Background
I am looking into enterotyping the gut microbiome data, obtained by shotgun sequencing. This essentially means performing the Principal Coordinates Analysis (PCoA) of the beta-diversity matrix (distance matrix), based on the abundance table of species/gene-counts for all possible species/genes in all samples: for sample $i$ the counts of species/genes are $\mathbf{x}_i=(x_{i1}, x_{i2},...,x_{im})$. Such a table necessarily contains many zeros, whenever a species/gene is not present in a sample. Some of the possible beta-diversity measures are listed in table 1 of this article.
Problem
Statisticallys peaking, such data are considered to be an example of compositional data, i.e., the meaningful information is contained only in the ratios of the counts, which makes log-based distances the most suitable ones. These are used in many statistical methods (see, e.g., here). However, the log-transofmation is meaningful only when all the entries in the count table are strictly positive $x_{ik}>0$. One thus faces a problem of dealing with zero entries.
Possible solutions
- Using metrics not sensitive to zero entries (excluding alr, ilr and other similar log-transformations, highly recommended by statisticians - this limits the choice of statistical methods)
- Imputation of zeros: this requires a principled/biologically-sound way of imputing the zeros, since the results may be potentially very sensitive to this choice.
Question
What are the commongly used imputation methods? What is their advantages/disadvantages and justification for their use?
Some references
- Here is a statisticians' view on imputation in compositional data: the methodology may get rather involved, but does not have any specific biological basis.