Odds Ratios and Risk Ratios

so I thought we'd take a second to discuss the difference between odds ratios and risk ratios since there seems to be some confusion between the two now what we're really looking at here is the relationship between an exposure to something so in this case we'll say a kind of drug and some kind of health outcome so here this guy's having a heart attack so how likely is this exposure going to cause that heart attack so that's really what we're trying to figure out what we want to know is what is the risk of having a heart attack in those people taking that particular drug so the first thing that we need to talk about is the difference between risk and odds and if you'll remember we had a previous video that looked at the difference between probability and odds and this is really just the same thing so let's look at both of them so we're going to look at that in the context of these ten patients here now you can see that all of them are taking this pill but only some of them had a heart attack so what is the incidence or risk or probability of having a heart attack if you're taking these pills versus the odds of doing this of the same thing so let's look at both of those so the probability risk or incidence is of having a heart attack in patients taking this pill is six there are six people who had this heart attack over the total number of people that we're looking at so that's 10 people now let's contrast that with odds so odds is the number of people who have a heart attack which is 6 over the number of people who don't have a heart attack so in this case that's 4 so the difference here is what is going in the denominator in probability it's all the cases in odds it's all the cases that you did not include in the numerator so for probability the the maximum value you can get is 1 so in this case the value is 0.6 four odds there is no maximum value it can be infinite or it could be zero in this case it happens to be six over four or three-halves or equal to 1.5 so you can see that it's greater than one so the main point you want to take here is that the difference between probability and odds it's all about the denominator baby now the next thing we need to look at are the different types of studies observational studies we're going to look at cohort studies and case control studies so here we look at a cohort study and with a cohort study you start with the exposure and then you're going to look you're going to check for the outcome so we have two groups here one group is not exposed and this group is exposed here so you can see all these people here are taking this particular pill and none of these people are and then you're going to look in each one of those groups and see who had the outcome so in this case who had the heart attack now let's contrast that with a case control study and here you're starting with the outcome and then you're going to check for exposure so again we have two groups but this time in one group everybody has a heart attack these are the cases and in the other group nobody has that I would come nobody has the heart attack those are the controls and then you look back to see who was exposed to the particular thing we're looking at so in this case taking that particular pill so once again let's look at both of them for the cohort study we're going to start with exposed patients and not exposed patients whereas in the case control we're going to start with the outcome versus not having the outcome and then in the cohorts that are going to see who develops the outcome and in the case control we're going to see who was exposed to that particular thing now what things can we calculate from this so let's look first at the cohort study we can calculate the risk of the heart attack in both of the groups risk of the heart attack and those not exposed and compare it to the risk of the heart attack in those exposed so here we have 10 patients three of whom had a heart attack so 3/10 of the patients who are not exposed heart attack as opposed to those who were exposed to those who were taking this particular pill six out of ten or 60% had a heart attack of those that were exposed so here we're using risk we're using probability so now let's look at the case control study instead so we have instead we're going to start with our cases and we'll start with their controls we're going to look back and time to see who was exposed so here we're going to use odds and I'll tell you why in a second but let's calculate the odds so we say alright all of these patients have heart attacks how many were exposed how many took the pill well seven of them and how many didn't three so seven thirds is the odds of developing of having of taking the pill if you had a heart attack now what about in the control group well we had three who were taking the pill so there are three patients who took the pill and there are seven patients who didn't take the pill so the odds of taking the pill if you didn't have a heart attack is three over seven so here we're using odds whereas in the cohort study we were using risks or probabilities so now you might ask yourself why did you calculate odds for the case control why can't we just calculate risk well we kind of can we could calculate the risk of taking pills in those who had a heart attack which really doesn't make any sense the risk of taking pills and that's not what we were looking for in the first place anyway right what we really want to know is the risk of having a heart attack if you're taking the pill not the risk of taking pills if you had a heart attack but we can't calculate that risk because we don't have that data in the case control study we don't have a group of patients who are all taking the pill we'll have a group of patients who all had a heart attack and some of them only took the pill and of those who didn't some of them only took the pill so we can't calculate risk or probability in the case control study like we could for the cohort study but we can calculate odds yes we are calculating the odds of taking pills and those who had a heart attack which doesn't make sense but hold on to that thought we'll get back to that okay but first let's look at odds and risk again and so here we're going to look again at these ten people three of whom had a heart attack and I made a pie graph of them okay so that the whole circle is the ten people three of them had a heart attack seven of them had no heart attack and then we talked about odds and probability before so odds we said was the number of people who had a particular problem over those who didn't have that problem okay and so probability was remember people who had a particular problem versus all of the people that we were looking at so again look at the difference it's all about the denominator baby right this piece is included in the probability evaluator but it is not included in this denominator so why the heck is that important well it becomes important when you are looking at rare diseases so look I drew another little pie graph here but now we have a thin sliver of red meaning only a few people have the disease and most people don't have the disease now odds and probability are both calculated the exact same way remember it's those who have the disease over those who don't versus those where the disease versus everybody but this number here those who don't have the disease when you have rare diseases is pretty darn close to this right this almost complete pie is close enough to this almost through this complete pie so in this case the odds and the probability are approximately the same approximately they're not the same but approximately you can use the odds to estimate the probability so that is true for rare diseases now remember when do we use case control studies we use