[Music] hi team welcome to health stats iq it's a video series dedicated to the critical concepts within health statistics and if you want to see any of these videos i'll put a link in the description to the playlist for all the health stats iq vids or else you can check out my website on zed statistics dot com but we're having a look at relative risk and odds ratio today so we'll jump straight into that shall we let's do it so we're first going to look at the intuition behind these two concepts and i'm going to use an example to show you how to calculate relative risks and odds ratios we'll then look at case control studies and that's where odds ratios really come into their own after that i'm going to see if i can make an equivalence between relative risks and odds ratios and i'm going to provide you this really interesting chart that shows what particular relative risk values equate to in odds ratios that's something i've not seen before in other videos on youtube so you might want to stick around for that and finally we'll look at some examples from research so you know what you're looking for when you're doing a bit of research of your own so let's jump into the intuition now relative risk which i'm terming rr and don't forget this may also be risk ratio some people call this risk ratio but i'm using relative risk which i believe is a bit more common relative risk and odds ratio are measures of group comparison used when we have a categorical exposure and a categorical outcome okay so typical exposures we might look at in health sciences might be something like an intervention group versus a control group so this is a categorical exposure because you're either in the intervention group so you've been given the medicine of interest that we're testing or you're in the control group where you're given the placebo or not given any medicine at all for example other types of categorical exposures might be when we look at say male versus female or we might even turn something numerical into a categorical exposure such as looking at bmi body mass index we might say there are two categories of body mass index if you're over 30 bmi that means you have the exposure of interest in that you are overweight and if you're under 30 bmi that means you're underweight more generally we might also say that someone has the morbidity versus someone doesn't have a particular morbidity so whether that's diabetes or a particular cancer or something like that so these are all types of categorical exposures and the categorical outcomes we tend to be interested in are a lot simpler they're either looking at whether someone died or survived or alternatively we might have a categorical outcome which is that they developed the disease versus not developing the disease so relative risks and odds ratios help us when we're trying to compare the probability of a negative outcome between the two exposure groups so let's take one of these and have a look at an example we're going to take the bmi over 30 and under 30 exposure and we're also going to look at the categorical outcome which is the development of a disease and in this case the disease of interest is whether someone has a stroke or not you can see we have the exposed group being those who are obese in that their bmi is above 30 and those unexposed are those who are well healthy is an interesting way of putting it just not being obese but we'll just call it healthy to make it easy less than 30 bmi is unexposed and of course there are two potential outcomes stroke and no stroke so let's put some numbers in here let's just say we had 100 people in our sample that were obese and 500 people that were healthy and you can see the numbers of strokes for each of those particular exposure groups now the first thing we might want to do is actually calculate risks so before we can get a relative risk we actually have to get the individual risks of each of the exposure groups so let's have a look at the obese group first the risk of a stroke for obese people in this sample is 20 on 100 which is 0.2 so you take the number of people who have had a stroke in that group divided by the total number of people in the group and you get 0.2 pretty straightforward whereas the risk for healthy people you can see we've only had fifty strokes out of five hundred so that's a risk of point one or ten percent now there are formula for this but i tend not to use formula on this channel when it's something that's very intuitive because i think it turns your brain off and i want your brains very much operational right now so i'm not going to feed you formula he says showing a formula although this one's just to show you that the relative risk is going to be the risk of the exposed group which is going to be the obese divided by the risk of the healthy group so we get a relative risk of two so the way we can interpret this relative risk is to say that obese people have twice the risk of developing stroke when compared to healthy people and this all makes a lot of sense and i think it's quite intuitive the idea of a risk and then a relative risk so let's go to the dark side now and have a look at odds ratios so whereas the risks were the number of people in the stroke outcome group divided by the total the odds are actually the people in the stroke outcome group divided by the people in the no stroke outcome group so instead of being 20 on 100 it actually it's actually going to be 20 on 80. that's for the