Deriving Ranges of Optimal Estimated Transcript Expression Due to Non-identifiability

Current expression quantification methods suffer from a fundamental but under-characterized type of error: the most likely estimates for transcript abundances are not unique. This means multiple estimates of transcript abundances generate the observed RNA-seq reads with equal likelihood, and the underlying true expression cannot be determined. This problem is called non-identifiability for probabilistic models, and is further exacerbated by incomplete reference transcriptome. That is, reads may be sequenced from unannotated expressed transcripts. Graph quantification is a generalization to transcript quantification, accounting for the reference incompleteness by allowing exponentially many unannotated transcripts to express reads. We propose methods to calculate a "confidence range of expression" for each transcript, representing its possible abundance across equally optimal estimates for both quantification models. This range informs both whether a transcript has potential estimation error due to non-identifiability and the extent of the error. Applying our methods to the Human Body Map data, we observe 35%-50% of transcripts potentially suffer from inaccurate quantification caused by non-identifiability. When comparing the expression between isoforms in one sample, we find that the degree of inaccuracy of 20%-47% transcripts can be so large that the ranking of expression between the transcript and its sibling isoforms cannot be determined. When comparing the expression of a transcript between two groups of RNA-seq samples in differential expression analysis, we observe that the majority of detected differentially expressed transcripts are reliable with a few exceptions after considering the ranges of the optimal expression estimates. The code for computing the range of expression is available at https://github.com/Kingsford-Group/subgraphquant. The code for the involved analyses is available at https://github.com/Kingsford-Group/subgraphquantanalysis.