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Risk is a percent: “win” over “total possible outcomes.”
If you flip a coin, the “risk” that you'll get “heads” is
“1 win out of 2 total possible outcomes” or 50%.
If you have a 4 sided die, the “risk” that you'll roll a “three” is
“1 win out of 4 total possible outcomes” meaning you'll roll a “three”, 25% of
the time.
Relative risk is comparing one risk, relative to another risk.
Thus the “relative risk” of winning a coin toss compared to rolling a die
is 50% to 25% - or two:
This makes sense: you're twice as likely to win the coin toss,
Thus, when you say “The relative risk getting cancer for smokers
is 4 times as large compared to non-smokers” You mean that 20 out of 100 non-smokers will
get cancer. And that 80 out of 100 smokers will get cancer.
Relative risk is NOT misleading.
What are the odds?
Risk is “wins divided by total possible outcomes.”
Odds are “wins divided by total possible losses.”
With a four sided die: The “risk” of rolling a “two” is “1
out of 4.” The “odds” of rolling a “two” is “1
out of three.”
Let's say you bet “twenty-five dollars” that you'll roll a two.
If you win, should you get one hundred dollars according to risk,
or seventy-five dollars according to odds?
If you rolled the die 4 times, you get these results:
Odds is the “Fair” payout: where the losses equal wins.
Now let's compare an 8 sided die to a 4 sided die.
The relative risk of winning is 1 out of 8, compared to 1 out of 4 -
again, twice the outcomes and a factor of two.
The odds ratio is 1 out of 7, compared to 1 out of 3 -
twice the outcomes, and “a factor that approximates two.”
So odds ratio approximates relative risk, when it's a rare event.
Pause and review
When it's a common event, odds ratio can exagerate misleadingly.
Normally, teenagers keep growing taller, it's common: let's say 80 out of 100.
Your wants to be a basketball athlete, Should he he buy an elixir that “approximately
doubles the odds ratio” that he will grow taller?
You examine the data and learn that instead of the normal “80 out of 100” to grow
taller, the elixer resulted in “90 out of 100 to
grow.”
The change in relative risk doesn't sound impressive.
However, the odds ratio sounds impressive: 8 to 2 (equal to “four to one”) compared
to “9 to one” - so it does double your odds ratio, since “nine”
is about “twice as much” as “four”.
Moral: Odds Commonly obfusKate; relative risk percent is “real.”
Pause and review
HelpHippo, Help your Hippocampus
(Relative) Risk STDS with “random ***” (“random”ized controlled trials and co”***”t
studies)
Case-control studies don't take as much time/effort/money, so there's less “risk” of waste.