obese group and the odds of experiencing stroke for the healthy group is not 50 on 500 but it's 50 on 450 so we actually get different numbers when we're calculating these odds they're different to the risks and once we calculate these the odds ratio is calculated very much like the relative risk was where we just take the top one divided by the bottom one and in this case we're going to get 2.25 so for the same data set we're going to get a different odds ratio than we will relative risk and if we were to interpret this odds ratio we'd say that obese people or the people in the exposed group have 2.25 times the odds of stroke when compared to the healthy group now this will raise a really important question and here it is what on earth did we need odds for it seems like we had everything we wanted with relative risks why do we need to create something which is less interpretable harder to actually visualize and provides an extra layer of complexity on things well in the particular example here there is no real reason to calculate odds ratios and while i haven't really mentioned it this particular example is what might be called a prospective study the idea being we kind of follow a bunch of obese and healthy people along and we follow them up to see whether they have the outcome or don't have the outcome and because it's prospective these individual rows are consistent so we have a hundred obese people in our sample and 20 of them had a stroke we had 500 healthy people in our sample and 50 of them had a stroke these are all internally consistent but what if we don't have a prospective study what if we have a case control study well let's find out you might be guessing that this is where odds ratios are actually necessary so if you haven't heard of case control studies before this is where i'll introduce them to you as well and they're very common this is a question that can be answered by a case control study does inner city living increase the risk of lung cancer okay so let's have a think about the exposure again we've got the city dwelling so if you live in the city you might think that you get exposed to more car fumes less natural environments and stuff so perhaps you're going to experience a larger probability of lung cancer so if we're going to do a prospective study here we need to find a lot of people in both these dwellings follow them up and see if they develop lung cancer or not the problem here is we're going to need a lot of people in both of these exposure groups because realistically lung cancer is pretty rare so we realistically have to follow let's just say 10 000 people in each of these groups just to get a decent amount of data with which to work so if we did this we could totally find relative risks and that would be fine but of course the reality is that's a very large study that we need to conduct very expensive it's going to take a long time because it's prospective don't forget we have to follow them up many years later because lung cancer is something that develops over many many years so this is realistically not doable what happens is we actually sample from a bunch of people that have lung cancer and then also a bunch of people that don't have lung cancer usually these people are matched or they're kind of very similar people to those in the lung cancer group but on all facets except for the fact that they have no lung cancer and in this way we're actually selecting cases these are called cases those that have lung cancer and those that don't have lung cancer are called controls now you don't actually have to sample the same number of cases and controls that tends not to happen exactly but let's just say in this case we've sampled 200 people with lung cancer and 200 people that have no lung cancer we then can survey them to say well where have you lived most of your life in inner city areas or in regional areas so let's just say that these are the numbers that we get from our sample okay so here are the six kind of calculations that we made on the previous slide we found the individual risks and the risk ratio then we found the individual odds and the odds ratio reg here just means regional dwelling city is for city dwelling my question is which of these calculations can you actually find from the data we've been given and the answer is only the odds ratio we can't calculate any of these other measures with the data we've been given why not why can't we calculate risks well think of it this way so we've selected 200 cases and 200 controls we didn't really need to select 200 and 200 we could have selected anything we wanted in each of these two groups and that would obviously change the calculation we'd make for the risk if we were to try to calculate a risk for the city dwelling we'd go 145 divided by the total but what does the total even mean it's totally dependent on how many cases versus controls that we've just chosen to sample if you tried to calculate it it would look like it's more than 50 percent of people getting lung cancer so clearly we can't calculate risks risk ratios similarly won't make any sense for the same reasons and the idea of calculating the odds for a city dwelling is is equally as silly because again it looks like we're going to have more people developing lung cancer than not developing lung cancer in the city you'd have 145 divided by 122. that's crazy so clearly we can't have any of these calculations why then can we still nonetheless calculate