  In mass spectrometry based quantitative proteomics research, the emerging
iTRAQ technique has been widely adopted for high throughput protein profiling,
as it enables one to measure multiple samples simultaneously in one multiplex
experiment and thus greatly enhances the throughput of protein quantification.
However, the technical variation across different iTRAQ multiplex experiments
is often large due to the dynamic nature of MS instruments. This leads to
strong batch effects in the iTRAQ data. Moreover, the iTRAQ data often contain
substantial batch-level non-ignorable missingness. Specifically, the abundance
measures of a given protein/peptide are often missing altogether in all the
samples from the same batch, with the missing probability depending on the
combined batch-level abundances. We term this unique missing-data mechanism as
the Batch-level Abundance-Dependent Missing-data mechanism (BADMM). We
introduce a new method, mixEMM, for analyzing iTRAQ data with batch effects and
batch-level non-ignorable missingness. The mixEMM method employs a linear
mixed-effects model and explicitly models the batch effects and the BADMM in
the likelihood function. With simulation studies, we showed that compared with
existing approaches that utilize relative abundances and ignore the missing
batches under the missing completely at random assumption, the mixEMM method
achieves more accurate parameter estimation and inference.We applied the method
to an iTRAQ proteomics data from a breast cancer study and identified
phosphopeptides differentially expressed between different breast cancer
subtypes. The method can be applied to general clustered data with cluster
level non ignorable missing-data mechanisms.
