Risk were 800%, then the number of cases goes from 300,000 to 2,400,000 cases. The increase in total cases is much, much higher because both the baseline Absolute Risk and the Relative Risk are increased.

An example I use daily in my medical practice is explaining the potential risk reduction of dying from a cancer if someone takes a recommended treatment (such as chemo). Look at how the numbers change even if the Relative Risk reduction of dying is the same if the same chemo is used.

· Baseline risk of death is 10%. A 50% Relative Risk reduction by using chemo translates into an Absolute Risk reduction of 5%, so the risk of dying of the breast cancer drops from 10% to 5% after chemo. The risks of having a serious problem from chemo could be 2%, let’s say, so the benefit is larger than the risk of chemo, but not by much.

· Baseline risk of death is 50%. A 50% Relative Risk reduction by using chemo translates into an Absolute Risk reduction of 25%, so the risk of dying of the breast cancer drops from 50% to 25% after chemo. The risks of having a serious problem from chemo could be 2%, let’s say, so the benefit outweighs the risk of chemo.

· Baseline risk of death is 90%. A 50% Relative Risk reduction by using chemo translates into an Absolute Risk reduction of 45%, so the risk of dying of the breast cancer drops from 90% to 45% after chemo. The risks of having a serious problem from chemo could be 2%, let’s say, so the benefit much outweighs the risk of chemo. However, there is still a sizable remaining risk of dying of the cancer even after chemo given the very high baseline risk even with a sizable Relative Risk Reduction.

There are many ways to try to explain this.

Another number worthy of knowing is the Number Needed To Treat (NNT).

Let’s say that chemotherapy has a 50% Relative Risk reduction in the risk of dying of breast cancer. If the Absolute Risk of dying of breast cancer without chemo is 10%, then the Number Needed To Treat with chemo to benefit one person is 20. That means 20 people get chemo so that one person can get the actual benefit. A lot of people would be getting chemo without benefit because the baseline Absolute Risk of death from the breast cancer is low and the Absolute Risk Reduction is low.

But, if the same 50% Relative Risk reduction from chemo is applied to a baseline Absolute Risk of 90% of dying without chemo, then the NNT is 2.2, which means that 2.2 people get treatment so 1 can benefit (which is the same as 22 people getting treatment so 10 can benefit).

Of course, nowadays, we are much better with individualized benefit and risk assessments of breast cancer to minimize people getting treatment that won’t benefit them, thereby focusing on giving treatment to the people who could benefit the most from it.

So, the next time you read a news story trying to wow you with statistics about how great something is, keep these questions in mind:

What is the baseline Absolute Risk of the disease?

What is the Absolute Risk Reduction of a treatment for the disease?

What are the risks of side effects of the treatment?

How many people need to be treated for one person to get benefit?

What is the cost for treating an individual and what are the costs for treating a whole population?