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These are the user uploaded subtitles that are being translated: 0 00:00:00,000 --> 00:00:02,333 PETER REDDIEN: So we'll have the data of the inheritance 1 00:00:02,333 --> 00:00:03,670 patterns of these repeats. 2 00:00:03,670 --> 00:00:05,430 And we want to know which of these repeats 3 00:00:05,430 --> 00:00:08,670 are linked with the individual-- with the allele 4 00:00:08,670 --> 00:00:10,660 of the gene causing the trait. 5 00:00:10,660 --> 00:00:12,420 So we need some statistical test for that. 6 00:00:12,420 --> 00:00:19,910 And, for that, we're going to use a LOD score, which 7 00:00:19,910 --> 00:00:21,215 is the log of the odds ratio. 8 00:00:21,215 --> 00:00:31,385 9 00:00:31,385 --> 00:00:32,385 So we'll have some data. 10 00:00:32,385 --> 00:00:37,200 11 00:00:37,200 --> 00:00:39,943 And what we want to do with the data 12 00:00:39,943 --> 00:00:41,235 is look at the odds of linkage. 13 00:00:41,235 --> 00:01:02,760 14 00:01:02,760 --> 00:01:06,720 We want to compare the odds of linkage, where we're 15 00:01:06,720 --> 00:01:13,840 given data, versus the odds of whatever we're comparing, 16 00:01:13,840 --> 00:01:16,975 the mark, the SSR in our disease-causing allele, 17 00:01:16,975 --> 00:01:18,100 the odds of being unlinked. 18 00:01:18,100 --> 00:01:30,740 19 00:01:30,740 --> 00:01:34,940 OK, so we can define some events here. 20 00:01:34,940 --> 00:01:47,780 21 00:01:47,780 --> 00:01:51,110 Event X is the marker is linked. 22 00:01:51,110 --> 00:01:54,455 We have not X as unlinked. 23 00:01:54,455 --> 00:01:59,770 24 00:01:59,770 --> 00:02:04,075 And then event Y will be our data in the pedigree. 25 00:02:04,075 --> 00:02:12,450 26 00:02:12,450 --> 00:02:15,810 OK, so we could get an expression that 27 00:02:15,810 --> 00:02:20,310 allows us to get this odds ratio by using Bayes' theorem where 28 00:02:20,310 --> 00:02:22,350 we could say the probability of X 29 00:02:22,350 --> 00:02:31,288 given Y. We could get an odds ratio here, 30 00:02:31,288 --> 00:02:32,830 sort of what I've set up there, where 31 00:02:32,830 --> 00:02:36,250 we get the ratio of the probability of X, 32 00:02:36,250 --> 00:02:40,180 the marker being linked given our data, divided 33 00:02:40,180 --> 00:02:45,135 by the probability of our marker being unlinked, given our data. 34 00:02:45,135 --> 00:02:46,510 That's going to be our odds ratio 35 00:02:46,510 --> 00:02:49,000 that we're trying to calculate. 36 00:02:49,000 --> 00:02:57,170 And so I'm just going to now use Bayes' theorem, which 37 00:02:57,170 --> 00:03:00,568 is listed up there for you, and say this 38 00:03:00,568 --> 00:03:02,360 will be equal to the probability of Y given 39 00:03:02,360 --> 00:03:08,360 X times the probability of X times 1 40 00:03:08,360 --> 00:03:17,550 over the probability of Y divided by the probability of Y 41 00:03:17,550 --> 00:03:23,670 given not X times the probability of not X times 1 42 00:03:23,670 --> 00:03:29,740 over the probability of Y. 43 00:03:29,740 --> 00:03:33,180 This cancels out. 44 00:03:33,180 --> 00:03:45,290 And this is sort of our posterior odds ratio, 45 00:03:45,290 --> 00:03:50,162 the odds of X given Y, given our data. 46 00:03:50,162 --> 00:03:51,245 This is sort of the prior. 47 00:03:51,245 --> 00:03:59,450 48 00:03:59,450 --> 00:04:02,920 And this is a relationship. 49 00:04:02,920 --> 00:04:04,450 What you'll see is that this odds 50 00:04:04,450 --> 00:04:07,120 ratio that we're interested in is directly related 51 00:04:07,120 --> 00:04:08,860 to this ratio. 52 00:04:08,860 --> 00:04:11,470 And this ratio, as you'll see in the next lecture, 53 00:04:11,470 --> 00:04:14,088 is something you can easily determine from the data. 54 00:04:14,088 --> 00:04:15,380 So that's why we're doing this. 55 00:04:15,380 --> 00:04:17,050 We can get the odds ratio we care about 56 00:04:17,050 --> 00:04:20,589 because this is something that we can determine. 57 00:04:20,589 --> 00:04:24,168 This prior is going to be the same, no matter 58 00:04:24,168 --> 00:04:26,210 what your data is or what gene you're looking at. 59 00:04:26,210 --> 00:04:29,200 So we're not really going to consider that further. 60 00:04:29,200 --> 00:04:30,940 But this relationship is what allows 61 00:04:30,940 --> 00:04:36,350 us to get a useful statistical test where our LOD score-- 62 00:04:36,350 --> 00:04:39,490 this is the last thing I'm going to write here-- 63 00:04:39,490 --> 00:04:49,360 is the log base 10 of the probability of the data, 64 00:04:49,360 --> 00:05:05,360 given linkage, at some distance theta-- 65 00:05:05,360 --> 00:05:08,270 OK, and I'm going to go into the details of this equation 66 00:05:08,270 --> 00:05:10,220 in the next lecture-- 67 00:05:10,220 --> 00:05:15,755 divided by the probability of getting the data if unlinked. 68 00:05:15,755 --> 00:05:25,710 69 00:05:25,710 --> 00:05:27,090 That is our LOD score. 70 00:05:27,090 --> 00:05:29,740 And that is going to be our statistical test. 71 00:05:29,740 --> 00:05:31,830 So what we're going to do next time, 72 00:05:31,830 --> 00:05:35,070 we're going to have pedigrees. 73 00:05:35,070 --> 00:05:37,230 We'll get data on the SSR genotypes 74 00:05:37,230 --> 00:05:39,125 and the segregation in the pedigree. 75 00:05:39,125 --> 00:05:40,500 And we'll calculate our LOD score 76 00:05:40,500 --> 00:05:43,670 and see if we can find where the gene is. 5422

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