Note on section "Results: Comparison with standard methods".
In this section of the paper, a comparison of our method with the standard methods is provided, for those cases in which standard methods are applicable. The standard methods involve tests like the t-test, which are applicable under certain assumptions, for example under the assumption that, for each gene and each of two groups being compared, the intensity distribution of the gene at that group is close to normal. (Note that the intensities considered in section Results: Application to an erythroid development nylon filter dataset are positive. However, we can assume that they have distributions close to normal as measurements are sufficiently positive to render the portions of the left tail of the normal fit falling to the left of the y-axis negligible, so that the error created by the simultaneous normality and positive-value assumptions is negligible.)
As mentioned in section Results: Comparison with standard methods, one needs to combine these tests, done on a gene by gene basis, with some Bonferroni-like correction in order to have control on the overall expected false-positive rate. This because the observed value of the test statistic (comparing a group to the reference one) at a particular gene might be high (resp. low) enough that the probability of observing it under the null hypothesis chance model of equal means is very small; however if one is looking at several hundreds of genes, the probability of observing such a high (resp. low) value might not be that small. In order to correct for this, one has therefore to account for the number of gene tags involved. The Bonferroni correction does so in a very conservative way, by basically choosing the significance threshold p for the test statistic (used on a gene tag by gene tag basis) so to ensure at high confidence that there are no false-positives. This is stricter than needed, as we want to allow a certain false-positive rate s%. Therefore comparing our method to the standard methods consisting of a combination of t-like tests plus the Bonferroni correction would not be fair to the standard methods. Corrections less strict, albeit in the same spirit, should be used instead; these are what we refer to as ``Bonferroni-like'' corrections.
If we knew the number M of genes which are not up-regulated (resp. down-regulated), then, when applying the standard methods, we would try to ensure at high confidence that the number of false-positives is no larger than s%M, which would give a false-positive rate of s%. (This correction can be done using a Poisson distribution with parameter Mp, whereby the significance threshold p that one needs to use in a t-like test, done on a gene tag by gene tag basis, can be determined.) This would put the standard methods on equal footing with our method, allowing a fair comparison. However, we do not know M. So in the paper we try to ensure a number of false-positives no larger than s% x (number of gene tags). This number is greater than or equal to s%M so, by applying a correction based on (number of gene tags) x p to the t-like tests (as done in the paper), we might still get with the standard methods a false-positive rate greater than the s% false-positive rate that we achieve with our method. Therefore, albeit doing this correction makes a comparison of our method with the standard methods less biased in favor of the standard methods than not applying a correction at all, it is still biased in favor of the standard methods. Thus, even with this correction, the standard methods cannot guarantee a false-positive rate comparable to that from our method.
In conclusion, in the paper we were ``harsher'' when judging our method than when judging the standard ones. When we mentioned that there were a few genes that were picked up by the standard methods, but not by ours, we were actually being ``lenient'' to the standard methods, in that indeed the standard methods did not really guarantee the desired false-positive rate. Nevertheless we thought useful to provide some kind of comparison and we preferred to be biased in favor of the standard methods than in favor of our methods (as we would have been if we had applied a strict Bonferroni correction).
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Last updated: April 12, 2000.
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