Estimating Risk Lecture.pdf

Study Guide Relative risk (RR) Attributable risk (AR) Attributable risk % (AR%) Population attributable risk (PAR) Population attributable risk % (PAR%) Odds ratio (OR) Interpretation of RR and OR 95% CI – Statistical significance Matched OR Calculations RR, OR, AR, AR%, PAR, PAR%, Matched OR, 95% CI Estimating Risk - Part 1: Introduction An es&ma&ng risk We'll mainly be learning about how to calculate measures which are important in public health and epidemiological research, par&cularly for those measures of associa&ons related to case control studies and cohort studies which are rela&ve risk and odds ra&os. When we think of Abby and the aims of epidemiology, they mainly pertain to disease preven&on, either by determining race of disease, iden&fying risk factors, or developing strategies that would best result in disease preven&on. To meet these objec&ves, we need to rely on several measures, and that's what we're going to learn about today. For instance, when we want to determine race of disease by person, place and &me, we turn to absolute risk, more speciﬁcally, incidence and prevalence, which you're all very familiar with already. Another objec&ve of epidemiology is to iden&fy risk factors for disease. We accomplished this by designing studies like cohort studies, case control studies. But how do we actually conclude or pinpoint what par&cular exposure is associated with our disease of interest? We use measures of associa&ons. For cohort studies, we use rela&ve risk. For case control studies we use odds ra&os. And lastly, when we're thinking about poten&al strategies to combat disease, we would like to have the highest yield in terms of disease reduc&on. To do this, we need to know how much of the disease would be reduced if we eliminated a certain risk factor. That way, we can target our strategies to focus on exposures that are contribu&ng the most to disease development. To do this, we rely on the measure of aEributable risk. Let's talk about absolute risk ﬁrst. Absolute risk is the likelihood of an individual in a popula&on developing a certain disease. It's essen&ally the incidence of disease within a given popula&on. This measure provides an indica&on of the magnitude of risk and a group of people who have a certain exposure the risk that you will get a disease over a period of &me. If we look back to incidents, we recall that incidence measures the new cases in a popula&on over &me. This essen&ally indicates the force of the disease or conversion of health status. You can either be expressed as cumula&ve incidence as shown in the top formula, or as incidence density which takes into account accumulated person &me. S does not, however, provide any informa&on about the associa&on between the exposure and the disease because there is no comparison that is made. If we look at some absolute risk examples, you see that there is an implicit comparison made. But to properly determine if an associa&on exists, we need to make an explicit comparison. You see on the slide 3 examples of absolute risk. The ﬁrst one is congenital rubella appears in 80 to 100% of infants if maternal infec&on of rubella occurs during the ﬁrst trimester pregnancy. This statement provides us informa&on about the absolute risk, but it doesn't give us informa&on about the measure of associa&on between maternal rubella infec&on during the ﬁrst trimester and congenital rubella in the infant because we lack a comparison group. What about the infants who had mothers who had maternal infec&on in the second trimester or the 3rd? And the second example is states ver&cal transmission of parvovirus B19 is approximately 35%. While this is important informa&on, it provides us with the absolute risk of parvovirus B19 from mother to child during gesta&onal development. But what it does not have is a comparison group that would lend addi&onal informa&on that is needed to determine associa&ons. The same is said about the last example. Approximately 90% of infants perinatally or infected during the ﬁrst year of life develop chronic hepa&&s B virus infec&on. Again, the comparison is only implicit. There is no explicit comparison which is needed to determine whether an associa&on exists. Thus, these examples are considered only as absolute risk. To truly examine whether an associa&on exists between exposure and a disease or health outcome, we need to have comparison groups. Groups without the disease, groups without the exposure. This way we can see if there is an excess risk of disease and the group that is. Exposed. If the socia&on is strong, then there is more evidence to support that the rela&onship is causal. A court team is always considered the inﬂuence of confounding factors, as we discussed in the previous lectures. Several studies are u&lized to help inves&gators examine research ques&ons that seek to learn more of the rela&onship between exposure and outcome, in par&cular case control studies and cohort studies. Each study design has a measure of associa&on that is linked to it, for example. The color study is able to yield a rela&ve risk. It can also yield an odds ra&o because of the way it's designed. But for the most part, a rela&ve risk is seen as a stronger measure of associa&on. So when people ask what the measure of associa&on for in a cohort study is, the answer is a rela&ve risk. Case central studies, on the other hand, cannot calculate rela&ve risk. They are only able to determine odds ra&os. So when you think of a case control study, you should immediately think of the odds ra&o. Before we go into calcula&on and interpreta&on of these measures, let's revisit the general steps in every research. We ﬁrst start with an idea, a research ques&on we would like to address and ﬁnd out more about. We hone our ques&on, and we look to see what our popula&on of interest is. We think about exposure assessment deﬁni&on of our outcome of interest. We sample our popula&on and determine exposure and disease status based on our conceptualized