A Bayesian random partition model for sequential refinement and coagulation.

We analyze time-course protein activation data to track the changes in protein expression over time after exposure to drugs such as protein inhibitors. Protein expression is expected to change over time in response to the intervention in different ways due to biological pathways. We therefore allow for clusters of proteins with different treatment effects, and allow these clusters to change over time. As the effect of the drug wears off, protein expression may revert back to the level before treatment. In addition, different drugs, doses, and cell lines may have different effects in altering the protein expression. To model and understand this process we develop random partitions that define a refinement and coagulation of protein clusters over time. We demonstrate the approach using a time-course reverse phase protein array (RPPA) dataset consisting of protein expression measurements under different drugs, dose levels, and cell lines. The proposed model can be applied in general to time-course data where clustering of the experimental units is expected to change over time in a sequence of refinement and coagulation.