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  Vaccine Science
   What is Relative Risk?
   by Helen Tucker

1.  What is relative risk?

How many times more likely?
Relative risk is used to calculate how many times more likely something may happen given a risk factor vs. no risk factor.  If someone says, the relative risk of sunbathing for skin cancer is 5, it means sunbathers are 5 times more likely to get skin cancer than non-sunbathers.  If they say the relative risk of sunbathing for skin cancer is 0.5, it means sunbathers are half as likely to get skin cancer than non-sunbathers. 

Confidence interval
Relative risk is usually presented in context of a 95% confidence interval.  For example, say the relative risk is 5 (95%CI, 2.5 - 7.5).  This means that there is a 95% chance the true relative risk falls in between 2.5 and 7.5. 

2.  In what kind of studies is relative risk usually used?

Medical studies of therapeutic outcome
Relative risk is a biostatistic used only in medical research.  Other fields do not use this statistic, and most scientists have never even heard of it, for reasons explained later.  It is usually used by pharmaceutical and medical industries to study therapeutic effectiveness or harm, to answer questions such as "Does medication X present a risk for outcome Y"?  Note that the outcome could be beneficial and desired as well as one that is harmful and undesired. 

Prospective studies
Relative risk is used for prospective studies, where the researchers study the subjects in the future to follow them for an outcome.  A similar equation called the odds ratio is used for retrospective studies, in which researchers study data that already exists from the past.  However, there are authors who inappropriately use relative risk for retrospective studies, or use the odds ratio but call it relative risk.

3.  How is relative risk calculated?

2 x 2 contingency table

  Primary Outcome  
Risk Factor  Present Absent Total
Present a b a + b
Absent c d c + d
Total a + c  b + d n = a + b + c + d

Equation

RR = a (c + d) / c (a + b)

4.  What are some examples?

Example #1:  Relative Risk = 1
Let's say you wanted to find out if wearing hats presents a higher risk for car accidents.  You decide to study 200 people. You have 100 wearing hats and 100 not.  You follow them for a day to observe for car accidents.  You find that 5 out of the 100 hat wearers had accidents, and 5 out of the 100 non-hat wearers had accidents..

  Car accidents in 24 hours  
Hats Yes No Total
Yes 5 95 100
No 5 95 100
Total 10 190 n = 200

RR  =  a (c + d) / c (a + b)
RR =  5 (100) / 5 (100)
RR = 500 / 500
RR = 1

In this case, the relative risk turns out to be 1, which means hat wearers have the same chance of getting into a car accident as non-hat wearers.

Example #2:  Relative Risk = 3
Let's imagine the data read differently.

  Car accidents in 24 hours  
Hats Yes No Total
Yes 15 85 100
No 5 95 100
Total 20 180 n = 200

RR = 15 (100) / 5 (100)
RR = 1500 / 500
RR = 3

In this case, hat wearers were 3 times more likely to be in a car accident as non-hat wearers.

Example #3:  Relative Risk is 0.33
Let's imagine yet another set of data.

Car accidents in 24 hours
Hats Yes No Total
Yes 5 95 100
No 15 85 100
Total 20 180 n = 200

RR = 5 (100) / 15 (100)
RR = 500 / 1500
RR = 1/3 = 0.33

In this case, hat wearers were 1/3rd as likely to be in a car accident as non-hat wearers.  Or you could change the risk factor around to say the RR for not wearing a hat is 3.  In other words, non-hat wearers are 3 times more likely to be in a car accident than hat wearers.

5.  What are the limitations of relative risk?

Observation only, no hypothesis testing, therefore no scientific proof
Relative risk is a simple ratio, comparing the proportion in one group with the proportion in the other group.  It is an observation, the preliminary step in the scientific method.   However, it stops right there.  Relative risk calculations do not involve any hypothesis testing, so it cannot be remotely construed to constitute scientific proof.

No statistical significance
Its main limitation is that it doesn't tell you if the difference between the two groups is statistically significant.  Without statistical significance, there is NO WAY you can tell if the difference between the two groups is due to random chance or if the difference is due to the risk factor.  Without statistical significance, this statistic can be easily manipulated to say whatever authors want it to say.

6.  What are examples of how relative risk can be manipulated?

Example#4:  Presenting same results regardless of significance
Let's take example#2 above, but increase the sample size to 10,000.

  Car accidents in 24 hours  
Hats Yes No Total
Yes 15 9985 10,000
No 5 9995 10,000
Total 20 19,980 n = 20,000

RR = 15 (10,000) / 5 (10,000)
RR = 150,000 / 50,000
RR = 3

As you can see, the RR comes out to 3, whether the sample size of each group is 100, 1000, or 10,000.   However, it should be obvious that 15 out of 100 is a much different proportion than 15 out of 10,000.  While 15 vs 5 out of 100 might be significant, 15 vs 5 out of 10,000 is completely meaningless.  Yet whether the data is significant or meaningless, relative risk would still pronounce that hat wearers are 3 times more likely to be in car accidents. 

Example#5:  Extrapolating from small sample sizes and inconsistent proportions 

Car accidents in 24 hours
Hats Yes No Total
Yes 1 4 5
No 1 9 10
Total 2 13 n = 15

RR = 1 (10) / 1 (5)
RR = 10 / 5
RR = 2

The relative risk here says hat wearers are twice as likely to be in car accidents than non-hat wearers.  At first glance, 20% (1 in 5) vs. 10% (1 in 10) appears to be an impressive difference.  However, small sample sizes cannot be statistically significant because these 1 or 2 cases may be due to flukes or random chances rather than caused by the risk factor.  These 1 in 5 or 1 in 10 ratios may very well not hold true if a lot more people are studied.  Furthermore, comparing 5 people in one group to 10 people in another group requires making assumptions instead of relying on data.  One has to extrapolate that the 1 in 5 ratio would become 2 in 10, rather than comparing factual findings there there were indeed 2 accidents out of 10.   Relative risk comes out to be the same number whether findings are factual or derived from extrapolations and assumptions.

7.  What can you conclude from a relative risk study?

Not much.  If the authors present the raw data, one can get a general idea if the differences between the groups might be statistically significant or if too much extrapolation is involved.  If the authors do not present data for a, b, c, and d, the relative risk coefficient itself is completely meaningless.  It can carry no empirical weight because no one has any idea if the number is caused by random chance or based mostly on assumptions.

Relative risk is a statistic that is very easy to manipulate to yield results that a researcher (or a research funding source) wants.  Studies that use relative risk should be strong in design and methodology.  If anything less than scientific rigor is used, the study is an advertisement.  (Think, how much do you trust the "research" that says "Four out of five doctors recommend....?")

8.  How is relative risk used in vaccine science?

Relative risk calculations are often presented as the ONLY evidence that "no link" exists between vaccines and undesirable outcome.  These studies are subsequently cited as conclusive scientific evidence that the risks of vaccines are negligible.  As you can see, such conclusions are patently unscientific and inappropriate.

 

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