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Mathster123

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If currently 1 out of 9 develops a certain disease, if the likelihood of developing it is Boosted by 84% what is this figure?
 

Subhotosh Khan

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If currently 1 out of 9 develops a certain disease, if the likelihood of developing it is Boosted by 84% what is this figure?
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Otis

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Is .84 the answer
Hi Mathster. The number 0.84 is the decimal form of 84%, not the answer. (The fractions 84/100 and 21/25 are two rational forms of 84%)

Boosting (increasing) a number by some percent means adding that percentage.

Here's an example: Increase 3.75 by 16%

We add 16% of 3.75 to the number 3.75

3.75 + (0.16)(3.75) = 4.35

We can use the 'Percent Change' formula to check the answer:

Percent Change = (New - Old) / Old

(4.35 - 3.75) / 3.75 = 0.16

It checks. Changing 3.75 to 4.35 is a 16% increase.


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Mathster123

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A Harvard report says taking benzos more than 6 months boosts chances of developing dementia by 84%. Does this mean 84 out of 100 taking benzos will go on to develop Alzheimer's. Or if currently 1 out of 9 develops Alzheimer's by 65 what does 84% mean? Many thanks for your help.
 

Otis

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… more than 6 months boosts chances of developing dementia by 84%. Does this mean 84 out of 100 taking benzos will go on to develop Alzheimer's…
No. It means the chance of getting Alzheimer's is 84% higher with benzos use than it is without. Let's look at the two chances (i.e., the probabilities with and without benzos) in more detail.

One out of every nine people in a control group developed Alzheimer's by age 65. In fraction form, we write that probability as 1/9 (one out of nine).

If we divide 1 by 9 on a calculator, we get an approximate decimal form of the probability.

1 ÷ 9 = 0.1111 (this approximation is correct to four decimal places; my choice to stop there)

0.1111 is also the decimal form of 11.11%

In other words, in the control group, everyone had an 11.11% chance of developing Alzheimer's by age 65 (1 out of 9).

The report says (based on some timeframe and dosing regimen) that more than six months of Benzodiazepine use boosts 0.1111 (the original probability) by 84%. That means 0.1111 increases by 84% of itself. To find the increased probability, we need to first calculate 84% of the number 0.1111 -- that percentage will be the increase.

Since we're working with decimal numbers, we use the decimal form of 84%, (which is 0.84) when doing the math to calculate 84% of 0.1111

0.84 × 0.1111 = 0.0933

84% of 0.1111 is 0.0933, so that's the increase.

Similar to the earlier example, we add the increase to the number that's increasing.

0.1111 + 0.0933 = 0.2044

Therefore, the boosted probability is 0.2044

0.2044 is the decimal form of 20.44%

The Benzodiazepine use boosted the probability of getting Alzheimer's (in the control group at age 65) from 11.11% to 20.44%

If we view those decimal probabilities as percents, then we see:

11.11% + 9.33% = 20.44%

This shows that benzos use raised the existing probability of Alzheimer's by about 9⅓ percent.



If we use the rational forms 1/9 and 84/100 for the probability and percent (when doing the math), then we get a different way of looking at the same 84% boost to the probability 1/9.

I'll skip some elementary arithmetic, but adding 84% of 1/9 to 1/9 (that is, adding fractions) requires a common denominator. I'll use 225.

25/225 is another way of writing the number 1/9. Therefore, 25 out of 225 people is the same probability as 1 out of 9 people (indeed, 25÷225 is 0.1111).

84% of 25 people is 21 people (0.84×25=21). So, an 84% boost means adding the increase of 21/225 to the original probability 25/225 to get the boosted probability 46/225.

This tells us that, without the benzos, 25 out of every 225 people in the control group developed Alheimer's by age 65, and, with the benzos, that probability was boosted to 46 out of every 225 people.

Feel free to ask additional questions, if you need more help understanding the 84% boost to the chance of getting Alzheimer's.

PS: A shortcut for increasing a number by 84% is to multiply it by 1.84, so we could also say that the benzo use increased the chances of Alzheimer's by a factor of 1.84. That's less than doubling the chances (which would be increasing by a factor of 2.00).

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