In this video I'm going to explain what likelihood ratios are and how to calculate them. Hi, and welcome back to physiotutors. Before you watch our video on likelihood ratios you should have knowledge about sensitivity, specificity and positive and negative predictive values so make sure to watch our parts on that before you continue with this video. So likelihood ratios summarise the information contained in both sensitivity and specificity and they tell us, how likely a given test result is in people who have the disease compared to how likely a given test result is in people who do not have the disease The positive likelihood ratio abbreviated as LR+ can be calculated by dividing sensitivity through one minus specificity and the negative likelihood ratio abbreviated as LR- can be calculated using one minus sensitivity through specificity We are talking about a good positive likelihood ratio if the value is bigger than 10 and we are talking about a good negative likelihood ratio if the value is smaller than 0.1 If the likelihood ratio, positive or negative is close to 1.0 this means that this test has very little influence on the fact that the patient does or does not have the disease. So in practice such a test is thus useless. Now how do you use those two values in practice. So first of all in your general practice the prevalence of an ACL tear based on literature is say 5% Then based on the anamnesis you found a couple of signs and symptoms like an audible pop during a soccer match Immediate swelling, hemarthrosis and a feeling of instability On top of that you have already excluded a knee fracture with the help of the Ottawa knee rules Based on a prevalence of 5% plus the information you got during anamnesis and assessment you estimate the chance for an ACL tear at about 60% So according to the meta-analysis of Benjaminse et al. in the year 2006 the Lachman test has a sensitivity of 85% and a specificity of 94% so that results in a positive likelihood ratio of 14 and a negative likelihood ratio of 0.16 With the use of the nomogram we can quickly determine the post-test probability of our test in percentages Mark your pretest probability on the left of the nomogram which is 60% in our case then mark the likelihood ratio of your test on the midline which is 14 for positive Lachman and 0.16 for negative Lachman At last draw a line through these two points to determine the post-test probability According to the nomogram we end up with a post-test probability of around 95% for positive tests and for negative tests we're going to end up with a post-test probability of about 18% for negative Lachman The second more exact option is to calculate the post-test probability. In order to do that I first have to convert the pretest probability into pretest odds and I can do that if I take our pretest probability which we said was 60% based on our anamnesis and examination and divide this probability through one minus pretest probability So in our case this would be 0.6 divided through 1-0.6 so we end up with odds of 1.5 Okay, then the second step is to calculate the post-test odds. Based on my positive likelihood ratio and based on the pretest odds that I just calculated. So in this case for a positive test, I would multiply the pretest odds, so 1.5 with the positive likelihood ratio for the Lachman test, which is 14 so we will have 1.5x14 and we end with post-tests odds of 21 Now so that this number has a meaning I have to convert it back into a post-test probability and I can do that if I take the post-test odds of 21 and divide it through the post-test odds plus one so I'll end up with 21 through 22 and this actually gives me 0.95 Which is a post-test probability of 95% in case of a positive test Now let's go through the whole calculation in case of a negative test. So we've already done the first step, so we have a pretest odd ratio of 1.5 And now we want to see what the post-test odds are first for a negative test. So in this case, we multiply the pretest odds of 1.5 with a negative likelihood ratio of 0.16 for the Lachman test so then we will end at 1.5x0.16 and we get 0.24 again, we have to convert this value back into a probability so in this case the post-test odds 0.24 divided through 0.4 plus 1 And then we're going to end up with 0.19, which is 19% post-test probability So to sum it up, in case of a positive test I started with a pretest probability of 60% based on my analysis and based on my examination and in case of a positive test I ended up at 95% chance that the patient actually has an ACL tear Now in this example with a negative test, I started with a chance of 60% that my patient has an ACL tear and in case of the negative test the probability decreased till 19% Okay to sum it up you want to use the test with the highest positive likelihood ratio in order to confirm your hypothesis and the test with the lowest negative likelihood ratio to reject your hypothesis. Okay, this was our video on likelihood ratios and how to calculate them. I hope you could follow because I know it's a complicated topic. If you could, give it a like if you still have any questions feel free to comment in the section down below and if you want to dive even deeper into this topic I recommend that you read my blog post on our web page physiotutors.com about how statistics will make you a better evidence-based physio Until then I'll see you in the next video. Bye!