Interpreting confidence intervals for the odds ratio

odds ratios are everywhere they are sometimes so important that they are in headlines in newspapers and Facebook posts today we're going to talk about interpreting the odds ratios as they might appear in an actual medical journal so typically you might see a sentence that says the odds ratios and then it will say parentheses 95% confidence intervals are presented in table 3 so table 3 and I just made up the RIA could be table 2 it probably wouldn't be table 1 table 3 could look something like this and feel free to pause the video and copy it down we have a risk factor and and these are completely hypothetical so this isn't a real study but these are the way odds ratios could look in a real study so we have these hypothetical risk factors like vitamin D supplementation vitamin C supplementation vaping and exercise and then I gave you two different odds ratios now I want you to notice that one of the odds ratios is less than 1 and the other odds ratio is greater than 1 now of course we're gonna go somewhere with this I did this on purpose and here we have some 95% confidence intervals and we're going to see if we can learn how to interpret these and it's actually a really simple idea but it requires you to sort of know a little bit what you're doing so the very first thing we should probably look for is to see if we can state the research question as a very simple question pause the video if you and try to do this welcome back so the research question is simple is there and association and it's very important to use the word association because odds ratios come from case control studies which can't test for causation only association so is there an association between the exposure variable or risk factor I'll just write I'll just write the exposure variable and disease so that is the research question and question should end with question marks now the next thing you should ask yourself is what would be even null hypothesis and what would be the alternative hypothesis pause the video and see if you can do this welcome back so the null hypothesis is that the true odds ratio is equal to one the number one unity against the alternative hypothesis that the true odds ratio is not equal to one now I phrased this very carefully we can we can talk a little bit more about this in detail but if you're simply testing for an association not in a specific direction this is the hypotheses that correspond to this research question as written okay now the next question you might have is well where did I get the number 1 from why is this a 1 why is this not a zero why is this not a 536 point 23 why a 1 well to answer that question we have to go back to the definition of what the odds ratio actually is and the odds ratio is a ratio of two terms now even if I didn't say what these two terms were the very fact that it's a ratio probably should give you a little hint here that if the numerator is equal to the denominator denominator not equal to zero of course then this ratio should be equal to one but let's put it any way so this is the odds so in a case control study which is where we're going to use the odds ratio this is the odds of randomly selecting a study subject who was exposed given that he or she was a case divided by the odds of randomly selecting a study subject who was exposed given that he or she was at control so if there's no different differential level of exposure cases versus control and these are exactly equal then under the null hypothesis you know if the numerator and the denominator are both the same then this odds ratio would be equal to one and that's what would happen if there was no link between exposure and case control status so with this in mind it should be kind of clear that this one is the busines magic number here and that under the null hypothesis the odds ratio is hypothesized to be one so one is a very very important number so let's go through this really really carefully and see if if you can figure out whether there is a statistically significant Association and if we do identify a statistically significant Association the important thing is to then ask yourself another question is there significant protection or is there significant risk so let's look at this really carefully now I would advise you to pause this video here and see if you can interpret these confidence intervals and then you know I'm gonna do it now welcome back okay so here we have an odds ratio observed to be 0.71 now I want you to notice that this odds ratio is less than one so that suggests the idea that vitamin D could be protective against getting this disease but we need to see whether this is statistically significant right less than one would be protective greater than one would be a risk factor so here what we do is we look at both bounds of this 95% confidence interval we look at the lower bound oh point 68 and we look at the upper bound point 84 and I want you to notice something both of these bounds are less than one so even accounting for chance both of these bounds are less than one so this is a statistically significant Association and it is a protective Association because both of these bounds are less than one so we call this we could call this significant I'm just gonna write sig for a significant significant protection of this right Prout for protection or this is a statistically significant protective very factor or variable so you know you guys who's who have followed my videos probably know that I love vitamin D and I'm a huge proponent of vitamin D and I think responsible sunlight exposure where you don't burn you know and go a little short of that too is probably healthy but I'm not a physician I'm a statistician not a physician so here vitamin D looks in this hypothetical data that I just made up looks like it's it's significantly protective because the point estimate is less than one and both bounds of the confidence Centreville are less than 1 so this is significant protection let's look at vitamin C by contrast I purposely wrote this to have the same exact odds ratio point estimate because I didn't want you to think that this is what's driving the statistical significance though this is what's driving the idea that there's there's possible