Detection of Differential Expression

On a basic level, many scientific studies report the results of their microarray experiment as a gene list. These lists contain all of the genes significantly up- or downregulated during the experimental conditions under study. A gene whose expression changes more than two-fold, either up or down, was often thought to be significantly differentially expressed. However, this is a completely arbitrary cutoff point, and a measure of statistical significance must be used. Simple statistical analysis using t-tests and analysis of variance (ANOVA) can be used, but they must take account of (a) the experimental structure and (b) multiple testing. The experimental structure may be regarded as hierarchical with biological replicates at the top and technical repeats below, as discussed above. The structure is an important consideration because t-tests, for example, assume that all data points are independent, i.e., that the replicates were performed at the same level. Moderated t-tests are better than standard t-tests as they account for the fact that outliers (very high or low data points) will influence a standard t-test and produce artificially high significance levels, increasing the number of false positives (see below). Even when a set of data has been assessed for its significance, we have to bear in mind that all statistical inferences have a probability of being incorrect. There are two important types of error inherent in statistical analysis: false positives and false negatives. The false negative rate is a reflection of the statistical power of the test being performed and can be reduced simply by increasing sample replicates.

The false positive rate is governed by the significance level being tested for (i.e., a P-value less than 0.05); however, it is influenced by the number of comparisons or tests being performed - known as multiple testing. 'Multiple' testing refers to the fact that a microarray experiment will perform thousands of multiple comparisons (one per gene) simultaneously. Using a standard significance cutoff of P <0.05 would fail to account for the effect of this many comparisons and would automatically lead to 50 genes being classed as "significant' per 1000 (5%) purely by chance. The most stringent method of compensating for this, known as the Bonferroni correction [40], can be applied in two ways. The first is to adjust the P-value obtained from each test by multiplying it by the number of genes being tested and then only accept its significance if P is still below 0.05. The second is to manipulate your original false positive rate (say 0.05), dividing it by the number of tests (say, 1000), which provides a new significance cutoff point of 0.00005. This is extremely conservative and will normally result in very few significant genes. The false discovery rate (FDR) is an alternative solution to the multiple testing problem in that it provides an estimate of the amount of false discoveries without being as conservative as the Bonferroni correction [41, 42]. The FDR returns an expected percentage of false predictions within the data set, defined as the ratio of the number of false predictions over the total number of predictions.

The situation can become extremely complex and biologists should collaborate with statisticians in order to analyze microarray data accurately. Ideally each should be aware of the other's expertise throughout a microarray experiment, from experimental design and execution through to analysis and interpretation. Reference [38] provides an excellent starting point for the finer details of data analysis.

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