WEBVTT 1 00:00:02.100 --> 00:00:07.100 Hello, students, and welcome to Biostat ER, 2 00:00:07.260 --> 00:00:09.840 chapter eight, example three. 3 00:00:09.840 --> 00:00:12.765 In this example, we will learn how to calculate sample size 4 00:00:12.765 --> 00:00:16.320 for two-matched samples, continuous outcome, 5 00:00:16.320 --> 00:00:18.750 to determine confidence interval. 6 00:00:18.750 --> 00:00:20.850 This example is from our textbook. 7 00:00:20.850 --> 00:00:23.400 So first, I'm going to read the problem statement, 8 00:00:23.400 --> 00:00:24.907 which is problem five. 9 00:00:24.907 --> 00:00:27.385 "A crossover trial is planned to evaluate the impact 10 00:00:27.385 --> 00:00:29.910 of an educational intervention program 11 00:00:29.910 --> 00:00:32.310 to reduce alcohol consumption 12 00:00:32.310 --> 00:00:37.080 in patients determined to be at risk for alcohol problems. 13 00:00:37.080 --> 00:00:39.540 The plan is to measure alcohol consumption, 14 00:00:39.540 --> 00:00:42.570 the number of drinks on a typical drinking day, 15 00:00:42.570 --> 00:00:46.325 before the intervention, and then again after participants 16 00:00:46.325 --> 00:00:49.593 complete the educational intervention program. 17 00:00:50.580 --> 00:00:53.670 How many participants would be required to ensure 18 00:00:53.670 --> 00:00:56.670 that a 95% confidence interval 19 00:00:56.670 --> 00:00:59.700 for the mean difference in the number of drinks 20 00:00:59.700 --> 00:01:03.630 is within two drinks of the true mean difference? 21 00:01:03.630 --> 00:01:06.900 Assume that the standard deviation of the difference 22 00:01:06.900 --> 00:01:10.470 in the mean number of drinks is 6.7 drinks 23 00:01:10.470 --> 00:01:13.930 and that 20% of the participants will drop out 24 00:01:13.930 --> 00:01:17.160 over the course of follow-up." 25 00:01:17.160 --> 00:01:18.603 So for the answer here, 26 00:01:19.710 --> 00:01:22.380 I have first inserted the formula here, 27 00:01:22.380 --> 00:01:27.380 and it is, as you can see, Z times sigma D, 28 00:01:28.470 --> 00:01:29.760 because it's a difference, 29 00:01:29.760 --> 00:01:34.760 we have paired samples, and then it is divided by E. 30 00:01:35.610 --> 00:01:39.330 So the Z value here is, again, going to be 1.96, 31 00:01:39.330 --> 00:01:42.210 as you have seen in the previous example. 32 00:01:42.210 --> 00:01:46.890 The sigma sub D is going to be 6.7, 33 00:01:46.890 --> 00:01:50.223 because that is what has been provided to us, 34 00:01:51.060 --> 00:01:52.860 and the E is going to be two, 35 00:01:52.860 --> 00:01:56.280 which is, again, what has been provided to us. 36 00:01:56.280 --> 00:01:58.875 So once we insert these values into the formula 37 00:01:58.875 --> 00:02:03.870 and we perform the algebra, we get 43.1, 38 00:02:03.870 --> 00:02:06.990 and we always round up for sample size calculation, 39 00:02:06.990 --> 00:02:11.990 so a sample size of N equal to 44 is required. 40 00:02:12.030 --> 00:02:13.950 Now, we are going to go to the next step, 41 00:02:13.950 --> 00:02:17.700 and we are going to address the loss to follow-up. 42 00:02:17.700 --> 00:02:21.330 So to account for 20% loss to follow-up, 43 00:02:21.330 --> 00:02:25.590 we have to use this formula, which is N, number to enroll, 44 00:02:25.590 --> 00:02:28.500 multiplied by the percent retained 45 00:02:28.500 --> 00:02:31.290 is equal to the desired sample size. 46 00:02:31.290 --> 00:02:34.830 So because we are losing 20% to follow-up, 47 00:02:34.830 --> 00:02:37.350 then percent retained is, of course, 80%, 48 00:02:37.350 --> 00:02:40.207 because we are subtracting it from 100. 49 00:02:43.619 --> 00:02:46.170 And then, once we insert these values, 50 00:02:46.170 --> 00:02:50.790 and again, we perform the algebra here, we get 55. 51 00:02:50.790 --> 00:02:55.790 So the investigators here need to recruit 55 participants.