  High throughput sequencing is a technology that allows for the generation of
millions of reads of genomic data regarding a study of interest, and data from
high throughput sequencing platforms are usually count compositions. Subsequent
analysis of such data can yield information on tran- scription profiles,
microbial diversity, or even relative cellular abundance in culture. Because of
the high cost of acquisition, the data are usually sparse, and always contain
far fewer observations than variables. However, an under-appreciated pathology
of these data are their often unbalanced nature: i.e, there is often systematic
variation between groups simply due to presence or absence of features, and
this variation is important to the biological interpretation of the data. A
simple example would be comparing transcriptomes of yeast cells with and
without a gene knockout. This causes samples in the comparison groups to
exhibit widely varying centres. This work extends a previously described
log-ratio transformation method that allows for variable comparisons between
samples in a Bayesian compositional context. We demonstrate the pathology in
modelled and real unbalanced experimental designs to show how this dramatically
causes both false negative and false positive inference. We then introduce
several approaches to demonstrate how the pathologies can be addressed. An
extreme example is presented where only the use of a predefined basis is
appropriate. The transformations are implemented as an extension to a general
compositional data analysis tool known as ALDEx2 which is available on
Bioconductor.
