how to interpret an odds ratio?

[WashMe]

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I saw an old thread on this, but I'm a little confused...

Say you have a disease, "step1itis", and being a med student is a risk factor for having it. It affected 3 out of 5 med students but only affected 1 out of 5 pre-meds, so your odds ratio is (3/2)/(1/4) = 6, right? What confuses me is that the odds ratio is 6, but it looks like the med student is only 3x as likely (3 out of 5 vs. 1 out of 5) to have had step1itis. Where does the number "6" come in there in a way that actually aids in our interpretation of the data?

 

[mastamark]

I saw an old thread on this, but I'm a little confused...

Say you have a disease, "step1itis", and being a med student is a risk factor for having it. It affected 3 out of 5 med students but only affected 1 out of 5 pre-meds, so your odds ratio is (3/2)/(1/4) = 6, right? What confuses me is that the odds ratio is 6, but it looks like the med student is only 3x as likely (3 out of 5 vs. 1 out of 5) to have had step1itis. Where does the number "6" come in there in a way that actually aids in our interpretation of the data?

6 times as likely if your OR is 6 as this relates to a hypothetical risk factor(being a med student), that's huge. The control group in this situation is your premeds and they shouldn't have high odds of the getting problem. so you want the odds of med student induced step1itis/premed step1itis to be high to prove your hypothesis is correct.

If it was 1, then 1X as likely so no real increased odds. Med students and premed student would have equal odds. If it's above 1 then there is a correlation between the risk and the event that the risk caused.

I hope my disorganized explanation made sense. I hope I'm right lol

Edit:Fixed

 

[mastamark]

BTW...I said risk, but I meant "odds."

Apologies, it is important to distinguish Risk from Odds. If you're lookin back at what happened with those students, you are looking for the "odds" that there was a correlation not "risk". The latter is talking in future tense.

 

[RapplixGmed]

I saw an old thread on this, but I'm a little confused...

Say you have a disease, "step1itis", and being a med student is a risk factor for having it. It affected 3 out of 5 med students but only affected 1 out of 5 pre-meds, so your odds ratio is (3/2)/(1/4) = 6, right? What confuses me is that the odds ratio is 6, but it looks like the med student is only 3x as likely (3 out of 5 vs. 1 out of 5) to have had step1itis. Where does the number "6" come in there in a way that actually aids in our interpretation of the data?

This is a very good question and one that I have thought about too from time to time and it takes a little bit of explaining:

The confusion comes out of another philosophy of looking at chance: the idea of "odds" rather than "probability." In common speak, we'd say, the odds are 2 to 1 that I win, meaning that a ratio exists where for every 2 positive outcomes that I could get by chance, there is also a chance of a 1 negative outcome. Odds are the probability of success divided by the probability of failure. Compare that to the statement "I have a 2 in 3 chance of winning", where we mean that out of 3 distinct possibilities, 2 are in my favor. Both statements are equivalent but just reflect different ways of thinking about chance.

So in your example, the probability of them getting the disease is 3 times better but the odds ratio (remember odds ratio, not odds by itself) really is 6 times better! This is actually a logically consistent statement!

The concept is a little easier to understand the way it is usually used in biostatistics. Relative risk is always used in prospective studies because we are defining the risk factors and we want to see what the effects are on the probability of outcomes. We have a ratio of target outcomes to all outcomes, which makes sense.

However, in the case-control studies where we use odds ratio, the outcome has already been determined and we are trying to work backwards to see what the risk factors were. In this scenario, the concept of a building a ratio of people with your risk factor of interest to those with "all risk factors" (your normal construct for probability) makes no logical sense. What in the world would "all risk factors" mean? You would have to construct a ratio of your risk factor of interest to those without your risk factor, which is exactly what the odds are.

The mathematics are a little complicated but they put to work this logical foundation. In fact, mathematically, as the incidence of the disease approaches zero, the odds ratio will approach the relative risk for the population from which the case-control was sampled. Thus, for all intents and purposes, you can interpret an odds ratio as if it was a relative risk assuming that it is a rare condition.

 

[WashMe]

This is a very good question and one that I have thought about too from time to time and it takes a little bit of explaining:

The confusion comes out of another philosophy of looking at chance: the idea of "odds" rather than "probability." In common speak, we'd say, the odds are 2 to 1 that I win, meaning that a ratio exists where for every 2 positive outcomes that I could get by chance, there is also a chance of a 1 negative outcome. Odds are the probability of success divided by the probability of failure. Compare that to the statement "I have a 2 in 3 chance of winning", where we mean that out of 3 distinct possibilities, 2 are in my favor. Both statements are equivalent but just reflect different ways of thinking about chance.

