Comparison criteria

Next we can check to select the filtering criterion to be applied when comparing the two groups. The compare criterion (1) requires the fold change between the group means to exceed a specified threshold. We can also check the “Use lower 90% confidence bound” to specify to use the lower confidence bound of fold changes for filtering. The computation of confidence intervals of fold changes and the application of using lower bound as filtering criterion are described in Li and Wong 2001b (page 6, section “Confidence interval for fold change”). Theta_1_hat and Theta_2_hat are the E and B described above (expression values in one samples or the mean expression of samples in the baseline or experiment group). The motivation is that we are really interested in the fold change of real expression values r = Theta_1 / Theta_2, rather than observed fold change Theta_1_hat / Theta_2_hat. 

A negative expression value (or group mean) for a probe set is truncated to 1 before calculating fold changes. When one expression is large (say 1000) and the other is -10 (at noise level of absent genes), it is helpful to bring -10 to a small positive number so a large fold change is calculated and the gene gets selected. In the comparison output file, fold changes are always larger than 1 with signs representing the direction of changes, while confidence intervals are for the absolute value of the fold change. We have found it useful to order genes by the lower confidence bound ("Lower CB" columns), which is a conservative estimate of the real underlying fold change. In some cases, one may get (0, infinity) as the confidence interval, indicating very unreliable estimated fold change.

The compare criterion (2) specifies the threshold for absolute difference between the two group means. Since the down-regulated genes and the up-regulated genes may have different change magnitude, once can specify different fold change criterion for E/B and B/E and different mean difference criterion for E-B and B-E. If the expression values have been log-transformed, E-B and B-E refer to the log fold change (logE* – logB* = log (E*/B*) when E* and B* are in original scale), and correspondingly the E-B and B-E threshold should also be specified in log scale. The criterion (1) is generally not used since they are more difficult to interpret when the expression value are in log scale.

 

The compare criterion (3) tests whether the mean difference in (2) equals to zero by the unpaired t-test. See t-statistic and its p-value. The default p-value threshold 0.05 filters genes that differ in group means with a two-tailed p-value < 0.05. When the sample size is small, the t-statistics and p-values should better be used only as a ranking or filtering device rather than the actual significance value, especially in the context of applying t-test on thousands of genes. If no multiple comparison adjustment is applied, one can specify very stringent p-value threshold (e.g. 0.05 divided by the total number of genes on the array; this is Bonferroni correction assuming all genes are independent).

 

The compare criterion (4) requires that the percentage of samples called “Present” in the samples used in both groups be larger than a threshold. In V1.3+, this criterion can be specified for the baseline and the experiment group separately. This can be used to obtain genes called as P in 100% samples of the B group and called as A in 100% samples of the E group. For example, if Comparison 1 is “P call of B >= 100% and P call of E >= 0%” and Comparison 2 is “P call of B >= 0% and P call of E >= 1%”, in "Compare samples/Combine comparisons" one can use "And not" to combine the two comparisons: Comparison 1 "and not" Comparison 2.

 

The compare criterion (5) specifies that the p-value threshold for the paired t-test. The “paired t-test” assumes the first baseline sample to be compared with the first experiment sample, and so on. To ease the pairing specification the samples can first be ordered at “Tools/Array list file”. When the baseline and experimental arrays are paired, using paired t-test has larger power than the unpaired t-test (detect more real changes).

 

Combing these statistics can help us focus attention on a small set of interesting genes. Typically one may need to estimate the number of differentially expressed genes beforehand, look at these statistics for known differentially expressed genes, and experiment with different parameters to finally filter a reasonable set of interesting genes.

 

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