them for rare diseases okay we're almost to the end so I hope you're with me so let's let's go over again the difference between cohorts and case control studies and cohorts we start with an exposure and then we look at the outcome and in these we can calculate risk in case controls we start with the outcome and then we look back and see who of those were exposed so in the case control studies we calculated the odds of people with a particular outcome like in this case heart-attack having a particular exposure taking a drug but that's not really what we were looking for right we didn't care of about knowing of people who had a heart attack who was taking a particular drug instead we care about is this drug going to give my patients a heart attack we're looking for the opposite what is at risk of having a heart attack and those taking a particular drug so if you're willing to not use risk but use odds instead then guess what strangely enough those things are the same mathematically the same the odds of having a heart attack and those taking a particular drug and the odds of taking a particular drug if you had a heart attack now you shouldn't believe me so we'll mathematically go through it really quickly so first remember what is the odds ratio it's it's a ratio of odds it's a odds in the numerator and in the denominator so in the numerator we have the odds of the exposure in those with a particular outcome and the denominator we have odds of exposure in those without a particular outcome so odds of taking a pill if you had heart attack or odds of taking a pill if you didn't have a heart attack not really what we're looking for but it's what we can calculate so I wrote that out here like this so this is the odds of taking a pill if you had an MI right so it's so this group is all people who had a heart attack and those taking the pill and the denominator as those not taking the pill and then since it's an odds ratio you have an odds in the in the denominator to it so these are patients who didn't have a heart attack though is taking the pill over those not taking the pill now let's do the math on and it's nothing more than grade school math okay so we know that if we have something in the denominator we can bring it to the numerator and just invert it so we'll take this put that there and take this and put it here and now we made that fraction there so now what we have here is the inversion of what was the denominator is now here in the numerator so now we have pill times pill add that pill in MI and the inverse of pill and not fill in those not having an mi now what we can do is just move around some of these factors here so we'll take this bottom here no pill in MI and put it under this one and we'll take this one here and put it under the first one right there okay and so now we have done nothing other than simple mathematic in pill and MI over pill and not MI and here we have no pill and not MI and no pill and mi so let's put this back let's put this one back at the denominator again which means that we have to invert it so we put this here and take this put it underneath there and make this fraction again now what do we have here this is really just that we have MI and not mi so in all patients taking the pill this is the odds of two of having an MI and what do we have in the denominator we have no pill that we have MI and not mi so this is again another odds it's it's the in patients not taking the pill am I in this numerator and not in the denon dilemma and the denominator so we have another odds here so we have in patients not taking the pill what is the odds of having an mi this is what we were looking for left in the whole beginning right we were looking at how likely is it that the pill is going to cause having an mi so the odds of having an mi in patients taking the pill and the odds of having an mi in the patients not taking the pill that is the odds ratio we have so in that case control study where we thought we were not getting good information we actually are getting some information we're getting an odds ratio of what we were looking for even though we were starting with the outcome and looking at the exposure we got the odds ratio of the exposure given causing a particular outcome so is that odds ratio the same is the risk of getting a heart attack if you're taking a pill no of course not because we said that the odds and the risk are not the same thing but we also said in rare diseases the odds ratio is a good estimate it's a good approximation for the risk so if the odds ratio equals it's a 5 then you would say that patients were taking the pill are more likely to have an MI than those not taking the pill if the odds ratio was let's say 0.1 then you would say patients taking the pill are less likely to have a heart attack if they're taking the pill if they're taking that pill now if the odds ratio is 1 then the it's there's no difference it's the exact same whether they're taking the pill or not taking the pill so the pill probably doesn't make you have a heart attack and the last thing I want to tell you is remember to look at the confidence intervals so even though this might say 5 and you say well that sounds like it's it's very likely if the confidence interval for this thing goes from zero point nine to eleven point two that crosses one that crosses the number that means there's no difference so this would not be statistically significant similarly for this one if this non-olympic from let's say 0.001 to one point zero two that also crosses one the number of no difference so this would not be statistically significant and so when you look at these confidence intervals for a ratio you want to know is the number one in the confidence interval if the number one is in that confidence interval then it is not statistically significant so I help hope that helped remember we're looking at odds ratios versus risk ratios and really what we're looking for does an exposure cause some particular disease and we know that there's a difference between probability and odds and that's all about the denominator baby and the denominator includes everybody in probability and it doesn't include everybody in odds and this is important because our two types of study the cohorts and the case control studies in the case control studies we can really only calculate odds in the case control studies in the cohort studies we can come we can calculate risk you can also calculate odds but you probably wouldn't do that because you can calculate the nicer number risk there are times you might calculate odds but that's beyond the scope of this video so with the case controls you calculate odds with the cohort studies you calculate risk and the odds we calculate though is something backwards because look we're not going this direction we're going back where we're going this direction but that really doesn't matter because we showed that going this direction going this direction we're numerically equivalent and so you get the odds of this way equaling the odds of that way and then for rare diseases for rare diseases we know that the odds approximates the probability and so the last point wind also said is you know just remember the confidence intervals look at those confidence intervals if the confidence interval includes one it's not statistically significant if the odds ratio is one then you know there's no difference and that's why if one is in the conference interval that means there's no difference alright thanks a lot thanks for listening I hope that helps someone and leave any comments if you want thanks and - bye

Channel: Rahul Patwari

Views: 234,134

Rating: 4.9238777 out of 5

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Id: hOtoV2Kjb0o

Length: 17min 25sec (1045 seconds)

Published: Mon Feb 23 2015