WEBVTT 1 00:00:03.990 --> 00:00:05.130 Hello students and welcome 2 00:00:05.130 --> 00:00:08.913 to Biostat ER chapter eight, example four. 3 00:00:10.320 --> 00:00:13.320 In this example, we will learn how to calculate sample size 4 00:00:13.320 --> 00:00:16.530 for two-independent samples, continuous outcome 5 00:00:16.530 --> 00:00:18.960 to perform hypothesis testing. 6 00:00:18.960 --> 00:00:21.330 This example is from our textbook. 7 00:00:21.330 --> 00:00:24.180 So as always, I'm first going to read the problem. 8 00:00:24.180 --> 00:00:25.980 So it's problem 10. 9 00:00:25.980 --> 00:00:29.730 Recently it has been observed that HIV infected patients 10 00:00:29.730 --> 00:00:34.140 develop peripheral lipoatrophy 11 00:00:34.140 --> 00:00:37.470 while on potent antiretroviral therapy. 12 00:00:37.470 --> 00:00:39.090 A clinical trial is planned 13 00:00:39.090 --> 00:00:43.200 to determine if a new chemical will improve this condition. 14 00:00:43.200 --> 00:00:45.840 In the trial, participants will be randomized 15 00:00:45.840 --> 00:00:48.570 to receive the new chemical or a placebo 16 00:00:48.570 --> 00:00:50.400 and changes from baseline 17 00:00:50.400 --> 00:00:53.820 in subcutaneous adipose cross-sectional area 18 00:00:53.820 --> 00:00:57.240 as measured by CT scan will be calculated 19 00:00:57.240 --> 00:00:59.850 after 24 weeks of treatment. 20 00:00:59.850 --> 00:01:01.540 Investigators hope to show 21 00:01:02.820 --> 00:01:05.610 that the increases in patients receiving the chemical 22 00:01:05.610 --> 00:01:07.950 are greater than the increases in patients 23 00:01:07.950 --> 00:01:09.960 receiving the placebo. 24 00:01:09.960 --> 00:01:14.960 They hypothesize that the participants 25 00:01:15.000 --> 00:01:17.370 assigned to the clinical arm will exhibit 26 00:01:17.370 --> 00:01:22.350 a mean change of 30% and the participants 27 00:01:22.350 --> 00:01:25.230 assigned to the placebo arm will exhibit 28 00:01:25.230 --> 00:01:27.480 a mean change of 0%. 29 00:01:27.480 --> 00:01:29.970 Prior literature suggests that the standard deviation 30 00:01:29.970 --> 00:01:33.813 of the changes will be 57% in both arms. 31 00:01:36.120 --> 00:01:40.320 So how many participants are needed to ensure 80% power? 32 00:01:40.320 --> 00:01:42.240 We will assume that alpha is equal 33 00:01:42.240 --> 00:01:45.450 to 0.05 equal numbers in each group 34 00:01:45.450 --> 00:01:49.110 and that 20% of the participants will drop out 35 00:01:49.110 --> 00:01:51.720 over the course of follow-up. 36 00:01:51.720 --> 00:01:54.870 So first here I have provided you with the formula, 37 00:01:54.870 --> 00:01:58.380 and as part of the formula, we will first proceed 38 00:01:58.380 --> 00:02:03.380 with calculating the denominator, which is ES, the effect size. 39 00:02:03.720 --> 00:02:07.830 Now for the effect size here, the mu one minus mu two, 40 00:02:07.830 --> 00:02:11.190 the differences here is directly provided to us 41 00:02:11.190 --> 00:02:14.250 in the problem and I have highlighted it in yellow 42 00:02:14.250 --> 00:02:15.960 for your convenience. 43 00:02:15.960 --> 00:02:19.860 And that is what I have inserted here, 0.30. 44 00:02:19.860 --> 00:02:22.740 And for the sigma, again, 45 00:02:22.740 --> 00:02:25.380 that is provided to us in the problem. 46 00:02:25.380 --> 00:02:27.900 And that is 57%, which again, 47 00:02:27.900 --> 00:02:31.560 I have inserted here as 0.57. 48 00:02:31.560 --> 00:02:34.323 So when we do the division, we get 0.53. 49 00:02:36.420 --> 00:02:41.310 So now for the next step, we will have to obtain that value 50 00:02:41.310 --> 00:02:44.220 for Z one minus alpha divided by two, 51 00:02:44.220 --> 00:02:48.060 which is again the Z 97 point fifth percentile. 52 00:02:48.060 --> 00:02:50.760 And that is going to be 1.96. 53 00:02:50.760 --> 00:02:55.050 Again, that is the Z value for which the 97.5% 54 00:02:55.050 --> 00:02:56.940 of probability lies below. 55 00:02:56.940 --> 00:03:00.600 The Z value one minus beta is the Z of the 80th percentile 56 00:03:00.600 --> 00:03:03.450 because one minus beta is the power of the study, 57 00:03:03.450 --> 00:03:06.210 and that is going to be 0.84. 58 00:03:06.210 --> 00:03:08.610 And of course we are going to obtain these values 59 00:03:08.610 --> 00:03:09.930 from the Z table. 60 00:03:09.930 --> 00:03:11.970 So once we insert all these values 61 00:03:11.970 --> 00:03:16.130 and perform the algebra, we get 55.8. 62 00:03:19.740 --> 00:03:21.360 Again, as always, we are going to round up 63 00:03:21.360 --> 00:03:23.520 because it is sample size calculation. 64 00:03:23.520 --> 00:03:27.030 So the sample size of N one is going to be 56 65 00:03:27.030 --> 00:03:29.400 and N two is going to be 56. 66 00:03:29.400 --> 00:03:31.860 And that will ensure that the test 67 00:03:31.860 --> 00:03:34.500 of hypothesis will have an 80% power 68 00:03:34.500 --> 00:03:37.220 to detect a 0.30-unit difference 69 00:03:41.160 --> 00:03:44.280 in change flow between groups. 70 00:03:44.280 --> 00:03:48.000 Now we have to also account for the loss to follow-up. 71 00:03:48.000 --> 00:03:50.730 So to account for 20% loss to follow up, 72 00:03:50.730 --> 00:03:55.730 the investigators need to recruit 140 participants. 73 00:03:55.980 --> 00:03:57.390 And how do we know that? 74 00:03:57.390 --> 00:03:59.880 We know that because we have this formula 75 00:03:59.880 --> 00:04:02.010 and we are going to insert the values in the formula. 76 00:04:02.010 --> 00:04:06.930 So it's going to be N, which is the number 77 00:04:06.930 --> 00:04:09.600 to enroll, multiplied by percent retained. 78 00:04:09.600 --> 00:04:12.930 And that is going to be equal to our desired sample size. 79 00:04:12.930 --> 00:04:16.350 And here we know that there's going to be a 20% drop, 80 00:04:16.350 --> 00:04:18.480 so it's going to be 0.80, 81 00:04:18.480 --> 00:04:22.170 and then it's going to be 112, 82 00:04:22.170 --> 00:04:23.747 Because when we add 56 83 00:04:23.747 --> 00:04:27.060 and 56 together, we are going to get 112. 84 00:04:27.060 --> 00:04:28.740 So once we insert that, 85 00:04:28.740 --> 00:04:31.923 and again, when we perform the algebra, we get 140.