I saw lots of high-through microarray or RNA-seq analysis, such as mRNA microarray, RNA-seq, use fold change > 2 and P-value <0.05 as the threshold of differential expression or differential change? How does it come? Will be acceptable without multiple-test correction?
These are first pass minimal rules of thumb to evaluate a data set. The actual criteria applied would likely be data set dependent. Without multiple test correction it would be hard to publish this as a primary result, but if you used this criteria to select genes of interest and that led you down a path for follow-up experiments, then this result is not the center piece and you can get away with a maximal un-adjusted p-value. But again, this is usually and example of the least stringent criteria. If you can adjust the p-values (and still see significance), then you should. Likewise, some data sets will have significant genes by p-value yet smaller fold-change values (i.e. 1.4 fold). The criteria you chose are typically a function of how the results will be further evaluated, and how stringent you can be without losing everything. If you adjust the p-values and all significance goes away - it doesn't necessarily mean your experiment failed (but it might), but it does suggest you will have lots of false positives. In the other direction, if you adjust p-values and apply increased stringency (e.g. adj. palue < 0.0001 and FC > 1.5), and you still end up 3000 genes, when your downstream experiments can only deal with 100 genes - then you would increase your stringency even more. In summary - the choices you make depend on the characteristics of the data set. The criteria you listed are simply a very minimal stringency.