an odds ratio now this is where i am going to give you a little bit of formula action for the first time on this channel i'll put some formula up here because i think in this case it is actually useful so on the previous slide we found that the odds ratio if the cells here are represented by a b c d the odds ratio was a on b that would be the odds for the exposed group divided by c on d which is the odds for the regional group now it doesn't take much maths to realize that it's actually the same as saying a on c divided by b on d so what you might think well the good thing about having a on c is that it is entirely internally consistent we've selected 200 people that have lung cancer so we know that of those that have lung cancer 145 of them live in the city so 145 divided by 55 is an internally consistent ratio that tells us the odds of living in the city if we have lung cancer so if we're to calculate the odds ratio we can go 145. now i've actually done it this sort of vertical way but you could have done it the original way we looked at the odds ratio by going 145 divided by 122 and then dividing all that by 55 on 78 but i've done it kind of the other way it'll get the same answer by going 145 on 55 divided by 122 on 78 and i get 1.686 so there we have the reason for odds ratios so even though you'd never use an odds ratio when you had a relative risk available in case control studies that's all you got so here we can say that city dwellers have 1.686 times the odds of developing lung cancer when compared to regional dwellers and as we're going to find out for rare diseases like lung cancer the odds ratio is actually going to be very very close to the relative risk anyway so this 1.686 we can almost take as a relative risk even though this is not a prospective study but that only works when cases are rare let's investigate that a little bit more so let's have a look now at the equivalence chart that i talked about at the start of this video before we look at the chart i just want to show you two particular scenarios in this first table up here you can see we have one case in the unexposed group and two cases in the exposed group so in other words one percent of the unexposed group become cases two percent of the exposed group become cases so the relative risk would be two it's just two percent divided by one percent similarly down here you can see we have forty percent of the exposed group become cases versus twenty so again the relative risk is going to be 2. 40 on 100 divided by 20 on 100. in each case the exposed group has twice the risk of becoming a case in other words developing the disease or dying for example than the unexposed group does so i've written here that the risk for the unexposed group is 0.01 on this first example and the risk for the unexposed group is 0.2 20 for this example if you were to calculate the odds ratio for each of these two examples here you'd find that you get 2.02 in this top example and 2.67 in the bottom example feel free to check these calculations by the way it's probably a good test if you like but you can see that the odds ratio is actually quite close to the relative risk when we have rare diseases in other words when cases are rare but when cases are not so rare the odds ratio will differ by a lot from the relative risk so what i've got here is a way of equating the relative risk with odds ratio and i'm starting with this blue line here which is where our unexposed risk is one percent so when it's a very rare disease you can see that as the relative risk increases to 1.5 to 2.53 all the way up to five the odds ratio kind of mimics it and by a relative risk of five the odds ratio is only slightly higher than five so that dotted line represents where the relative risk is equal to the odds ratio so this basically shows you that when you have a rare disease the relative risk that you calculate will be very similar to the odds ratio you can see what happens though when we have a slightly more common disease or when the cases are slightly more frequent the odds ratio actually starts increasing quite a bit above the relative risk so it's still quite close when you've got relative risks of say 1.5 and 2 but let's add now a 10 risk in the unexposed group and you can see what's going to happen we've got 10 percent 15 there's 20 30 percent and even 50 percent so if the risk in the unexposed group was 50 your odds ratio is going to be a lot higher than the relative risk that you create i thought this was useful to see because when i was studying this i was like well what are the differences in terms of magnitude of relative risks and odds ratios and hopefully this chart can give you that kind of impression when the overall risk of developing the disease is low they're very similar but when the overall risk increases your odds ratio is going to be a lot larger than your relative risk so the final thing we're going to have a look at in this video is an example from research looking at relative risks and an example from research looking at odds ratios so the first one comes from kerhan in 2019 and i'll put the link in the description of the video if you want to check out the actual study so what kerhan did was look at the effect of hearing loss on cognitive decline in old patients so the idea being that if you have more hearing loss you're actually more likely to have a higher degree of cognitive decline so they created categories of hearing loss and also categories of