Composite Hypothesis Testing of Differential Gene Expression Based on Poisson Models: A Validation Study and Some Considerations

Composite hypotheses testing of differential gene expression combines multiple tests (experiments) into a single hypothesis-based test, which can be very useful for the understanding of genetic pathways of complex diseases. There are two common types of composite hypothesis testing of differential gene expression: the union-intersection test (UIT) and intersection-union test (IUT), both of which apply a set of individual hypotheses tests yet with different interpretations. For example, consider the expression of one gene evaluated at three treatment conditions, all contrasted with the same control condition. UIT determines whether this gene is differentially expressed under at least one treatment condition whereas IUT tests if this gene is differentially expressed under all of the three treatment conditions.

Four statistics were evaluated in the context of composite hypotheses using both simulation and real datasets: LOD score and fold change of the gene expression, and the p values and its Bayesian equivalent, the posterior probability, of the test, with the gene expression under a single condition described by a Poisson model. Monte Carlo simulation was used to obtain the p value and the posterior probability. The results showed parallel correspondence between the p value and the posterior probability of the test, but they did not shown general agreement with LOD score and fold change. The latter two statistics are simple to use, but they do not have appropriate implications on this hypothesis-based composite test. Some discussions are given as well on the use of composite hypotheses testing for differential gene expression.