measures of them. We then es&mate whether an associa&on exists between our exposure and disease using appropriate sta&s&cal models and evaluate whether the ﬁndings support of poten&al causal. Socia&on. These two steps are where we are now in the semester here today to discuss es&ma&ng risk. To do this, we rely on the handy dandy con&ngency table, otherwise known as the two by two table. This is an important tool that's u&lized to help determine the associa&on between exposure and disease by cross classifying exposure status and disease status. The columns of a two by two table represent disease status, yes or no and the rows represent exposure status, yes or no. Some people switch it up depending on what they're examining. My sugges&on is to only s&ck with one format as to not get confused with the formulas as you start the calcula&ons. As men&oned earlier, your columns are disease status. First column consists of people who have the disease, the second column is of people without the disease. The rules represent exposure status. The ﬁrst row is for everyone who is exposed, The 2nd row is for everyone who is not exposed. So what you end up with are 4 categories of people and block A. You have people who are disease but who are also exposed and block B. You have people who were exposed but do not have the disease, and block C you have people who have the disease but were not exposed. And then in block T you have not diseased people who were not exposed. You can have your totals on the sides of the table. At the far right you have your total number exposed as a sum of A + B. You have your total unexposed right underneath with C + D. Then your totals for disease on the very boEom le\ with A + C and the total number of undisclosed with B + D This table is really important as you move forward in calcula&ng measures of associa&ons for case control and cohort studies.When you're asked to construct a two by two table, refers to the side and set up the two by two table. This way you ﬁll in the table with the informa&on that is given the prompt. Estimating Risk - Part 2: Relative Risk Rela&ve risk is the probability of an event happening in exposed people compared to the probability of the event happening and the non exposed people. So think back to the design of a cohort study. You start with exposure status and you follow people for a speciﬁed period of &me to determine whether disease develops. So it makes sense that the rela&ve risk, the measure of associa&on for coerce studies is deﬁned as a probability of disease development and exposed compared to the probability of disease development and the unexposed. It's essen&ally a ra&o of two incidence rates. Remember, we cannot calculate a rela&ve risk and. Case control study because case control studies do not have incidence data because they start with disease and then go to exposure. The rela&ve risk has and the numerator the condi&onal risk of disease among the exposed. The denominator has the condi&onal risk of disease among the unexposed. This translates to the formula on the boEom right of the slide and the numerator we have A / A + B. Which is the number of exposed people who get the disease over the total number of people exposed? And the denominator we have C / C + D, which is the number of unexposed people who get the disease divided by the total number of people who were unexposed. The calcula&on itself is preEy easy, but what does this number mean? If we were to get a rela&ve risk of one, that means that the risk of the exposed is equal to the risk of the unexposed. So there's no evidence to suggest that there's any associa&on. But if the rela&ve risk is greater than one, then there is a posi&ve associa&on because the risk among the exposed is higher than the risk among the unexposed. In some instances, you will see that the rela&ve risk is less than one indica&ng an inverse associa&on. Because the risk among the exposed is actually less than that of the unexposed. This means that there is a protec&ve associa&on. An example could be between physical ac&vity and obesity development. The rela&ve risk would most likely be less than one for a study examining this research ques&on, so let's take a look at some examples. In the ﬁrst example, we are examining the associa&on between cigareEe smoking, deﬁned as greater than or equal to 1 pack per day, and heart aEacks yes or no. And we are looking at a ﬁve year follow up number for each group's exposure and disease status is within the two by two table If we want to calculate a rela&ve risk, we need to look at the incidence and the exposed compared to the incidence and the unexposed. So let's start with incidents and the exposed. We would take the number of people who smoked and who got heart aEacks and divided by the total number of people who smoked, which was 1074. So we would get 8.2% for the ﬁve year incidence rate among smokers or among our exposed group. For unexposed, we would take the 26 non-smokers who got heart aEacks and divide that by the total number of people who did not smoke or who were unexposed, which was 1076. For unexposed we would take the 26 non-smokers who got heart aEacks and divide that by the total number of people who did not smoke or who were unexposed. So that would be 1076. Using this formula we would get it incidence among no cigareEe users as 2.4%. We can use these numbers to get our rela&ve risk. The formula for the rela&ve risk can be seen on the boEom of this line. We plug the values of the incidences that we just calculated into the formula 8.2% for the numerator because this is incidence among the exposed, and then 2.4%. For the denominator, because this is the cumula&ve incidence of the unexposed and then we will calculate this out to be a rela&ve risk of 3.4. So what do these numbers even mean? Or how do we go about interpre&ng these numbers? So let's start with the ﬁve year incidence we calculated for smokers and non-smokers. As you recall, the incidence for smokers was 8.2%. This means that the probability