I’m throwing up this post on the concept of relative risk as a time saver. I’m going to be doing some posting soon in which relative risk plays a role as it has in many of the postings in the past. Instead of taking time in each post to explain relative risk, I will simply be able to link to this one and get on with it.
Let’s say we are studying the rate at which people taking a particular medication get cancer. If we randomize our study population into two groups and give one group the drug and the other group a placebo, we can wait around for 5 years (or 10 years or 20 or whatever our protocol is) to see how many develop cancer in each group. Then we can compare.
If after 5 years we find that 10 of the subjects taking the drug develop cancer and only 5 of the subjects taking the placebo get cancer, we can say (assuming there were equal numbers of people in both study groups to start) that twice as many people taking the drug got cancer. We can then say that the relative risk (usually written as RR) of getting cancer from taking the drug is 2.
The relative risk is the number of subjects who develop the problem divided by the number who didn’t. In our example above it would be 10/5 = 2.
Another way to present this data is to say that the relative risk of not getting cancer by not taking the drug is 0.5. In other words, people who didn’t take the drug had half the risk of getting cancer compared to those who did.
In our simple example we assumed that there were exactly the same number of subjects in both groups. In reality this usually isn’t the case. There will be a difference in group sizes so instead of using numbers of subjects, researchers will use percentages. So in our case above, let’s say that 4 percent of the subjects taking the drug got cancer and 2 percent of those taking the placebo got cancer. We have the same relative risk of 2. (4 divided by 2 = 2)
It all seems pretty straight forward. But it often isn’t as it seems. There can be two studies that show the same relative risk but there is a world of different meaning for the relative risk. This idea is what we want to focus on because this is the one that researchers use all the time to scare us needlessly.
I’m going to create an example loosely based on the facts to show you what I mean. Let’s compare the safety records of two airlines over the past 25 years. In 1985 Delta had a crash in Dallas (in which one of my best friends was killed) and in 2001 American had three crashes. The two from 9/11 and one going from New York to San Juan, Puerto Rico. Let say that there were 200 people killed in the Dallas Delta crash and 600 people killed in the three American crashes.
Let’s assume that both airlines fly about the same number of miles each year. American has about 4000 flights per day, so if we assume an average distance (probably too short) of 500 miles per flight, we get 730 million miles flown per year. If we multiply by 25 to get the miles flown in 25 years we come up with 18.25 billion miles flown. Let’s assume the same for Delta. If we divide the number of victims of crashes from the two airlines by the number of miles flown, we can come up with a risk of dying per mile flown on each of the airlines. If we do this for Delta we discover that the risk of dying comes out to be 200 divided by 18.25 billion or about 0.00000001096. This tiny number represents the number of people who have died per mile flown by Delta. If we do the same calculation for American we find that the number is 0.00000003288 deaths per mile flown.
Now if we want to calculate the relative risk of flying on American verses flying on Delta we divide the American risk by the Delta risk (0.00000003288 divided by 0.00000001096) and we get 3. So, the relative risk of flying on American is 3 compared to flying on Delta based on the last 25 years of crash history. This means that it is 3 times more risky to fly American than it is to fly Delta. Based on these figures you are 3 times more likely to die if you fly American than if you fly Delta. It’s true, and these figures prove it.
We all know that it’s hogwash. There is no difference in risk between flying these airlines because the numbers are so low as to be ridiculous, which is the precise reason I used this example. The total numbers make a difference.
What if there were an airline that had 90 deaths for every 100,000 miles flown and another that had 30 deaths for each 100,000 miles flown. The relative risk for flying the first as compared to the second would be 3 just as it is with American verses Delta, but the real risk would be much, much different. In fact, you wouldn’t want to fly on either of these airlines because they are both too risky. But if you had to fly on one, you would much prefer the one with only 30 deaths per 100,000 miles.
Many drug companies use the relative risk in their propaganda. They might do a study with two groups of 40,000 people with one group taking their drug and the other taking a placebo and monitor them for 5 years. If the drug is supposed to prevent heart disease, then the researchers would tabulate the number of cases of heart disease that arose over the 5 years, then see how many cases developed in the subjects taking the drugs compared to the ones taking the placebo.
If there were 43 people who developed heart disease while taking the placebo and 31 who developed heart disease while taking the drug, then the relative risk of not taking the drug would be 43 divided by 31 which is 1.39. The drug company then proclaims that people not taking their drug had a 30 percent greater chance of developing heart disease, which sounds pretty significant. But it’s a lot like the Delta/American example: the numbers aren’t all that large.
What it really means is that out of the 40,000 people who took the placebo for 5 years only 12 more developed heart disease than in the group of 40,000 people who took the drug. Thats 2.4 people out of 40,000 per year. (12 people divided by 5 years = 2.4 people per year) If the drug costs a lot of money and has unpleasant side effects associated with it (think statins), would you be willing to pay the bucks and put up with the side effect hassle on the chance that you might be one of the 2.4 out of 40,000 who might be saved from developing heart disease? Or would you just take your chances? I would definitely take my chances.
2.4 people out of 40,000 per year sounds a lot less risky than a 39 percent increased risk that the relative risk implies.
One other way the relative risk can be used to flim flam people is when it is too small to be meaningful yet is touted as having great merit.
Without going into all the statistical detail (which if you’re interested in you can read about here and here from previous posts) suffice it to say that relative risk ratios below 2 are pretty much meaningless. So when you see a relative risk of 1.28 and hear someone say that represents a 28 percent increased risk, you can blow it off. Once the relative risk gets to the 2 or greater level, then it starts to have some meaning. But, once again, only if the numbers aren’t so small as to be meaningless. Remember, the relative risk of flying American is three times that of flying Delta if you simply look at the relative risk. In reality, however, the numbers are so small that the differences are meaningless.