WEBVTT 1 00:00:00.840 --> 00:00:02.010 Hello students. 2 00:00:02.010 --> 00:00:05.250 Welcome to Biostats ER example 8 chapter 6. 3 00:00:05.250 --> 00:00:07.170 In this example, we are going to learn how 4 00:00:07.170 --> 00:00:11.373 to calculate the 95% confidence interval for odds ratio. 5 00:00:12.210 --> 00:00:14.940 We are going to use the same problem 6 00:00:14.940 --> 00:00:17.370 that we used, for example 6 and 7, 7 00:00:17.370 --> 00:00:19.503 which is from our textbook problem 7. 8 00:00:22.320 --> 00:00:26.250 I'll first read the problem, which states a clinical trial 9 00:00:26.250 --> 00:00:29.040 is conducted to compare an experimental medication 10 00:00:29.040 --> 00:00:32.460 to placebo to reduce the symptoms of asthma. 11 00:00:32.460 --> 00:00:35.370 200 participants are enrolled to the study 12 00:00:35.370 --> 00:00:37.830 and randomized to receive either the experimental 13 00:00:37.830 --> 00:00:39.840 medication or the placebo. 14 00:00:39.840 --> 00:00:43.560 The primary outcome is self-reported reduction of symptoms. 15 00:00:43.560 --> 00:00:44.940 Among a hundred participants 16 00:00:44.940 --> 00:00:47.070 who received the experimental medication, 17 00:00:47.070 --> 00:00:50.160 38 report reduction in symptoms as compared 18 00:00:50.160 --> 00:00:55.160 to 21 participants of 100 assigned to placebo. 19 00:00:55.890 --> 00:00:58.410 For your convenience, I have presented the information 20 00:00:58.410 --> 00:01:00.900 in a tabular format here, 21 00:01:00.900 --> 00:01:05.670 and then I have stated the formula. 22 00:01:05.670 --> 00:01:09.930 However, before we start solving the problem, 23 00:01:09.930 --> 00:01:13.410 I want to let you know that for this Biostats ER example, 24 00:01:13.410 --> 00:01:14.880 the solution is typed 25 00:01:14.880 --> 00:01:17.100 because once I heard from a student that 26 00:01:17.100 --> 00:01:21.120 all of my Biostats ER examples are solved by hand. 27 00:01:21.120 --> 00:01:24.390 Hence, I have again typed the solution here, 28 00:01:24.390 --> 00:01:26.943 but I am going to go through it step by step. 29 00:01:28.890 --> 00:01:33.030 So as you can see from this formula, the first thing we need 30 00:01:33.030 --> 00:01:37.800 to calculate here is the OR hat. 31 00:01:37.800 --> 00:01:42.030 And the formula to calculate the OR hat is presented here. 32 00:01:42.030 --> 00:01:46.830 So to calculate the OR hat, we need to know the p1 hat 33 00:01:46.830 --> 00:01:49.770 and the p2 hat and one minus p1 hat 34 00:01:49.770 --> 00:01:51.480 and one minus p2 hat. 35 00:01:51.480 --> 00:01:56.480 So I have provided you with formulas 36 00:01:57.180 --> 00:01:59.610 in terms of how to obtain those values. 37 00:01:59.610 --> 00:02:03.030 And once we obtain those values, we insert it here. 38 00:02:03.030 --> 00:02:07.980 So as you can see here in the numerator, we have 0.38, 39 00:02:07.980 --> 00:02:09.930 which we obtained from here, 40 00:02:09.930 --> 00:02:13.440 and 0.62, which we obtained from here. 41 00:02:13.440 --> 00:02:17.014 And then for the denominator we have 0.21, 42 00:02:17.014 --> 00:02:19.290 which is obtained from here. 43 00:02:19.290 --> 00:02:23.400 And then we have 0.79, which is obtained from here. 44 00:02:23.400 --> 00:02:26.922 And after that, when we perform the division 45 00:02:26.922 --> 00:02:30.243 and then again to the final division, 46 00:02:32.940 --> 00:02:37.500 which is dividing 0.61 by 0.27, 47 00:02:37.500 --> 00:02:39.810 we get 2.26. 48 00:02:39.810 --> 00:02:43.390 Then we take this value 2.26 and insert it here 49 00:02:44.670 --> 00:02:48.660 and obtain the natural log of 2.26 50 00:02:48.660 --> 00:02:50.730 by using our calculator 51 00:02:50.730 --> 00:02:55.020 and we get 0.815. 52 00:02:55.020 --> 00:02:59.100 Now we have to look at the other parts of this equation, 53 00:02:59.100 --> 00:03:02.763 which requires us to obtain the 95% Z value, 54 00:03:03.690 --> 00:03:07.080 which is 1.96 and we insert it here. 55 00:03:07.080 --> 00:03:10.900 Then it requires us to subsequently insert the values 56 00:03:13.260 --> 00:03:15.843 for x1, which is 38, 57 00:03:16.883 --> 00:03:19.623 n1 minus x1, which is 62, 58 00:03:20.940 --> 00:03:25.940 x2, which is 21 and n2 minus x2, which is 79. 59 00:03:26.850 --> 00:03:30.400 So after we insert all these values, what we have to do is 60 00:03:32.040 --> 00:03:36.120 one at a time perform these divisions 61 00:03:36.120 --> 00:03:38.433 and then add them all up. 62 00:03:39.960 --> 00:03:44.960 So once we perform the division and add them all up, 63 00:03:45.210 --> 00:03:46.710 we need to take the square root 64 00:03:46.710 --> 00:03:51.710 of that number and that is 0.321. 65 00:03:52.200 --> 00:03:56.713 Then we have to multiply 0.321 by 1.96, 66 00:03:57.780 --> 00:04:02.780 which will give us 0.628. 67 00:04:02.850 --> 00:04:07.850 Then we have to subtract and add 0.628 to 0.815. 68 00:04:14.370 --> 00:04:19.117 So when we subtract 0.628 from 0.815, 69 00:04:19.980 --> 00:04:22.830 we get 0.187. 70 00:04:22.830 --> 00:04:27.830 And then when we add it, we get 1.443. 71 00:04:28.020 --> 00:04:33.020 So the 95% confidence interval for the natural log of OR 72 00:04:33.750 --> 00:04:36.877 is 0.187, 1.443. 73 00:04:39.570 --> 00:04:44.010 Now to generate the confidence interval for the odds ratio, 74 00:04:44.010 --> 00:04:45.580 we take the anti-log 75 00:04:48.960 --> 00:04:51.840 of the upper and lower limits. 76 00:04:51.840 --> 00:04:56.840 And when we do that, we get 1.21 and 4.23. 77 00:04:58.290 --> 00:05:01.320 So the confidence interval here, as you can see, 78 00:05:01.320 --> 00:05:03.720 does not include a one. 79 00:05:03.720 --> 00:05:07.560 Therefore, we can state with 95% confidence 80 00:05:07.560 --> 00:05:10.890 that there is a difference in the odds of symptom relief 81 00:05:10.890 --> 00:05:12.213 between the two groups, 82 00:05:14.160 --> 00:05:16.260 which is the exposed experimental group 83 00:05:16.260 --> 00:05:18.783 and the unexposed placebo group. 84 00:05:20.310 --> 00:05:22.530 Thank you very much for your time and attention 85 00:05:22.530 --> 00:05:24.453 and I'll see you in the next video.