So in your example, the probability of them getting the disease is 3 times better but the odds ratio (remember odds ratio, not odds by itself) really is 6 times better! This is actually a logically consistent statement!

The concept is a little easier to understand the way it is usually used in biostatistics. Relative risk is always used in prospective studies because we are defining the risk factors and we want to see what the effects are on the probability of outcomes. We have a ratio of target outcomes to all outcomes, which makes sense.

However, in the case-control studies where we use odds ratio, the outcome has already been determined and we are trying to work backwards to see what the risk factors were. In this scenario, the concept of a building a ratio of people with your risk factor of interest to those with "all risk factors" (your normal construct for probability) makes no logical sense. What in the world would "all risk factors" mean? You would have to construct a ratio of your risk factor of interest to those without your risk factor, which is exactly what the odds are.

The mathematics are a little complicated but they put to work this logical foundation. In fact, mathematically, as the incidence of the disease approaches zero, the odds ratio will approach the relative risk for the population from which the case-control was sampled. Thus, for all intents and purposes, you can interpret an odds ratio as if it was a relative risk assuming that it is a rare condition.

Thanks man!

 

[shaman06]

Odds are the probability of success divided by the probability of failure. The concept is a little easier to understand the way it is usually used in biostatistics. Relative risk is always used in prospective studies because we are defining the risk factors and we want to see what the effects are on the probability of outcomes. We have a ratio of target outcomes to all outcomes, which makes sense.

However, in the case-control studies where we use odds ratio, the outcome has already been determined and we are trying to work backwards to see what the risk factors were. In this scenario, the concept of a building a ratio of people with your risk factor of interest to those with "all risk factors" (your normal construct for probability) makes no logical sense.

The mathematics are a little complicated but they put to work this logical foundation. In fact, mathematically, as the incidence of the disease approaches zero, the odds ratio will approach the relative risk for the population from which the case-control was sampled. Thus, for all intents and purposes, you can interpret an odds ratio as if it was a relative risk assuming that it is a rare condition.

Another quality post from this Rapplix dude! I'll be succinct, since he already hit a ton of the 'meat' of the concept.

This is critical: in case-control studies, you CANNOT determine the prevelance of the disease, and therefore you cannot use a risk-ratio to compare groups. Case-controls are great when diseases are rare; you can gather up 10 disease + people, and match them with a random 10 disease - group, and look retrospectively to peek at risk factors predisposing for the disease. Again, think here: this CANNOT possibly infer prevalence because you are artificially creating the sizes of disease postive and disease negative indidividuals.
But Grapplix also correctly pointed out that as the disease becomes more and more rare (prevelance or incidence approaches zero), the odds-ratio better approximates the risk-ratio (if one was to run a massive prospective cohort study - or live in Scandanavia!)

Just know - case-control = ODDS RATIO; risk-ratios are used when prevelance of the disease can be ascertained (prospective studies). I think that'll be more than enough for Step1.

 

[WashMe]

Another quality post from this Rapplix dude! I'll be succinct, since he already hit a ton of the 'meat' of the concept.

This is critical: in case-control studies, you CANNOT determine the prevelance of the disease, and therefore you cannot use a risk-ratio to compare groups. Case-controls are great when diseases are rare; you can gather up 10 disease + people, and match them with a random 10 disease - group, and look retrospectively to peek at risk factors predisposing for the disease. Again, think here: this CANNOT possibly infer prevalence because you are artificially creating the sizes of disease postive and disease negative indidividuals.
But Grapplix also correctly pointed out that as the disease becomes more and more rare (prevelance or incidence approaches zero), the odds-ratio better approximates the risk-ratio (if one was to run a massive prospective cohort study - or live in Scandanavia!)

Just know - case-control = ODDS RATIO; risk-ratios are used when prevelance of the disease can be ascertained (prospective studies). I think that'll be more than enough for Step1.

Thanks bro! You guys are on the ball. I might not flunk after all, with your help 😀

 

[WashMe]

Let's say the odds of a woman having an ectopic without STI exposure could be 10% vs 90% that are ectopic free giving us the odds of 10/90 or 0.11

yeah the whole (x:y) versus x/(x+y) is a brain bender... we rarely use the former in our daily logic.

 

[tco]

BTW...I said risk, but I meant "odds."

Apologies, it is important to distinguish Risk from Odds. If you're lookin back at what happened with those students, you are looking for the "odds" that there was a correlation not "risk". The latter is talking in future tense.

OP, an easy way to remember this is that O comes before R in the alphabet.