In working with the summary p-value rather than the complete data, some information is lost, and a single analysis of the data may be more efficient. A natural approach is to estimate all gene effects together in regression model. On the genome-wide scale, a fixed-effects regression is impractical, requiring estimation of many more parameters than there are observations. Therefore, several methods proposed for microarrays regard a gene as having a random effect, and model the distribution of gene effects by parametric forms that can be estimated. A simple model is to assume a normally distributed effect around zero [35], although this may lack power when most genes have no effect. The model can be extended by assuming that the effect variability comes from small and stronger effects, with inference based only on the stronger effects [36]. Another alternative is a mixture of a zero-centred normal and a point mass at zero[37] or, more generally, a mixture of three normals with respectively positive, zero and negative means [38]. Here, the zero-centred distribution is regarded as the null distribution, which allows for small nonzero effects to be regarded as uninteresting if there is sufficient evidence for stronger effects.
