sleuth-CN

Preprint available here! If you use this tool, any constructive feedback is greatly appreciated.

Compositional Data Analysis approach to Sleuth

This is an extension of sleuth that treats the data as compositional data. Applying the ideas of John Aitchison, as well as the ideas found in the R packages ALDEx2 and compositions, this performs a logratio transformation of data created by kallisto or salmon to be analyzed by sleuth.

The "CN" stands for Compositional Normalization. Note that this approach is different from a formal compositional data analysis approach, which focuses its attention purely on the relative abundances. This approach explicitly attempts to recover the absolute abundances by anchoring the data on defined "negative control" features (spike-ins, reference genes, etc). Even when such features are not present in the data, it provides a more accurate interpretation of the data (how all other features are changing relative to a defined set of features).

See the preprint for full details.

Installation

To install, use devtools:

devtools::install_github('https://github.com/warrenmcg/sleuth-ALR')

Usage

See the vignette for full details!

Compared to running sleuth_prep and sleuth_fit, the only new arguments are the following:

• null_model: specify both the full and null model, in order to run an LRT
• lr_type: this specifies what kind of logratio transformation you want. use alr for additive logratio transformation, and use clr for centered logratio transformation (the geometric mean in each sample is the denominator).
• denom_name: this must be specified if you choose alr for your lr_type. This is the target ID (or index number of the target ID) that you wish to be used as a 'reference gene'. If you specify more than one, the geometric mean between all of the selected reference genes will be used as the denominator.
• additional arguments taken by choose_denom and get_lr_functions. See the help pages for those functions for additional details.

Options to handle zeros for ALR transformation

The ALR transformation involves the logarithm of a ratio, so a zero in either the numerator or the denominator is a problem. The question of how to handle zeros remains an area of active research within Compositional Data Analysis. For a review of this work, please see Chapter 4 of Compositional Data Analysis.

sleuth-ALR takes the following approach:

1. Essential Zeros: If any feature is zero in all samples, or is otherwise filtered out by the sleuth filtering step, it is considered an "essential zero". Biologically, the interpretation is that this feature is likely in a region of heterochromatin and is silenced. These features can be safely excluded from analysis.

2. Rounded Zeros: Any feature that has zero in at least one sample, but otherwise passes the sleuth filtering step, it is considered a "rounded zero". Biologically, the interpretation is that this feature is likely in a region where expression is occurring, but is below the limit of detection. The samples with zeros are imputed using the "multiplicative strategy" described in Chapter 4 (link above).

Briefly, the features within a sample that are zero are replaced with delta. The non-zero features within that sample are replaced by the following formula:

old_value = x ==> new_value = x * (1 - (# of zero features) * delta / sum constraint)

The sum constraint is the total for that composition (if TPMs, it would be 1 million; for counts, it would be the library size).

Two additional arguments that can be specified are used in the ALR transformation:

• delta: you can specify delta to be used for imputing (default: NULL and impute_proportion is used)
• impute_proportion: if delta is NULL, the minimum non-zero value is taken to be the detection limit, and impute_proportion is what proportion of this detection limit should be used as delta. (default is 65%).

Chapter 4 from Compositional Data Analysis mentions the recommendation of 65%, hence the choice of default. However, our own sensitivity analysis with knockout datasets indicates that a default value of delta = 0.5 minimizes unstable variation in low-expression samples when there is a significant down-regulation of expression.