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The proposed model includes random baseline means μi to allow for variation of
the amount of tripeptides in the original phage display peptide library. It is important
to include such random effects. Large counts at the third stage can be explained by
either preferential binding of a certain tripeptide, or simply random high initial count
in the original library. The inclusion of the random baseline means allows us to
differentiate these two cases.
In selecting the tripeptide-tissue pairs with increasing means across the three
stages, we face a massive multiplicity problem. Ji et al. approach this problem
through the application of a simple Bayesian FDR, providing the investigator with an
estimate of the error rate in the selection procedure. Their approach can be embedded
in a decision theoretic framework where the utility function takes into consideration
statistical significance, that is, the proportion of false positives and false negatives;
but it does not take into account the biological significance such as the size of the
mean increase through the three stages. Our decision theoretic approach specifically
targets this issue through the definition of its corresponding utility function, and the
estimation of the error rate in the selection procedure, such as the FDR and false
negative rate, can also be computed using this methodology. Other utility functions
can be considered.
The nonparametric nature of our model is an improvement in sophistication over
its parametric version. Nevertheless, the MCMC simulation scheme of the posterior
sample is straightforward. The posterior distribution of any parameter given the rest
can be derived directly and has an analytical expression due to the use of conjugate
families. The computing time necessary to generate the MCMC sample is relatively
short.
The simulation study we performed was satisfactory. If the data is generated
according to the parametric version of our model, our nonparametric model is able to
detect the event of interest with high accuracy; the observed FDR and false negatives
rate are close to their respective expected values.