of heart aEacks is 8.2% among people who smoke at least one pack a day. The probability of a heart aEack among people who were unexposed or people who did not smoke is 2.4%. The rela&ve risk we obtained was 3.4. This means that there is a 3.4 greater probability of heart aEacks for people who smoke at least one pack of cigareEes per day compared to people who did not smoke at all. This indicates a posi&ve associa&on in excess risk among the exposed of our disease of interest. And the second example. We are examining the rela&onship between history of sexual abuse and suicide aEempts and adolescents. We have our numbers for each group listed in the table. We again calculate the incidence rate among the exposed and the unexposed. We get 60.8% as the incidence of suicide aEempts for people who had a history of sexual abuse. Compared to 24.7% among people who did not have a history of sexual abuse. We can take the incidence among our exposed and our unexposed groups to calculate our rela&ve risk. We plug the incidence values into the formula with 16.8% going into the numerator because this represents the instance of our outcome suicide aEempt among people who were exposed, meaning that people who had a history of sexual abuse. And then we take 24.7% and we plug that into our denominator because this represents the incidence among adolescents with no history of sexual abuse. We calculated this out to get a rela&ve risk of 2.46. So let's quickly review what we found. We found that the probability of suicide aEack among adolescents with the history of sexual abuse was 60.8%. Among our exposed group, we found that the probability of suicide aEempts was only 24.7%. This rela&ve risk of 2.46 indicates a posi&ve associa&on, an excess of suicide aEempts among adolescents who were sexually abused compared to adolescents who were not sexually abused. Based oﬀ of this value, we can say that there is a 2.5 fold greater probability of a suicide aEempt for adolescents with a history of sexual abuse compared to adolescents with no history of sexual abuse. And the third example, we would like to compare the incidence of lung cancer between two ci&es, Springﬁeld and Shelbyville. Both ci&es have a small popula&on of 100 residents and Springﬁeld there is polluted air. Thus this city is going to be categorized as our exposed other Springﬁeld residents we. 20 cases of lung cancer. And our second city, we have Shelbyville. Shelbyville does not have polluted air, thus they're going to be considered as our unexposed group. And Shelbyville, there are 10 cases of lung cancer. We again construct our two by two table using the informa&on that we were given. This &me for our exposure status rose. We have Springﬁeld for exposed and Shelbyville for unexposed. We calculate the incidence rate for each city. Springﬁeld has an incidence rate of 20% because 20 out of the 100 residents developed lung cancer. And Shelbyville? This number is halved because only 10 out of the hundred of his residents were diagnosed with lung cancer. In this scenario, because our exposure status is basically being a resident in either Springﬁeld or Shelbyville, we can calculate the rela&ve risk for each city. So let's start with Springﬁeld. What is the rela&ve risk for lung cancer among Springﬁeld residents? We would have the incidence of Springﬁeld and the numerator, and then in the denominator we will put the incidence of lung cancer among Shelbyville residents. So we plug in 20% / 10%, which will result in a rela&ve risk of two. So what if we look at the rela&ve risk from the other ci&es perspec&ve from Shelbyville being the exposed. So let's bring up all the numbers that we already have, 20% incidents in Springﬁeld, 10% incidence in Shelbyville. Now in the rela&ve risk formula you have in the numerator the incidence of lung cancer among Shelbyville because now Shelbyville is considered your exposed group and that would be 10% and the and the denominator you have the incidence of lung cancer in Springﬁeld because now it's ﬂipped. We are going to consider Springﬁeld as our unexposed group. And this was 20%. You end up with a rela&ve risk of 0.5 for lung cancer among Shelbyville residents. So how do we interpret these ﬁndings? First, let's quickly review our probabili&es. The probability of lung cancer among Springﬁeld residents was 20%. The probability of lung cancer among Shelbyville residents was 10%. We calculated A rela&ve risk of lung cancer for Springﬁeld as two, with Springﬁeld being the exposure. We can interpret this as there's a two fold greater probability of lung cancer among Springﬁeld residents compared to residents of Shelbyville. When we looked at it from Shelbyville's perspec&ve, you think Shelbyville as the exposed group, we calculated A rela&ve risk of 0.5. We can say that residents of Shelbyville have a 50% reduc&on in risk of lung cancer compared to residents of Springﬁeld. If you want to interpret the ﬁnding or inverse associa&on based oﬀ a rela&ve risk less than one. Then you can interpret this as a reduc&on in risk. Now the rela&ve risk here is 0.5. To get the percentage of reduc&on in risk, you would do 1 -, 0.5, which equals to 0.5. So that would be a 50% reduc&on here. Now if the rela&ve risk was let's say 0.7. Then it would be 1 -, 0.7. And then you would interpret this statement as resonance of Shelbyville have a 30% reduc&on in risk of lung cancer compared to residents of Springﬁeld. So when you want to interpret it as a reduc&on in risk is always a diﬀerence from the null value 1 minus whatever rela&ve risk you got. That was less than one. Now, if you don't want to go that route in terms of interpre&ng it as a reduc&on in risk, you can simply use the rela&ve risk of 0.5 in your interpreta&on and you can state residents of Shelbyville have 0.5 &mes the risk of lung cancer compared to residents of Springﬁeld. Both these interpreta&ons are correct. The interpreta&on was the percentage of reduc&on in risk is a liEle bit tricky because you do have to remember to do that subtrac&on. If you put solely the rela&ve risk there for the percentage and reduc&on of risk, then the interpreta&on is going to be inaccurate. So let's go ahead and calculate the rela&ve risk for this research ques&on, the prompt states. A course study was conducted to study the associa&on of coﬀee drinking and anxiety and a popula&on based sample of adults. Among 10,000 coﬀee drinkers, 500 develop anxiety among 20,000 non coﬀee drinkers. 