Separating measurement and expression models clarifies confusion in single-cell RNA sequencing analysis
Sarkar A, Stephens M. Separating measurement and expression models clarifies confusion in single-cell RNA sequencing analysis. Nat Genet. 2021 Jun;53(6):770-777. doi: 10.1038/s41588-021-00873-4. Epub 2021 May 24. PMID: 34031584; PMCID: PMC8370014.
scRNA-seq studies use poorly-defined terms like dropout, missing data, imputation and ,zero inflation that lead to confusion during analysis and interpretation. This study proposes that the observed data be considered as reflecting both the true gene expression levels and the measurement error and that method should start with a simple Poisson model and add complexity as necessary instead of starting with a complex model.
Problematic Terms
“Dropout” refers to the failure to measure a gene and lead to some genes showing higher measured expression in some cells than others. However this is inconsistently used in publications and may refer to observed zeroes, undetected but expressed zeroes, or undetected molecules. There is no period during a scRNA-seq experiment where the data is left unobserved, so any zeroes are 0s - noisy zeroes that are as noisy as any other observation. The use of dropout and “missing data” to refer to observed zeroes leads to “imputation” methods that attempt to fill in those zeroes. Since zeroes are not “missing”, the imputed values are specious.
Zero-inflated models are used to deal with the “extra zeroes” in scRNA-seq data by accounting for the extra zeroes as being inflated by some process. However there is little evidence to support their use. A process that somehow introduces zeroes would suggest a systematic effect that only affects specific genes from specific cells.
Modeling scRNA-seq measurement
The Poisson model can be used in both bulk and scRNA-seq data and can account for the many zeroes in scRNA-seq data. It accounts for the lack of observations of every molecule in every cell. Zeroes are measurements like any other and need no special treatment. Observing a zero for a gene suggests that the relative proportion of that gene in the cell is low.
The use of the Poisson model is dependent on three assumptions, with the first being the most plausibly violated:
in each cell, each RNA molecule is equally likely to be observed
each molecule is observed independently
only a small proportion of the total available molecules in the cell are observed
The Poisson model can be modified with bias terms to account for biased sampling of molecules. When biases are consistent across cells, the model is robust to ignoring them. When random biases occur, a negative binomial model could deal with the additional noise better than a Poisson model. How much overdispersion to allow for remains an open question. However, most datasets will have a small measurement overdispersion. They emphasize that the Poisson model is specifically for the measurement model and not the observation model.
The measurement model connects the observed counts to the expression levels by specifying the conditional distribution of the probability of the observed counts \(X\) given the expression levels \(\Lambda\): \(p(X|\Lambda)\). An expression model is a model for the expression levels \(p(\Lambda)\).
A more flexible model like a negative binomial or a zero-inflated negative binomial can capture additional variation. These models derive from a Poisson measurement model combined with expression models.
Generally the Poisson model fits the data well enough for differential expression analysis, clustering, and dimension reduction. There are instances such as long-tailed distributions where genes don’t quite fit the models above and require additional care.