protection here so I'm gonna write poss for possible possible protection because the point estimate is less than 1 but you're gonna be disappointed when you look at the bounds of the confidence interval because see the lower bound point 42 you might get excited but say all vitamin D seems like I'm sorry vitamin C vitamin C seems like it's protective look this mound of the confidence interval is less than 100 but this bound is greater than 1 this would suggest vitamin C is protective the lower bound but the upper bound would suggest that vitamin C is actually a risk factor well confidence interval make up your mind well this is the whole point that the variability is so large in this point estimate that this is not a statistically significant effect so I would interpret this as possible protection but not significant so I'm gonna write this down but not significant and when I say significant I mean statistically significant at the 5% significance level because that's what we use in our culture so this bound again possible protection well you could get excited this bound possible risk they don't agree too much variability alright let's look at thinking of course I made this up I'm not a huge proponent of vaping I I wonder about this but you know I've never studied it myself I just made this up so let's say the odds ratio for vaping was observed to be one point twenty one twenty one percent increased risk alright so the lower bound of this confidence interval which is really the best case scenario for vaping still has this above one so even accounting for chance there's still seven percent increased risk this is above 1 so and in the upper bound you know is fifty-six percent increased risk I mean so both of these bounds agree they're both above one which says significant risk so anybody looking at this confidence interval would probably if this is true you know I just made this data up you know would think that vaping is probably a significant risk factor let's look at exercise now I made this up now I purposely gave exercise the same point estimate of 1.21 but you'll notice here the lower bound is less than one and you might say oh yeah Oh exercise yeah yeah let's exercise because the lower bound is less than one this could be protective oh I'm excited but oh no look at the upper bound the upper bound has a 69% increased risk for getting the disease well for differential exposure not really getting these disease so yeah the bounds don't agree this bound looks like exercises protective the lower bound this bound looks like exercise has 69% more exposure in cases relative to controls right you know taking into you no chance this is the actual point estimate though really what we observed was 21% more exposure to exercise in cases relative to controls on the odd scale so if we look at this over here this is a non significant effect so you could say yeah there might be some possible protection [Music] I'm sorry possible risk sorry there might be some possible risk but it's not significant so here you basically now it is possible to see an odds ratio that's one point zero zero I've seen it before when the sample sizes are extremely small in let's say a certain subgroup that they might not have really planned for but it happens that in a certain subgroup that's important you might get so few study subjects that you could in theory see something like this you might actually see this now notice of course you know I put the point zero zero in this shows that these things are rounded off you know this is this is just data you could see that and you'll typically see this when the sample size is really low in a certain subgroup you'll see this of course you know you take one look at this you know nothing's going on here there's you know no significant association from the data but even looking at this you might have a little column for n somewhere to see how many subjects were used well it would be in the cases and the controls really but just looking at this you could almost be correct in guessing that chances are when you see this you're in a subgroup that has a very few number of cases and a very few number of controls and this is really the best you can do but this when you see something like that the better inference to take would be you probably don't have enough data to make any inference at all but some people would say oh well nothing's going on here you know our confidence interval is exactly one point zero zero when you see this take this with a grain of salt and I always look back to see you know how much data you know how many cases you actually had how many controls you actually had with this particular risk factor and subgroup you were looking at probably very very small number of subjects and so be a little careful of this this situation don't jump to the no Association conclusion better jump to that how many people were actually studied conclusion probably more helpful so let me summarize this idea for you guys here we have point estimates that are less than 1 so you're thinking protection but you have to look at the confidence intervals to see if the protection is statistically significant both bounds are lower than 1 significant protection one bound is lower than 1 one bound is upper than one possible protection but it's not statistically significant here we have an odds ratio estimate that's greater than one so you're thinking risk here both bounds are greater than one so this is statistically significant risk but here you have a bound less than 1 and you have a bound greater than 1 they don't agree so the point estimate suggests possible risk but there's too much variability in this to really conclude any kind of statistical significance so if you've enjoyed this video please give me a thumbs up and subscribe to my channel so I can be encouraged to make more videos like this and if you didn't like this video and you think there's something I could do better shoot me a comment and maybe I can improve my delivery thank you

Channel: College Statistics

Views: 14,167

Rating: 4.9223299 out of 5

Keywords: odds ratio, Interpreting confidence intervals, Interpreting confidence intervals for the odds ratio, Statistics

Id: 9n96ABSGz9U

Length: 18min 51sec (1131 seconds)

Published: Fri Apr 10 2020