[MUSIC] Welcome, in this segment we will discuss the odds ratio. In this segment, you will learn how to define, calculate and interpret the odds ratio. In a case-control study, we calculate the exposure odds ratio. The odds ratio approximates the incident rate ratio or risk ratio under certain conditions. Remember that odds is p divided by 1 minus p. The probability of an event occurring divided by the probability of it not occurring. When Odds Ratio is equal to 1 then there is no association between the exposure and the outcome of interest. When the Odds Ratio is greater than 1. There is a positive association. And when the odds ratio is less than one, there is a negative association. Be careful of how you set up your 2.2 table here. Cross, the cross product formula only works if the table is set up correctly. For this epidemiology MOOC, we will use the convention of disease on the top, and exposure on the side. However, outside this course, you may see these switched. As I said before, in a case control study, the odds ratio is the exposure odds ratio, which is the odds of being exposed in the cases equals a divided by c. Divided by the odds of being exposed in the controls or b divided by d. Mathematically, this is the same as the cross product, which is equal to a times d divided by b times c. The odds ratio is the ratio of the odds of the health outcome or disease in the exposed Relative to the odds of the disease or health outcome in the none exposed or less exposed group. Odds ratios can be calculated in cohorts studies and in case control studies. Prevalence odds ratios can be calculated for cross sectional studies. There are different ways that you can interpret a measure of association and words as illustrated here. You could say ,those in a traffic ac, accident were 1.62 times as likely to have been texting while driving compared with those who were not in a traffic accident in the past year. Or those in a traffic accident were 62% more likely to have been texting while driving. Then those who were not in a traffic accident in the past year. But the most precise interpretation is as follows the odds of a traffic accident among those who texted while driving was 1.62 times the odds of a traffic accident. Among people who did not text while driving. Be careful, you cannot calculate a risk or rate directly from case control data. The denominators obtained in a case control study do not represent the total number of exposed and non-exposed person in the source population. The investigators arbitrarily decide how many controls will be selected to compare with the cases. We cannot directly measure risks or rates because the population at risk in the denominator is not ascertained. Under certain conditions, we can obtain a valid estimate of the rate ratio risk ratio using the odds ratio. But we won't go into those conditions for this MOOC. So let's review. We can't estimate a risk or rate directly from a case control study Because we or the researchers, decide on the number disease people, the cases. And the non-disease people are controls. When we design our study. So the ratio of controls to cases is not biologically or substantively meaningful. Instead We estimate the risk ratio or the rate ratio in a case control study using the odds ratio. Lets look at an example of calculating and interpreting the odds ratio, using childhood vaccines and human papillomavirus. Researchers conducted a case control study to examine whether childhood vaccines Protected children against HPV in real world conditions i.e. Rural areas with little access to regular health care. Note this is a hypothetical example. A total of 25 cases and 19 controls were identified. Data obtained from the cases and controls found that 15 cases and 12 controls had received the vaccine. Another way to interpret the effect of the vaccine is to compare the odds of those who did not get the vaccine to those who did. To do so, you take the reciprocal of the odds ratio i.e. 1 over 0.875, which gives you 1.14. So children who did not receive childhood vaccines were 1.14 times as likely to have HPV compared to children who did receive childhood vaccines. Okay, let's try another example. You are investigating an outbreak of paralytic shellfish poisoning among patrons of an Alaskan restaurant. You conduct a case control study to identify food associated with the illness. A total of 240 cases and 134 controls were identified. Data obtained from the cases and controls found that 218 cases and 45 controls consumed scallops. Now I'd like you to create a two by two table and calculate the odds ratio for this example and interpret your results, and then check back in a minute. This is what your table would look like. 218 cases of paralytic shellfish poisoning and 45 controls who consumed scallops. And then we see there were 22 cases in 89 controls who did not consume scallops. So to calculate the odds ration, you take the cross product, which is 218 times 89, divided by 45 times 22. And you get 19.6. To interpret this. You can use the following interpretation. There are other permutations, but here's a short one. Cases were 19.6 times as likely, compared to controls to have eaten the scallops.