A first principles approach to differential expression in microarray data analysis.

Rubin RA - BMC Bioinformatics (2009)

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Figure 4: P-values for testing the hypothesis of no differential expression as a function of the median ANOVA (1-p) scores for the case of 11 probes per probe set. These charts show the unadjusted p-values corresponding to median ANOVA (1-p) scores for a specific number of probes per probe set. Similar curves can be obtained for any number of probes per probe set by means of the pbeta function in the R package stats, or the tools for working with sums of random variables in the R package distr. Figure 4(a) shows the full curve, while Figure 4(b) zooms in on the portion of the curve most involved with deciding on the question of differential expression.
Mentions: Obtaining the p-value (unadjusted for multiple hypothesis tests) for a median ANOVA (1-p) score, x, is straightforward. For an odd number, n, of probes, p-value = 1 - pbeta(x, m, m) where pbeta is the beta cumulative distribution function in the CRAN R stats package and m = (n+1)/2. (For an even number, n, of probes, p-value = 1-p(x), where p is the cumulative distribution function of the mean of two beta distributions, (B(m,m+1) + B(m+1,m))/2, and m = n/2. We can obtain p(x) from the tools for working with distributions of sums of random variables found in the CRAN R distr package.) The unadjusted p-values for the median ANOVA (1-p) scores are shown in Figures 1, 2 and 3. Figure 4 shows the unadjusted p-values for the hypothesis test as a function of the median ANOVA (1-p) scores for the case of 11 probes per probe set, which is the case for the HGU-133A chip. Figure 4(a) shows the entire curve, and 4(b) shows the portion of the curve of greatest importance.

Bottom Line: Here we take the approach of making the fewest assumptions about the structure of the microarray data.We applied the technique to the HGU-133A, HG-U95A, and "Golden Spike" spike-in data sets.The resulting receiver operating characteristic (ROC) curves compared favorably with other published results.

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Affiliation: Mathematics Department, Whittier College, 13406 E. Philadelphia St., Whittier, CA 90608, USA. brubin698@earthlink.net

ABSTRACT

Background: The disparate results from the methods commonly used to determine differential expression in Affymetrix microarray experiments may well result from the wide variety of probe set and probe level models employed. Here we take the approach of making the fewest assumptions about the structure of the microarray data. Specifically, we only require that, under the hypothesis that a gene is not differentially expressed for specified conditions, for any probe position in the gene's probe set: a) the probe amplitudes are independent and identically distributed over the conditions, and b) the distributions of the replicated probe amplitudes are amenable to classical analysis of variance (ANOVA). Log-amplitudes that have been standardized within-chip meet these conditions well enough for our approach, which is to perform ANOVA across conditions for each probe position, and then take the median of the resulting (1 - p) values as a gene-level measure of differential expression.

Results: We applied the technique to the HGU-133A, HG-U95A, and "Golden Spike" spike-in data sets. The resulting receiver operating characteristic (ROC) curves compared favorably with other published results. This procedure is quite sensitive, so much so that it has revealed the presence of probe sets that might properly be called "unanticipated positives" rather than "false positives", because plots of these probe sets strongly suggest that they are differentially expressed.

Conclusion: The median ANOVA (1-p) approach presented here is a very simple methodology that does not depend on any specific probe level or probe models, and does not require any pre-processing other than within-chip standardization of probe level log amplitudes. Its performance is comparable to other published methods on the standard spike-in data sets, and has revealed the presence of new categories of probe sets that might properly be referred to as "unanticipated positives" and "unanticipated negatives" that need to be taken into account when using spiked-in data sets at "truthed" test beds.

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