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Steps for controlling for false discovery rate:Ĭontrol for FDR at level α *(i.e. However, guarding against any single false positive may be too strict for genomewide studies, and can lead to many missed findings, especially if we expect there to be many true positives.Ĭontrolling for the false discovery rate (FDR) is a way to identify as many significant features as possible while incurring a relatively low proportion of false positives.
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So if alpha was 0.05 and we were testing our 1000 genes, we would test each p-value at a significance level of 0.00005 to guarantee that the probability of having one or more false positives is 5% or less. If we test each hypothesis at a significance level of (alpha/# of hypothesis tests), we guarantee that the probability of having one or more false positives is less than alpha. The commonly used Bonferroni correction controls the FWER. Typically, multiple comparison procedures control for the family-wise error rate (FWER) instead, which is the probability of having one or more false positives out of all the hypothesis tests conducted. This method is too liberal, since we do not want to have such a great number of false positives. For example, if we were doing a genomewide study looking at differential gene expression between tumor tissue and healthy tissue, and we tested 1000 genes and controlled the FPR, on average 50 truly null genes will be called significant. This method poses a problem when we are conducting a large number of hypothesis tests. So if we control the FPR at an alpha of 0.05, we guarantee than the percentage of false positives (null features called significant) out of all hypothesis tests is 5% or less. The false positive rate (FPR), or per comparison error rate (PCER), is the expected number of false positives out of all hypothesis tests conducted. The more features you have, the higher the chances of a null feature being called significant. When we are conducting multiple comparisons (I will call each test a “feature”), we have an increased probability of false positives. In other words, we want the probability of a type I error, or a false positive, to be less than 5%. When we set our alpha to 0.05, we are saying that we want the probability that a null finding will be called significant to be less than 5%. We usually like to keep this probability under 5%. Since this is a small probability, we reject the null hypothesis and say that the means are significantly different. If we had a p-value of 0.03, for example, that would mean that if our null hypothesis is true, there would be a 3% chance of obtaining our observed test statistic or a more extreme. When conducting hypothesis tests, for example to see whether two means are significantly different, we calculate a p-value, which is the probability of obtaining a test statistic that is as or more extreme than the observed one, assuming the null hypothesis is true. In order to be able to identify as many significant comparisons as possible while still maintaining a low false positive rate, the False Discovery Rate (FDR) and its analog the q-value are utilized. Use of the traditional Bonferroni method to correct for multiple comparisons is too conservative, since guarding against the occurrence of false positives will lead to many missed findings. When analyzing results from genomewide studies, often thousands of hypothesis tests are conducted simultaneously. Achieving two significant results is much more demanding, not least because of the Bonferroni correction: having both treatments turn up significant 80% of the time would require 3000 subjects.This page briefly describes the False Discovery Rate (FDR) and provides an annotated resource list. The results of this simulation are graphed below: with 800 or so subjects equally allocated between the three treatments, this experiment is about 80% likely to recover at least one significant result. Points(possible.ns, power.fullranking, col="blue") Points(possible.ns, power.bothtreatments, col="red") Plot(possible.ns, power.atleastone, ylim=c(0,1)) This operation can be done with an analytically derived formula, but this simulation will provide the basis for more complicated designs. We then vary the total number of subjects to see how power will vary with sample size. We have to make assumptions about the size of the treatment effect and the standard deviation of the outcome variable. The standard design randomly assigns subjects to either treatment or control with probability 0.5. Please check out EGAP’s 10 Things You Need To Know About Statistical Power for some intuition and guidance when using this code. This page gives code in R for some basic and some more complicated power analyses.