I am trying to analyze a microarray dataset from GEO in which one of the patients has 5 technical replicates. Should I calculate the average gene expression of 5 replicates? What is the best solution?
The best way to handle technical replicates often depends on the context and the overall experimental design, which you haven't told us much about. Why did the experimenters make the technical replicates? What were they hoping to learn? Generally, however, if you have multiple arrays from one same patient sample while all other patient samples have only one array, then averaging the 5 arrays would be the logical strategy. Alternatively you might choose the best array out of the 5 in terms of quality criteria and discard the other four.
The plots actually tell you nothing about the relative quality of the arrays. The microarrays have been quantile normalized, which forces every array to have the same expression density and the same boxplot, so plotting those things becomes uninformative. An MDS plot of all 152 arrays would be more relevant. You want to see the technical replicates clumping together relative to other arrays.
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Can you elaborate what a technical replicate in microarray experiments is? In RNA-seq it means resequencing the same library > 1, but what is it in the array world?
I think that the definitions are almost the same. Here means taking one sample from the same patient and analyzing it 5 times across multiple arrays.