 Relations and formulas associated with risk, we have relative risk reduction. So relative risk reduction is the proportion of risk that's reduced and can be attributed to the intervention, comparing that to the control. So to calculate relative risk reduction, we're going to do 1 minus our relative risk, which we talked about earlier. Here's an example of relative risk reduction. If 2% of the patients receive flu shots, develop the flu, while 8% of unvaccinated patients develop the flu. So to calculate our relative risk reduction, we're going to do 1 minus, and then our relative risk of 2% develop the flu with the shot, and then 8% are unvaccinated and develop the flu. Calculating that out, we get 1 minus 0.25, and that equals 0.75. So our relative risk reduction in this case is 0.75. The attributable risk is the difference in risk between exposed groups and unexposed groups. So our calculation of our attributable risk is A over A plus B minus C over C plus D. So let's add this into a calculation. So we're going to say that risk of lung cancer in smokers is 21%, and risk in non-smokers is 1%. So we can calculate our attributable risk as 21% minus our non-smokers being 1%. That equals to 20. So our attributable risk to smoking and lung cancer is 20%. We can make that into a percentage by adding in this calculation that our relative risk minus 1 times 100 is equal to our attributable risk percentage. Finally, the absolute risk reduction. This is the difference in risks, not a proportion, but a difference in risks that's attributed to the intervention as compared to the control. So that formula is C over C plus D minus A over A plus B. This is very similar to attributable risk, so you need to make sure you're very aware of the different formulas and the different ways that this formula is set up so that you can get these questions answered really quickly and easily. So let's take an example here, 8% of the people receive a placebo vaccine will develop the flu, and we'll compare that to 2% of the people who receive the flu vaccine. So to be able to do that, our attributable risk reduction, we're going to take that 8%, and we're going to subtract the 2% that developed the flu. That gives us 6%, or 0.06 is our attributable risk reduction of the flu shot to developing the flu. Furthermore, the number needed to treat is the number of patients who need to be treated for one patient to benefit. So our calculation here is going to use the attributable risk reduction that we discussed earlier, and we're going to do 1 over our attributable risk reduction to get the correct answer for our number needed to treat. Obviously, a number needed to treat that is high means that this specific treatment is not going to be very effective, because if we have to treat 10 patients before one of them is actually receiving the benefits, then there's 9 patients that are not receiving any benefits from that treatment. Number needed to harm, however, is different in that so many patients need to be exposed to a risk factor before one can be harmed. So our calculation of number needed to be harmed, or number needed to harm, is calculated as 1 divided by the attributable risk. So we're going to take our previous calculation we've already discussed and learned, and apply this to number needed to harm. Finally, our case fatality rate is known as the percentage of deaths that occur among those with disease. So we can take that and calculate out the number of deaths divided by the number of cases, multiply that times 100, and we get our percentage of our case fatality rate. So in this example, if we have 10 patients that have meningitis and 4 of them die, we do 4 divided by 10, multiply that times 100, and that will give us our percentage of a case fatality rate of 40%. And this is going to be over a certain period of time. Let's compare and contrast.