200 of these individuals developed anxiety. So what is the rela&ve risk of anxiety associated with coﬀee use? So I went ahead and helped you guys out here and I'll label the columns with our outcome which is anxiety and I label the rows with your exposure which is coﬀee consump&on. So go ahead and pause the lecture and give it a try. Calculate the rela&ve risk and this scenario. To the prompt says that there are 500 of the 10,000 coﬀee drinkers that developed anxiety. Coﬀee drinking the AR, exposure and anxiety being our outcome. So based oﬀ of these numbers, we would take 500 and put that number in cell A. We know that 10,000 people were exposed, so to obtain the number for cell B we would subtract 500 from 10,000, which would result in 9500. Let's look at the prompt again to get our last row of numbers. It says that a total of 20,000 people were non coﬀee drinkers. So these 20,000 people are are unexposed people. So of the unexposed people, these 20,200 of them had anxiety. So then we would take 200 and put it in block C. That would make Cell did 19,800. So let's go ahead and sum up all the rows so we have our numbers of exposed and unexposed handies for our calcula&on. So we have 10,000 people who were exposed, 20,000 people who were unexposed. These numbers will serve as our denominators when we calculate out the incidence of anxiety among the two groups, the exposed group and the unexposed group. The formula for the rela&ve risk is displayed on the slide. We have A / A + b and the numerator and the denominator we have C / C + d. We plug in the respec&ve numbers from the table and we get a rela&ve risk of ﬁve, which indicates a posi&ve associa&on. We can't interpret this as coﬀee consump&on is associated with ﬁve &mes higher risk of anxiety. But is this result sta&s&cally signiﬁcant? Our sample popula&on may not represent the exact disease and exposure that is seen in the target popula&on. We are going to consider Spring0ield as our unexposed group, with a probability of lung cancer among residents being 20%. In comparison, Shelbyville residents have a 10% probability of lung cancer, resulting in a relative risk of 0.5. This means that there is a twofold greater probability of lung cancer among Spring0ield residents compared to Shelbyville residents. However, when looking at it from Shelbyville's perspective, the relative risk is 0.5, indicating a 50% reduction in risk of lung cancer for Shelbyville residents compared to Spring0ield residents. To interpret this as a reduction in risk, we can calculate the percentage by subtracting the relative risk from 1. For example, a relative risk of 0.7 would result in a 30% reduction in risk for Shelbyville residents. It is important to remember to subtract the relative risk from 1 when interpreting as a reduction in risk. Alternatively, we can state that residents of Shelbyville have 0.5 times the risk of lung cancer compared to residents of Spring0ield. Both interpretations are correct. Now, let's calculate the relative risk for the research question provided. The study aimed to investigate the association between coffee consumption and anxiety in a population-based sample of adults. Among 10,000 coffee drinkers, 500 developed anxiety, while among 20,000 non-coffee drinkers, 200 developed anxiety. This results in a relative risk of 5, indicating a positive association between coffee consumption and anxiety. However, it is important to note that this result may not be statistically signi0icant as our sample population may not accurately represent the target population. Estimating Risk - Part 3: Attributable Risk The aEributable risk is a measure that has more of a clinical and public health impact. When we want to ask how much a disease is linked to a certain exposure, we're going to refer to the aEributable risk, which is deﬁned as the amount of disease incidence that is aEributed to a speciﬁc exposure. This measure is used to help. Let's ﬁgure out how much of the disease risk can't be prevented if we remove the exposure itself. It is the incidence of a disease and the exposed popula&on that would be eliminated if exposure was removed. We can get aEributable risk by taking the diﬀerence in the incidence of disease and the exposed by the incidence of disease and the unexposed. We subtract the incidence of disease and the unexposed because this represents the background risk. The aEributable risk percent is the percent of disease incidence and the expose that is due to the exposure itself. I know this sounds very familiar to AEributor risk, but there is a slight dis&nc&on. While the aEributable risk is the amount of disease incidents that can be aEributed to a speciﬁc exposure, at Trudeau risk percent is a propor&on or percentage. So is the propor&onal percentage of the incidence of disease and exposed that would be eliminated if exposure was removed. So aEributable risk looks at amount, aEributable risk percent looks at percent. To calculate the aEributable risk percent, we would take the aEributable risk and divide that by the disease incidence and the exposed, followed by mul&plying this value by 100. Popula&on aEributable risk represents the amount of disease in the whole popula&on that may be prevented if one risk factor was completely removed. If we look at an example of aEributable risk graphically, we see the rate of type 2 diabetes among the exposed, which in this case is being either overweight or obese. We also see the rate of type 2 diabetes among individuals who are considered as unexposed. So these individuals have a normal weight. From this