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I've done a differential expression analysis with transcriptomic information (microarrays and RNAseq) from different datasets by applying for some of them t-test and for the rest Wald-test. I've got many coincidences for these significant genes so I want to recalculate my p-values (or my adjusted p-values, obtained by the BH method) using all these datasets. What is the proper method to do this (if possible)? I am completely new in this field so any additional information would be appreciated.

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For cDNA-derived data have a look at the DESeq2 analysis guide.

The general process is to convert all your input data into an integer count matrix (not expression matrix), with genes in rows and samples in columns, and pair it with a metadata data frame that has one line per sample (ordered in the same way as the columns), and indicates the conditions for each sample (including sequencing batch). By incorporating the sequencing batch into the statistical model, it's possible to reduce any technical error associated with consistent linear changes in expression based on the batch (e.g. different runs giving different numbers of total reads).

Microarrays can be combined, bearing in mind that microarray results are often inconsistently presented as normalised / non-normalised, or linear / log. I've found that normalising within-batch then converting to log space usually seems to work well. There is a verbose Users Guide for Limma Voom, but I've found it to be tricky to navigate - it's less friendly to new users.

Combining microarrays and RNASeq is complicated, because the data have different dynamic ranges, and different biases. I think the best thing to do is to process the microarray data separately from the RNASeq data and generate two lists of biologically-interesting genes, then look at the set relationships (e.g. intersection, exclusion).

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What is the proper method to do this (if possible)?

Please use dedicated software for RNA-seq and microarray analysis and not naive tests such as the t-test. For microarray one commonly uses limma and for RNA-seq either DESeq2, edgeR or limma-voom, all are available as Bioconductor packages in R.

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