cognitive decline for which to make this comparison now because this was a prospective study where we followed up people that had hearing loss to see whether they developed cognitive decline well guess what then we can use relative risks so let's have a look and see the table that they had in this paper so here we have table 3 which looks at the hearing status of the person so this shows them what this shows us which exposure group each of the people are in so no difficulty hearing is the unexposed group mild hearing loss is the sort of i guess first stage of exposure moderate hearing loss is a higher exposure group severe hearing loss with no hearing aid is a higher exposure group still and then there's another exposure group being severe hearing loss using a hearing aid you can see we have the number of cases here showing us the number of people that developed cognitive decline and we have the age adjusted relative risks so forget about the age adjustments for the moment what this is showing us is the risks of developing cognitive decline compared with the reference category of no difficulty so in brackets here this says ref in this first one because this is our reference category 1.28 in this particular category for mild hearing loss means that if you have mild hearing loss you have 1.28 times the risk of cognitive decline of someone that has no hearing loss so your risks are increased essentially by 28 if you have mild hearing loss if you have moderate hearing loss your risks are increased by 34 or in other words you have 1.34 times the risk of someone in the reference category and if you're in the severe group you have 1.44 times the risk of cognitive decline of someone in the reference category now for the record all we're doing when we age adjust things or when we adjust things for other variables as well is just making sure that people in each of these exposure groups the mild hearing loss group the moderate hearing loss group and the severe hearing loss group are actually similar on a whole bunch of other variables it's possible that people with severe hearing loss might have other comorbidities that are creating their cognitive decline so when we adjust for those other comorbidities that's when we get these different relative risks but anyway i thought you'd show i thought i'd show you an example of where relative risks are used in practice now wrench does a study just from the year 2020 comparing the experiences of covert with different ethnicities so what wrench does is that they look at black white and hispanic people using their ethnicity as the exposure of interest and then seeing how that might affect the outcome of developing covert but then also of dying from covert as well so they do a lot here but the key point to note is that it's a case control study they select people that have covered and then they select people that do not have covert so they're actually looking at the cases and controls and going backwards to then assess their ethnicities and potential their ethnicities and other factors as well so let's have a look at that particular paper so here's what is called a forest plot so i'm showing you a lot in this video but what this is showing us is the odds ratio where we compare different ethnicities in terms of a positive test result for covert so when we compare white to white obviously the odds ratio is going to be one we need a reference category which in this case is going to be white people so black people have 1.93 times the odds of testing positive for covert than white people do hispanic people have 1.84 times the odds of testing positive for covert that why people do and again they actually compare different age groups as well for some reason they've chosen 60 to 69 as the reference group so you can see that as you get younger you're actually more likely to test positive for covert but interestingly if we look on the right side here you've got the 30-day mortality among cases clearly as your young if you're younger you're going to have you're going to have a lower odds of dying from coven so that's what this right side looks at here it shows us that there's not much difference in terms of the actual mortality between white black and hispanic people there is a difference between those in various age brackets and interestingly it looks like while male people have much more positive test results they also in fact look like they have slightly higher mortality as well so their odds of dying from covert is 1.48 times that of females but you can see these are or odds ratios why because it's a case control study we look at we've collected data from those that have covered and we've compared them to those people that do not have covert or in this case we've looked at people who have died from covert and compared that to people who have not died from cope so that's it guys there's a big video but we're looking at relative risk and odds ratio i thought i would try to make it extensive if you liked that please subscribe to the channel and if you know anyone that is into health sciences share these videos around because i think it's going to become quite a nice little extensive look at health statistics which will help clinicians hopefully epidemiologists and some budding statisticians themselves i would think anyway my name's been justin zeltzer i hope you've enjoyed you can check out all the videos from this series and others on zedstatistics.com i'll catch you around [Music]