graph, we know that the rate of type 2 diabetes among individuals who are overweight or obese is 30%, whereas among normal weight individuals it is only 7%. That would mean that 23% of the rate of type 2 diabetes among those who are exposed, meaning that those who are overweight or obese is actually due to being exposed, or in this case, is actually due to being overweight or obese. This 23 percent is your tribunal risk. So why is this 23% considered the aEributable risk? Well, to calculate aEributable risk, we would take the type 2 diabetes among the exposed and subtract the type 2 diabetes among the unexposed. As you recall, it was 30 for the exposed and seven for the unexposed. So this will result in 23 of the 30 instances of type 2 diabetes and the overweight or obese group being aEributed to the fact that they were overweight or obese. Looking at the graph again, we see the doEed horizontal line running across the graph at 7%. This represents type 2 diabetes rate among the normal weight individuals, or in other words the unexposed. So this 7% is the background rate. Any excess amount a\er 7% that we see in the exposed group, the overweight or obese would be due to the exposure itself, which is basically high out of pacity. So this 23 percent is their total risk of Type 2 diabetes due to being overweight or obese. If we wanted to calculate the aEributable risk percent, we would take the aEributable risk and divide that by type 2 diabetes among those who were exposed. Which was again 30. A\er which we will mul&ply it by 100 to get 77%. AEributable risk percent represents A propor&on or percentage, whereas aEributable risk is the amount itself. So for aEributable risk percent, 77% of the type 2 diabetes among the exposed group may be aEributed to being overweight or obese, which would mean that 77% of type 2 diabetes. Diagnosis could be prevented if we were able to decrease adiposity in the popula&on to the point that everyone is within the normal weight category. So let's look at another example where an inves&gators would like to look at ﬁsh consump&on and stroke. Now this example non ﬁsh eaters are those who report never ea&ng ﬁsh and they are considered to be the exposed group. So keep that in mind as we move forward daily ﬁsh consump&on is considered as non exposed or unexposed. We have on the right side of the slide several incidents calcula&ons for various groups. We have incidents among our exposed group, so our non ﬁsh eaters being 5.03 per 100 by taking the number of people who had a stroke and dividing it by the total number of people who were exposed. So that was 82 / 1631. The second incidence we have on the screen is the incidence among our unexposed group people who eat ﬁsh daily. We calculated this by taking the number of unexposed people who have a stroke, 23, and dividing it by the total number of unexposed people, which was 802. And lastly, we have our incidence of stroke and the en&re popula&on. So that's the en&re study popula&on and this is regardless of exposure status Here we're taking the total number of strokes, 105 and then we're going to divide that by the total number of people in the en&re study, which was 2433. To get an incidence of 4.32 per 100. We can use these numbers to calculate a rela&ve risk. We take the incidence among the exposed and then we divide it by the incidence among the unexposed to get a rela&ve risk of 1.75, indica&ng that there is a posi&ve associa&on. So people who never consume ﬁsh have 1.7 &mes higher risk of a stroke compared to people who eat ﬁsh on a daily basis. All these summers can help us calculate all the forms of a tribunal risk we've learned so far. These incidence values are displayed on the le\ hand side of the slide now, so let's use some in our calcula&ons star&ng with AEribute or Risk, which tells us the amount of disease incidents that can be aEributed to a speciﬁc exposure. We will take the incidence and the exposed and subtract that by the incidents and the unexposed, which gives us an atrial risk of 2.16 per 100. For the aEribu&ve risk percent, we would take that amount and divide it by the incidence among the exposed, and then we apply a mul&plier. Doing this, we get in a chorus percent of 43. For popula&on aEributable risk, we take the incidence of stroke in the popula&on and subtract the incidence among the unexposed, here being the incidence among ﬁsh eaters, and then we get a 1.4 per 100. If we would like to get popula&on aEributable risk, which gives us the propor&on rather than the amount, we would divide the popula&on aEributable risk by incidents in the total popula&on and apply the mul&plier to get 33.6%. In terms of the interpreta&ons, A rela&ve risk of 1.75 would mean that people who are exposed, so people who never eat ﬁsh, have 1.7 &mes higher risk of a stroke compared to people who are not exposed, so those who eat ﬁsh on a daily basis. The aEributable risk is 2.16 per 100. This means that if people who do not eat ﬁsh change their ea&ng habits and begin to eat ﬁsh on a daily basis, then their incidence of strokes would decrease by 2.16 per 100 individuals. For a child to risk percent, we can interpret this in two ways. We can either say that there would be a 43% reduc&on in stroke incidence if exposure was completely eliminated, or we can simply say that it represents a 43% reduc&on in stroke incidence among the exposed individuals. For popula&on aEributable risk and popula&on of tribal risk percent, we're thinking about trivial risk in terms of the popula&on instead of focusing on the exposed group. So star&ng with popula&on of total risk of 1.45 per 100, this could be interpreted as there would be a reduc&on of about 1.45 new cases of stroke per 100 individuals in the popula&on. If everyone eats ﬁsh on a daily basis. For popula&on of Trudeau risk, there would be a reduc&on of 33.6% and stroke incidence in the popula&on if everyone eats ﬁsh on a daily basis. So let's revisit our example of lung cancer and air pollu&on in our two ci&es of Springﬁeld