An idealized version of a label-free discovery mass spectrometry proteomics experiment would provide absolute abundance
measurements for a whole proteome, across varying conditions. Unfortunately, this ideal is not realized. Measurements are made on
peptides requiring an inferential step to obtain protein level estimates. The inference is complicated by experimental factors
that necessitate relative abundance estimation and result in widespread non-ignorable missing data. Relative abundance on the log
scale takes the form of parameter contrasts. In a complete-case analysis, contrast estimates may be biased by missing data and a
substantial amount of useful information will often go unused.
To avoid problems with missing data, many analysts have turned to single imputation solutions. Unfortunately, these methods
often create further difficulties by hiding inestimable contrasts, preventing the recovery of interblock information and failing
to account for imputation uncertainty. To mitigate many of the problems caused by missing values, we propose the use of a Bayesian
selection model. Our model is tested on simulated data, real data with simulated missing values, and on a ground truth dilution
experiment where all of the true relative changes are known. The analysis suggests that our model, compared with various
imputation strategies and complete-case analyses, can increase accuracy and provide substantial improvements to interval
coverage.