Spearman's footrule as a measure of cDNA microarray reproducibility

Replication is a crucial aspect of microarray experiments, due to various sources of errors that persist even after systematic effects are removed. It has been confirmed that replication in microarray studies is not equivalent to duplication, and hence it is not a waste of scientific resources. Replication and reproducibility are the most important issues for microarray application in genomics. However, little attention has been paid to the assessment of reproducibility among replicates. Here we develop, using Spearman's footrule, a new measure of the reproducibility of cDNA microarrays, which is based on how consistently a gene's relative rank is maintained in two replicates. The reproducibility measure, termed index.R, has an R2-type operational interpretation. Index.R assesses reproducibility at the initial stage of the microarray data analysis even before normalization is done. We first define three layers of replicates, biological, technical, and hybridizational, which refer to different biological units, different mRNAs from the same tissue, and separate cDNAs from a cDNA pool. As the replicate layer moves down to a lower level, the experiment has fewer sources of errors and thus is expected to be more reproducible. To validate the method we apply index.R to two sets of controlled cDNA microarray experiments, each of which has two or three layers of replicates. Index.R shows a uniform increase as the layer of the replicates moves into a more homogeneous environment. We also note that index.R has a larger jump size than Pearson's correlation or Spearman's rank correlation for each replicate layer move, and therefore, it has greater expandability as a measure in [0,1] than these two other measures.