Background. DNA microarrays measure the expression levels of tens of thousands of genes simultaneously. Some differentially expressed genes may be useful as markers for the diagnosis of diseases. Available statistical tests examine genes individually, which causes challenges due to multiple testing and variance estimation. In this Master's thesis, Bayesian confirmatory factor analysis (CFA) is proposed as a novel approach for the detection of differential gene expression.
Methods. The factor scores represent summary measures that combine the expression levels from biological samples under the same condition. Differential gene expression is assessed by utilizing their distributional assumptions. A mean-field variational Bayesian approximation is employed for computationally fast estimation.
Results. Its estimation performance is equal to Gibbs sampling. Point estimation errors of model parameters decrease with increasing number of variables. However, mean centering of the data matrix and standardization of factor scores resulted in an inflation of the false positive rate.
Conclusion. Avoiding mean centering and revision of the CFA model is required so that location parameters of factor score distributions can be estimated. The utility of CFA for the detection of differential gene expression needs also to be confirmed by a comparison with different statistical procedures to benchmark its false positive rate and statistical power.
