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Stating a percentage increase that is calculated by subtraction rather than division is nearly always misleading. The increase in risk is 0.43%, which is still

by ascar 6y ago

Stating a percentage increase that is calculated by subtraction rather than division is nearly always misleading. The increase in risk is 0.43%, which is still low but two orders of magnitute higher than your statement. What you are calculating is the increase in percentage points [1] [1] https://en.wikipedia.org/wiki/Percentage_point https://en.wikipedia.org/wiki/Percentage_point

elcritch 6y ago
When dealing with relatively low probabilities (<0.5%), I prefer the percentage points as they give better context. That context being the overall risk to my life or health on an intuitive human level. For example, one medication I take “doubles my risk of some cancer” (over some ill defined period). That sounds terrible until you take the percentage points and realize it’s still less than a rounding error (or risk from driving in the USA) and therefore its easier to decide if the benefits outweigh the “doubled risk of xyz cancer”. From a policy decision perspective or for larger risks (>0.5%) the normal risk may be better.
- ascar 6y ago
  My main point is that you should clearly state it as percentage points if that's what you're calculating and want to express. That includes not using the percentage sign and indicating that these are percentage points. An increase in percent is without context interpreted as a relative increase not an absolute. Both statements have merit. If my risk of getting cancer per year is 1% rather than 0.5%, knowing this is 100% higher is useful. This is not a 1% chance in total but per year. For context, if we simplify this to a binomial distribution for a 20 year old with 60 more years to live (i.e. we calculate for each year getting cancer=p), the lifespan chance of getting cancer increases from 26% to 45%. Also the probability of the event is actually around 1% here (around 1000 in 100000), so higher than the 0.5% you mentioned.
  - andybak 6y ago
    To my mind both your point and the point you're replying to have merit. Saying "your chances of x have doubled" is flawed because that relies on knowing the probability of x. Saying "The risk of x happening is n% per day" (or an increase of n) is flawed because daily risks aren't what people care about - it's lifetime risk. So ideally the information should be phrased as something like "this increases the chance of the thing from x% to y% over an average lifetime." And then the footnotes can give deeper context.
    - elcritch 6y ago
      Thanks, both of you make good points. It probably would help if I called it "absolute" or "total risk" increase as that clarifies it. Of course stats is generally difficult for these vary reasons. > So ideally the information should be phrased as something like "this increases the chance of the thing from x% to y% over an average lifetime." I've personally never seen medicine info sheets give probabilities much less lifetime risks. > For context, if we simplify this to a binomial distribution for a 20 year old with 60 more years to live (i.e. we calculate for each year getting cancer=p), the lifespan chance of getting cancer increases from 26% to 45%. That would be more useful as well. > Also the probability of the event is actually around 1% here (around 1000 in 100000), so higher than the 0.5% you mentioned. It's really a rule of thumb for small values. In this case, I was interested in understanding the "4 extra people out of 100,000" as the article reports it (which is well below my 0.5% guideline) and not the baseline risk of illness per year. Ideally one compares both total and relative risks profiles. I'll be careful to add total risk vs relative risk to my descriptions in the future as that helps distinguish them.

by ascar 6y ago

elcritch 6y ago

When dealing with relatively low probabilities (<0.5%), I prefer the percentage points as they give better context. That context being the overall risk to my life or health on an intuitive human level. For example, one medication I take “doubles my risk of some cancer” (over some ill defined period). That sounds terrible until you take the percentage points and realize it’s still less than a rounding error (or risk from driving in the USA) and therefore its easier to decide if the benefits outweigh the “doubled risk of xyz cancer”. From a policy decision perspective or for larger risks (>0.5%) the normal risk may be better.

ascar 6y ago
My main point is that you should clearly state it as percentage points if that's what you're calculating and want to express. That includes not using the percentage sign and indicating that these are percentage points. An increase in percent is without context interpreted as a relative increase not an absolute. Both statements have merit. If my risk of getting cancer per year is 1% rather than 0.5%, knowing this is 100% higher is useful. This is not a 1% chance in total but per year. For context, if we simplify this to a binomial distribution for a 20 year old with 60 more years to live (i.e. we calculate for each year getting cancer=p), the lifespan chance of getting cancer increases from 26% to 45%. Also the probability of the event is actually around 1% here (around 1000 in 100000), so higher than the 0.5% you mentioned.
- andybak 6y ago
  To my mind both your point and the point you're replying to have merit. Saying "your chances of x have doubled" is flawed because that relies on knowing the probability of x. Saying "The risk of x happening is n% per day" (or an increase of n) is flawed because daily risks aren't what people care about - it's lifetime risk. So ideally the information should be phrased as something like "this increases the chance of the thing from x% to y% over an average lifetime." And then the footnotes can give deeper context.
  - elcritch 6y ago
    Thanks, both of you make good points. It probably would help if I called it "absolute" or "total risk" increase as that clarifies it. Of course stats is generally difficult for these vary reasons. > So ideally the information should be phrased as something like "this increases the chance of the thing from x% to y% over an average lifetime." I've personally never seen medicine info sheets give probabilities much less lifetime risks. > For context, if we simplify this to a binomial distribution for a 20 year old with 60 more years to live (i.e. we calculate for each year getting cancer=p), the lifespan chance of getting cancer increases from 26% to 45%. That would be more useful as well. > Also the probability of the event is actually around 1% here (around 1000 in 100000), so higher than the 0.5% you mentioned. It's really a rule of thumb for small values. In this case, I was interested in understanding the "4 extra people out of 100,000" as the article reports it (which is well below my 0.5% guideline) and not the baseline risk of illness per year. Ideally one compares both total and relative risks profiles. I'll be careful to add total risk vs relative risk to my descriptions in the future as that helps distinguish them.