and Shelbyville, and we can calculate aEributable risk and aEributable risk percent. We can do this from the standpoint of Springﬁeld because Springﬁeld is considered as exposed due to its air pollu&on. So for a Trudeau risk, we would again take the incidence of lung cancer in Springﬁeld and subtract the incidence of one cancer in Shelbyville. When we do this, we get 10. For aEribute risk percent, this is a propor&on of aEributable risk. So we take a trivial risk and divide that by the incidence of lung cancer and they expose and we get 50%. We can say that 50% of lung cancer cases can be aEributed to living in Springﬁeld. If we remove Springﬁeld the exposure to air pollu&on, we reduce the risk of lung cancer by 50%. You can also say that if individuals moved away from Springﬁeld or no longer lived there. Remember that a rela&ve risk is a measure of associa&on. It's important for determining whether an associa&on is present between exposure and disease, and to see if there is enough evidence to support a causal inference. It is a measure of associa&on in court studies when researchers are inves&ga&ng disease ideology. However, the aEribu&ve risk measure is important when we think of clinical prac&ce and public health. It tells us how much the disease risk is aEributed to a certain exposure. It helps people in the public decide which strategies to focus on for reducing disease. This slide displays the aEributable risk, aEribute risk percent and rela&ve risk for smoking and lung cancer, as well as coronary heart disease. We see that the rela&ve risk for smoking lung cancer is 14 compared to smoking and coronary heart disease which is 1.6. We have our aEributed risks telling us that 256 per 100,000 deaths from coronary heart disease could be prevented if smokers would quit. 130 deaths per 100,000 from lung cancer would be prevented if smokers would quit. So why is it that fewer deaths are prevented from lung cancer 130 if smoking was eliminated compared to 256 for coronary heart disease, when their children risk percent as lower for coronary heart disease compared to lung cancer? This is because of the number of people who smoke who die from coronary heart disease is much higher than for lung cancer. You have 669 smokers who die of coronary heart disease compared to 140 smokers who die of lung cancer. So the aEributable risk is much higher for coronary heart disease than for lung. It has to do with the amount, not necessarily the propor&on. Estimating Risk - Part 4: Odds Ratio Are generally thought of when you think of case control studies, even though you can calculate it, and cohort studies as well. When you think of the case control study, you merely think of an odds ra&o as the measure of associa&on because of the design itself. OZ ra&os are used when studies start with disease status and informa&on on exposure status is collec&ve retrospec&vely. As I men&oned, oscilla&ons can be calculated in cohort studies as well. For the case control study, the odds ra&o is propor&on of cases who were exposed compared to the propor&on of controls who were exposed. Course studies have as their measure of associa&on the rela&ve risk. This is because they are powerful enough to their ability to establish temporality. That being said, if they can calculate a rela&ve risk which requires temporality, then they can calculate an odds ra&o which does not require temporality. But I want you to remember that even though the cohort study can calculate both a rela&ve risk and an odds ra&o, whenever you think of a cohort study, think of rela&ve risk. For cohort studies, the ICE ra&o is the propor&on of exposed people who developed the disease compared to the propor&on of unexposed people who developed the disease. Before we get into how to calculate an Oz ra&o and how to interpret them, let's backtrack a bit to cover probability and odds. So what is probability? Probability measures the number of &mes the outcome occurs rela&ve to the number of observa&ons or sample size. Odds, on the other hand, measures the number of &mes the outcome occurs. Relate. Times it does not. So the diﬀerence is that probability compares it to a sample size and Oz compares it to the number of &me diseases not occur. And ﬁnally, the Osprey show compares the odds of those exposed to the risk factor and the odds of those unexposed. What's the diﬀerence between risk and odds? This looks at the chances of something happening rela&ve to the chances of everything happening, whereas all Z is a chance of something happening, rela&vely chance of it not happening. If I were to choose someone from the Classic, what's the likelihood that I will pick you? If we say that the class is only comprised of 60 word for simplicity, what is the risk? The IQ? It would be one out of six because the chances of it happening is 1. The chances of all things happening is 6. This is because the class is made of six people, including yourself. The odds are that you are going to plan out of ﬁve or 20% because the chance I picked this one and the chance that I won't pick was ﬁve since I can pick any of the ﬁve other students in the class. So then that would mean that the all the you is about 20% compared to the risk of Edu which is only 16%. The odds ra&o is the ra&o of odds that cases were. As shown in the formula display. To calculate an observa&on on a case control study, we'll start by focusing on our two groups. Here says it's a case control study. We look at disease status, so by the columns. We look at the odds by disease group, your cases, and your controls. What is the number of &mes exposure occurs among? That would be a / C everyone in. The. Keep on the. Some&mes exposure. This would be divided by. If you. Yep. Eight &mes. This is. Let's calculate an oscilla&on recently case which was. And this paper they. Chili. 