Deriving Ranges of Optimal Estimated Transcript Expression due to Nonidentifiability.

Current expression quantification methods suffer from a fundamental but undercharacterized 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 is called nonidentifiability in probabilistic modeling. It is further exacerbated by incomplete reference transcriptomes where reads may be sequenced from unannotated 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 nonidentifiability and the extent of the error. Applying our methods to the Human Body Map data, we observe that 35%-50% of transcripts potentially suffer from inaccurate quantification caused by nonidentifiability. 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 other isoforms from the same gene 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.