  We propose a new statistical approach to obtain differential gene expression
of non-detects in quantitative real-time PCR (qPCR) experiments through
Bayesian hierarchical modeling. We propose to treat non-detects as non-random
missing data, model the missing data mechanism, and use this model to impute Ct
values or obtain direct estimates of relevant model parameters. A typical
laboratory does not have the resources to perform experiments with a large
number of replicates; therefore, we propose an approach that does not rely on
large sample theory. We aim to demonstrate the possibilities that exist for
analyzing qPCR data in the presence of non-random missingness through the use
of Bayesian estimation. Bayesian analysis typically allows for smaller data
sets to be analyzed without losing power while retaining precision. The heart
of Bayesian estimation is that everything that is known about a parameter
before observing the data (the prior) is combined with the information from the
data itself (the likelihood), resulting in updated knowledge about the
parameter (the posterior). In this work we introduce and describe our
hierarchical model and chosen prior distributions, assess the model sensitivity
to the choice of prior, perform convergence diagnostics for the Markov Chain
Monte Carlo, and present the results of a real data application.