1st. This. The numbers. Which is? A\er we do this, we. The interpreta&on for the osprey. To the direc&ons. The interpreta&on that. But again, the odds ra&o. There is no associate. This means that the odds of. PreEy much the same as the. If the odds ra&o is greater than one, that there's a. Because the. Cases is going to be greater than the. However, if the odds ra&o is less. Specia&on. This is because the odds of exposure in your. In our case, study examining the rela&onship with Interprets. So there is a posi&ve aspect. These ﬁndings sta&s&cally signify. We have the steps to calculate the. It's slightly diﬀerent for Osman. If you're. Is slightly. Table. Let's ﬁrst look at her standing. Need to plug in the. Why this? And then we get a. We have one more. To get. We. 3. So. Measure with socia&on. But no&ce. This is because. So now it's your turn to calculate the odds. And this example the inves&gators want to examine vitamin D. They found that. Single year in the United. 600. Mothers were given a dietary. Deﬁciency. 84 said they did not divide. Of the control. Did not use. Construct. Table and calculate the odds. Also ﬁgure out if the odds ra&o is sta&s&cally signiﬁc. Go ahead and pause the lecture. So we have the outcome. And then? Supplementa&on on the. With ﬁve in use, yes, and. States that. Dicta&on. Number of. I did. So that would be 180. Controls were exposed to the. Dicta&on. We know that. Of 600. Without. Oﬀ. 37. So that's. A\er. 30. PreEy easy. It should be 84. Just a. Taxi. Plug. And we get an Oscar. This. Use has. There's. The reason why? Because for all. Less than one. Pause. That would be. If you want you can also. As. 7 hours odds. During. What are the? To determine this. First calculate. You goEa stand. East. Uses. It comes out. This is your. Based on the 95% conﬁdence. There's been some &me interpret. This table is from a study. Perspec&ve. Examine the associate. And. About. They usually just suppress. And. Let's take a look at the. Happening. But before we do. We have two varia&ons of the outcome here, one being ever. I had it in the past. And the second outcome varia&on is currently. The exposure. See Return of smoking. For this exposure, they actually had three category. Instead of. They. Then they have two other. 1. They also examined. This. Someone else? This miracle is a douche. Either. You see the value? We. This. Not. Table. Just. OSU ra&o. Just. Which of the following statements about the table is not? He says that there is no associa&on between the. Smoke during the post employment and children ever have. If you look at the results between coastal living with the household smoker and ever in current. The ﬁndings are not sta&s&cally signiﬁcant because the 95. Because of this, the statement is true. The results you must do so on the adjusted. Because the adjusted model is the ﬁnal model. Takes it to the. Here the inves&gators adjusted for a number of import. These are listed on the boEom of the table. You said that. Please. The number of children at baseline. Dicta&on. History of. As well. So they took it to account number. This is why I always these argumenta&ons of essay on the. Let's go ahead and move. It says that there is no associa&on. Pregnancy. It also speciﬁes that it's referring to both ever and current asthma. Par&cular. The adjusted oscilla&ons from this exposure outcome rela&onship is also not. Because of this, the statement is. The third statement says that children currently have an absconding higher. Specials for this. Which would indicate a posi&ve rela&onship, but as stated, we cannot conclude that there is a posi&ve rela&onship. 95%. Readers from 0.64 meters here in the studio with. Mode. Pinnacle really applies to the volunteer because that is where Donald Trump is trying to scramble constantly to ﬁgure out what he's going to do. And they really don't have any idea how they're gonna handle this and they are just days away now when it comes to the. Was moving conﬁrmed that he is. It says that there is no rela&onship between. Whether it be at any&me recently? Second one. They are not ci&zens. Now. You get the access of star&ng your expose and divide that by 1 minus. That is, this does not to the right and the denominator you would get the incidence of disease and the unexposed and divide that by 1 minus that incidents. Once you simplify all that down you get the formula that looks. Which is 8 * B / B * C and o\en if we look at the calcula&ons for Oz ra&os for case control studies and core studies side by side, we see the diﬀerences and the similari&es. So what are the diﬀerences? Well for the case control study we're looking at it from a disease status, also exposure and cases rela&ve to odds of exposure and controls. For the cohort study, we're looking at it from an exposure status posi&ve disease and exposed rela&ve to odds of disease and unexposed. A\er we simplify everything, we end up with the exact same equa&on, A * D / B * C so that makes things a lot easier. We can use the same formula to calculate the odds ra&o in a case control study. As a cohort study. So let's look at observa&ons from case control studies and AUZ ra&os from cohort studies. We can look at this and an example of a study that looks at the rela&onship between congenital malforma&ons and metal blastoma status. First, this complete and odds ra&o from a case material perspec&ve. What are the odds of congenital malforma&ons? For cases? It would be 23 / 217 because that would be the number of cases exposed, which is 23 divided by the number of cases are not exposed, which is 2/17. This one is sought in 0.105 for the oz ra&o you can calculate using the standard formula. 