A first principles approach to differential expression in microarray data analysis

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 null 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.