What does a 2x risk of AD mean?

[Nick]

What does a 2x (or 3x or 4x, etc) increased risk of AD mean?

If I read that the general population has a 1 in 9 risk of ABC at age xx, one could assume that a 2 x risk means 2x are in a population group where 2 in 9 get ABC. Then you see that 1 in 2 will get ABC at age yy. Using above logic, that implies that in our 2x group 2 of 2 would get ABC. But that does not make sense when you look at 3x or 4x.

As I recall, statins halve the risk of heart conditions measured. It goes from 4% general risk to 2%. When you look at those numbers you really wonder about the value vs risk of using statins. So when I see that a 3/4 is 2x (by some estimations but not all) it begs the question of what that actually means. This is not meant to minimize the seriousness of AD risk. Just trying to understand the "magnitude".

[Julie G]

Welcome, Nick! Great question. I'm no statistician, but my understanding is that 1 in 9 in the average population will develop AD by age 65 which represents an 11% risk. Two times the risk would increase the odds to 22%, three times to 33%, four times to 44%. Does that seem right?

[Nick]

Your math seems right at first glance. But when you apply it to 1 in 2 at 85 (as I recall), which is 50%, then at 2x there is 100% chance which I understand is not the case (100% of 3/4's do not develop AD). If the risk is 3x, than at 50% at 85 the number would be 150% which does not make sense (you can't have more than 100% risk).

I've often looked at problems and analysis at the extremes to see if the numbers still work. It appears they do not work using the above math. When that is the case, one can suspect they don't work as discussed in the first case (1 in 9) and further analysis is needed.

I hope this explains the "why" behind my question.

[Julie G]

FWIW, per The Alzheimer's Association, 33% of 85 y/o will develop the disease, not 50%. That being said, I'm wide open to being proven wrong. I hope our statisticians will hop in with a better response. I share your curiosity.

[Nick]

33% looks better than 50% The Promethease report indicates 2x for 3/4 but other web pages have differing numbers upwards of 4x.

+1 for the statisticians.

[SusanJ]

Nick, try this one for an explanation.

https://cpmc.coriell.org/genetic-educat ... nding-risk

[Nick]

Thanks Susan..the link does a great job of framing the issue and provides insight.

I was a marketing person and the question was "what story do you want to tell?" relative numbers (such as percentage and x factors) hide details and make things look impressive (depressing). For example, from a operating cost perspective, which is more desirable given current US price structure:
- 100% efficient electric furnace
- 75% efficient gas furnace

The answer is the 75% gas furnace. But I digress.

And I'm still having troubles with relative numbers that when applied to x of y populations yield more than the y population.

[Julie G]

Nice link, Susan. So, the 11% risk by age 65 is an absolute risk and the genotype specific risks (like 2x, 3x 4x, etc.) are relative risks. I would assume that inclusive in the absolute risk is all APOE genotypes whereas the relative risk would be specific to that APOE genotype.

With that understanding, look how this blurb from the Alzheimer's Organization (link above) is worded:

Having the e4 form increases one’s risk compared with having the e3 form, while having the e2 form may decrease one’s risk compared with the e3 form. Those who inherit one copy of the e4 form have a three-fold higher risk of developing Alzheimer’s than those without the e4 form, while those who inherit two copies of the e4 form have an 8- to 12-fold higher risk.25-26 In addition, those with the e4 form are more likely to develop Alzheimer’s at a younger age than those with the e2 or e3 forms of the APOE gene.27 Researchers estimate that between 40 and 65 percent of people diagnosed with Alzheimer’s have one or two copies of the APOE-e4 gene.23,28-29

For those with a singular E4 allele, the risk is compared to those with zero E4 alleles thereby raising the risk to 3x whereas E4 homozygotes are purported to have an 8-12 fold higher risk using the same comparison.

And I'm still having troubles with relative numbers that when applied to x of y populations yield more than the y population.

My guess is that in that case the y population is being defined with zero E4 alleles which is not a true absolute risk artificially raising the relative risk to be higher than the true absolute risk. Make sense?

[Nick]

I would assume that inclusive in the absolute risk is all APOE genotypes

... I think that is fair to say but read on.

FWIW, per The Alzheimer's Association, 33% of 85 y/o will develop the disease

The document says:
- "About one-third of people age 85 and older (32 percent) have Alzheimer’s disease.1"
- Then in figure 3 it says "Estimated Lifetime Risk for Alzheimer’s, by Age and Sex, from the Framingham Study" 10% men and 20% women for 85YO's

So the first line result sums "85 and older" . That includes everyone older so 33% is not a fair risk factor for an 85YO. The Figure 3 numbers (M-10% or F-20%) are a better estimate for an 85YO (and not just because it is more optimistic).

But going back to the core question ...given the numbers in The Alzheimer's Association document figure 3 for an 85 YO women in the Framingham Study (a US population sample set as I recall), women in the US (or maybe only applying to Farmingham) have a 20% chance of Dementia or AD. If a 4/4 women has a 10x (avg. of 8x to 12x) rate over the population whole, then 200% (10x20%) of the 4/4 subset would develop D or AD.

But the math has to top out at 100%. 200% is nonsensical. And getting a 200% answer raises the question of the suitability of the math (risk multiplier times base rate). Put another way, we all have 100% chance of dying. There is nothing we can do to increase that rate. You cannot have a 200% or 2x the 100% base rate. You can't double a 100% death risk/rate.

Yes, 3x20% (60%) for a 3/4 works but10x20% (200%) doesn't work and you can't use an equation that sometimes works. Both results are likely skewed.

So is multiplying risk factor by base rate sorta like multiplying apples by oranges?

whereas the relative risk would be specific to that APOE genotype.

Since it is a "relative number" it has to compare to some other group, and not itself. But we don't have all the numbers to determine that number.

I'm thinking the best answer we could have is a table where on one axis you have the Ex/Ey combination and age on the other axis with the field filled with the statistics/probability. Then the increased rate (relative rate) can be calculated from there.

To disassemble each of the numbers presented in Figure 3 and the rest of the document, one needs to know more numbers than presented herein. Specifically, IMHO, at a minimum we need the population size data per E combination as well as D & AD rates per E combination.

I hope I don't come across as obstinate or a troll. And I apologize for being a bit long winded. The more I dig into this, the less I like the multipliers as presented even though they would be useful numbers when accurate and understood.

Maybe this is a question for the folks who put together the referenced document. UPDATE: I did pop an email off to them for their response.

Update 2: It would be technically more accurate to say that not more than 100% of the group can die. That said it is the same message.

[Julie G]

Maybe this is a question for the folks who put together the referenced document. UPDATE: I did pop an email off to them for their response.

Good for you, Nick. As we both know, statistics can be manipulated to make a point and the Alzheimer's Organization has come under recent fire for using scare tactics to fundraise. That being said, multiple sources arrive at different risk levels for ApoE4 carriers leading to confusion. Adding to the uncertainty, many variables including gender, age, race, education level, etc. further change the odds. From what I've learned, as a 3/4 male without a family history (especially maternal,) your risk is only slightly above that of average... whatever that is . That being said, there are many simple lifestyle changes you can make to further mitigate your risk.