8 * b / b * C to get 2.1. When we talk about an ostrich or using the same example but as if the study was a course that you were asking what the odds of a child would be exposure is of developing neuroblastoma. You would take the number of exposed to have neuroblastoma rela&ve to the exposed who do not have neuroblastoma. So that would be 23 / 116. And this equals to 0.2. We can again calculate an odds ra&o using the same formula and then we get 2.1 which is the same number. Let's visit another example focusing on a historical event, the Sinking Representa&ve. Here we're examining the rela&onship between sex and death. Just glancing at the numbers in the con&ngency table, we can see that the mail is risk factor of death on the Titanic. But how much more likely is a mellow to dive than a female? What are the odds of dying for each sex? Trial for females, you have 154 who die rela&ve to 308 did not die, resul&ng in 0.5 medical. The odds are two to one against dying for females Now you have 709 miles dying rela&ve to 142 live, resul&ng in ﬁve. This means the osmer 5 to one in favor of death for melts. Now we should calculate the odds ra&o using the formula A * D / B * C. He's going out a\er recording ar&st from the table we get in Oswayo of 10. We would interpret that as there's a tenfold greater odds of death when Bell sends emails. We should calculate rela&ve risks using the same table. For females, the probability of death is 33% as 154 out of the 462 female style. For males, the probability of death is 83% since 709 out of the 851 mels died The rela&ve risk of death is 2.5 a\er we do the calcula&on, meaning that there is a posi&ve associa&on. We would interpret this as there is a 2.5 greater probability of death from males than females. So let's stop these measures of associa&on. For an OSS ra&o we got 10. There is a tenfold greater odds of death from males and females. For rela&ve risk, we got a 2.5, meaning that there is a 2.5 greater risk of death from males and females. Both these measures come to the same conclusion, saying that males are more likely to die on the Titanic. But the odds ra&o implies that men's likelihood of dying is far worse than females than the rela&ve risk es&mate 10 versus 2.5. So which of these is the fair comparison? Well, there really isn't a right or wrong way, but we just need to remember that a rela&ve risk measures events in a way that is more interpretable and is more in line with the way people think from exposure to disease. But our rela&ve risk can't always be computed, it's only possible in court semngs. So some&mes you must rely on an OZ ra&o. And remember that the Oz racial interpreta&on should be carefully wriEen. You shouldn't save risk of disease because it doesn't measure risk, it measures odds. And that is why for the interpreta&on here is states that there's a temporal greater odds of death for mills than females. And some instances the OZ ra&o can es&mate the rela&ve risk. There are three instances in which it can do this. 1st, when the cases and your case control study are representa&ve of all the people with the disease with regard to exposure prevalence. Same goes for controls. So when controls are representa&ve of all the people without the disease with regard to exposure prevalence, then at this point the odds ra&o can possibly es&mate rela&ve risk. So basically for those two bullets, when cases and controls are representa&ve. And lastly if the disease being studied is rare. So we covered how to calculate your standard OZ ra&o, but what about case control studies where you match based oﬀ of a confounder? Do you have a mashed cakes Mitchell study? Then you would need to calculate the odds ra&o using a diﬀerent formula. You cannot use the standard A * C divided by me &mes C. You need to analyze the data based oﬀ of case control pairs rather than individual subjects. So we would have four combina&on of pairs. Two sets of pairs would be concordant pairs, wherein pairs of cases and controls would both be exposed, and pairs of cases and controls would both be unexposed so they match according to their exposure status. Then you have two sets of pairs that are considered as discordant. Among the discorded pairs you have pairs where the case was exposed with control was not and then and the second set of this coordinate pair you would have controls over exposed and cases who were not. So the discordant pairs would have pairs that diﬀer with regard to exposure status. For a match case control study, we set up the two by two table diﬀerently. We have controls for the columns and cases for the rows. So previously we had disease for the columns and exposure for the Rose. But here the columns and the rows have two sets of informa&on, so in square A. This would represent a concordant pair, a pair that was essen&ally matched with regard to exposure status. Both your cases and your controls are exposed here. And square B we have a discordant pair with a control that is not exposed in a case that is exposed. Foresee this is also a discordant pair. We have a controller exposed in a case not exposed. And ﬁnally, it's weird. We have our last concordant pair with both cases and controls that were not exposed. To calculate odds ra&os and match samples, we focus solely on the discorded pairs, so we ignore the concordant Paris because they don't contribute to the calcula&on of eﬀect es&mate. Remember they are the same with regard to exposure status. So the match odds ra&o is a ra&o of discordant pairs, the number of pairs in which the cases were exposed rela&ve to the number of pairs in which the controls were exposed. So B / C. An example of a match case control study that examines the risk factors of brain tumors in children. Inves&gators hypothesized that children with certain childhood cancers are more likely to have higher birth weight. Cases are children with brain tumors. Controls were those without brain tumors and exposure is based oﬀ a cut oﬀ of birth rate greater than. 8 lbs. To calculate the match oz ra&o, we would use the formula B / C and focus on the discordant pairs. We reﬁlled the formula with 18 / 7 to get 2.6 as the match oz ra&o. This indicates a posi&ve associa&on. We can interpret this. There's a 2.6 Volt greater odds of children with brain tumors having a birth rate greater than 8 lbs compared to having a birth rate less than or equal to 8 lbs. The calcula&on of a 95% conﬁdence interval in a match case control study is a bit more complicated, so we won't be calcula&ng it in this course.

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