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Working on Statistics

Absolutely Relative

March, 2019 | By Michael Guren

The other day, I came across an article, "...heart drug obtains breakthrough status". I was intrigued. They had me at "breakthrough." So I opened the study to read the results.

The highlight of the study was the fact that this drug reduced the mortality (death) rate by 37% at six months; compared to placebo. That sounds incredible.

Wait, what does a 37% reduction in death rate mean? How should we think about a "37% reduction in mortality"? To make an informed decision about whether to prescribe or take a prescription drug, it is important to understand what these types of results mean.

To answer this question, we have to dip our toes into the pool of statistics. Don't worry, we're not staying long.

Here are the raw study results from the breakthrough trial touting a 37% reduction in mortality (with decimals intentionally left off):

- Placebo: ~11% mortality rate (i.e., ~11% of placebo-taking patients died)

- Study Drug: ~7% mortality rate (i.e., ~7% of drug-taking patients died)

I don't see 37% anywhere in the above numbers, so where did the number originate? The answer is, it's relative.

The ABSOLUTE difference in mortality rates is 11% minus 7% = 4%. Meaning that there was a 4% absolute difference in mortality rates between placebo and study drug.

The RELATIVE difference, however, is ~37%. We can even show this using a formula: (11 minus 7) divided by 11 = ~0.37 or 37%. Relatively speaking, the study drug reduced the risk of dying by 37% when compared to placebo.

Almost all drug studies present the relative difference between treatments, which can be misleading. For this reason, it is imperative that you understand which type of risk reduction a study is referencing. Is it absolute (e.g., 4%)? Or is it relative (e.g., 37%)?

Let's dive a little deeper for a second and discuss the medical term, Number Needed to Treat (NNT). NNT is often used within the medical community to understand how many people need to take a drug to have one person benefit. For example, an NNT of 10 means that ten people need to use a particular medication for one person to show any benefit. The other nine people will have no benefit.

How is NNT calculated? It's pretty simple. Divide 100 by the absolute risk reduction. So, using our example from above, the absolute risk reduction was 4%. Therefore, the NNT would be 100 divided by 4 = 25. In other words, 25 people will need to take this new drug for 1 person to show any benefit.

Let's recap.

This "breakthrough" drug, touting a 37% reduction in mortality, actually has a 4% ABSOLUTE risk reduction in mortality and requires 25 people to be treated to save one life.

Using our statistical knowledge from above, let's explore a more common drug class — cholesterol-lowering medications (aka "statins").

In high-risk patients with existing heart disease, statins reduce the risk of having a heart attack by about 35%. Thirty-five percent mortality reduction is roughly the accepted number used within the medical community.

Do you think 35% represents the absolute OR relative risk reduction?

If you said 'relative,' you are correct! So what is the absolute risk reduction? How about the Number Needed to Treat (NNT)?

First, we need raw numbers. In high-risk patients with existing heart disease, the following is generally true:

- Placebo: 9% heart attack rate

- Statin: 6% heart attack rate

Just like the above example, let's calculate absolute vs. relative risk reduction:

- The ABSOLUTE difference between heart attack rates is 9% minus 6% = 3%.

- The RELATIVE difference is (9% minus 6%) divided by 9% = 0.33 * 100 = ~35%

So that's where the 35% reduced risk of heart attacks originates!

How about the Number Needed to Treat (NNT)? Well, like before, we divide 100 by the absolute risk reduction (e.g., 3%). So 100 divided by 3 = ~33.

Therefore, 33 people would need to take a statin for one person to prevent a heart attack.

(Note: The actual heart attack risk reduction and NNT for statins vary slightly depending on the study in question. http://www.thennt.com/nnt/statins-for-heart-disease-prevention-with-known-heart-disease/ )

I am not advocating that you alter drug therapy based on these over-simplifications. Hopefully, this knowledge will help foster more productive conversations between you and your Doctor (or patient).

So the next time you hear "This drug reduces mortality by 40%!". You'll know the right questions to ask to determine the absolute truth.