# Odds ratio and units of increase/decrease

#### mdstat

##### New Member
Hi!

I have the following question: If I perform a logistic regression for "amount of fluid" (independent variable, unit is milliliters) and the outcome "pass = 1 vs. fail = 0" (as dependent variable) and receive the following results for b = 0,205 > so the odds ratio is 1,227 (EXP of 0,205).

Is it correct to say that:
1. an increase of 1 milliliter of fluid results in an increase of odds for pass by 1,227 and this is equal to an increase by 22,7 percent
2. a decrease of 1 milliliter of fluid results in a decrease of odds for pass by 0,814 (1 / 1,227) and this is equal to a decrease by 18,5 percent (1 - 1/1,227)

As one milliliter is of less interest than a change of 10 milliliters - is it correct to say that
3. an increase of 10 milliliters of fluid results in an increase of odds for pass by 7,768 (1,227^10) and this is equal to an increase by 776,8 percent

if 3. is correct, how can I calculate the odds for pass for a decrease of 10 milliliters as factor and percent?

Thank you for any help!

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#### hlsmith

##### Less is more. Stay pure. Stay poor.
1.) a 1 mL increase in fluid was associated with a 1.2 (95% CI: ???, ???) times greater odds of a status of pass.
a 1 mL decrease in fluid was associated with a 0.2 (95% CI: ???, ???) times lower odds of a status of pass.

2.) a 1 mL increase in fluid was associated with a 0.8 (95% CI: ???, ???) times lower odds of a status of failed.

3.) a 10 mL increase in fluid was associated with a 7.8 (95% CI: ???, ???) times greater odds of a status of pass.

You can change the 95% to whichever values would be applicable to your context and field.

#### mdstat

##### New Member
@hlsmith

You used rounded values, so I'm not quite sure if I understand you correctly:

1.2 is from 1.227 - ok.
0.2 is the inverse value of 0.8, which comes from 0.814? Why is my interpretation of (2.) incorrect?
7.8 comes from 7.768 - ok.

Thank you!!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yeah those all seem correct. I could remember that the inverse is the same as changing the outcome reference, but could remember if it was the same as switching the exposure reference level. Which it appears to be.

So 1/OR gives the the OR for the switching the outcome or exposure reference group.

#### mdstat

##### New Member
@hlsmith

I'm sorry, but could you maybe repeat your first answer with the use of my values with the three decimals? I'm afraid I interpret your explaination incorrectly.

Why is my interpretation of (2.) incorrect?

Thank you!!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Yeah these things always seem trickier than they are. The odds are 1.227 times higher or an increase of 22.7%. They are the same thing.

Of note, I rounded the estimates, since really no one on the planet will care about the thousandths place - it is moot. However, if you are presenting protective (<1.0) estimates and harmful (>1.0), you can report to hundredths, since it kind of makes the two congruent in values. If submitting this to a journal - it will be up to their formatting requirements. It is a typical junior investigator thing to report any estimate to an obnoxiously low decimal place, but we aren't NASA or SpaceX so it doesn't matter as much and the target audience usually is indifferent.

Welcome to the forum!

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