Comparison of Statistical Data Models for Identifying Differentially Expressed Genes Using a Generalized Likelihood Ratio Test

Currently, statistical techniques for analysis of microarray-generated data sets have deficiencies due to limited understanding of errors inherent in the data. A generalized likelihood ratio (GLR) test based on an error model has been recently proposed to identify differentially expressed genes from microarray experiments. However, the use of different error structures under the GLR test has not been evaluated, nor has this method been compared to commonly used statistical tests such as the parametric t-test. The concomitant effects of varying data signal-to-noise ratio and replication number on the performance of statistical tests also remain largely unexplored. In this study, we compared the effects of different underlying statistical error structures on the GLR test's power in identifying differentially expressed genes in microarray data. We evaluated such variants of the GLR test as well as the one sample t-test based on simulated data by means of receiver operating characteristic (ROC) curves. Further, we used bootstrapping of ROC curves to assess statistical significance of differences between the areas under the curves. Our results showed that i) the GLR tests outperformed the t-test for detecting differential gene expression, ii) the identity of the underlying error structure was important in determining the GLR tests' performance, and iii) signal-to-noise ratio was a more important contributor than sample replication in identifying statistically significant differential gene expression.