Some help on genome analysis

Question

I have an exam tomorrow about statistics for genome analysis and I'm having some troubles with some questions from an example exam. All help would be very welcome!

These are the questions:

1. The single step maxT procedure as explained in the course notes is a nonparametric exact correction and takes the dependence between tests into account. Why do we introduce the false discovery rate if this single step maxT procedure has such nice properties?

2. After preprocessing the probe-level data you obtain an expression value for each probeset on each array. Suppose that you use these probeset intensities to conduct e.g. a t-test for differential gene expression, while ignoring the variability eduction caused by preprocessing. Is this problematic (from a statistical point of view)? Why / why not?

Answer 1

1. If we have relatively few hypothesis we wish to test, we usually aim to adjust for multiplicity by controlling for FWE, which is the probability of detecting at least one erroneous significance. However, if we wish to control for thousands or even millions of tests, such is standard in genomics and astrophysics, controlling the FWE makes the inference procedure very conservative. Imagine using Bonferroni adjustments in these cases! The problem lies in that requiring the FWE to be controlled does not scale up well with increasing number of tests. I think it was Benjamini and Hochberg (1995) who introduces the false discovery rate, which replaces the probability of a single false rejection with the expected proportion of false rejections. Therein lies the problem with the MaxT procedure, as it controls the FWE and not the FDR. Now, I know this is not a complete answer but it might be helpful to you anyway. There is a great example of the difference between controlling the FWE FDR in Westfall et. al (2011) p. 497.

2. Unfortunately I am a novice in the area of genomics and I can not answer this question, or as in 1) even hint at an answer or a place to look.

Answer 2

1. maxT controls the family-wise error rate, which is the probability of a single false positive under the null. As noted in the other answer, this may not always be the goal.

2. I think this question involves tradeoffs. Earlier preprocessing was model-based and because of this, an attempt was made to account for the uncertainty of preprocessing. The criticism of these strategies is that they are simultaneously complex, but still not addressing other biases and sources of variation. One could reasonably argue that the most common preprocessing methods (RMA) ignore this uncertainty. However, this strategy is commonly accepted in the field because of non-statistical evidence (spike-in experiments), and has the support of many thoughtful statisticians.