I am familiar with the use of tag-SNPs in genome-wide association studies to identify gene loci involved in complex traits, but I keep seeing the term "conditional analysis" used without any explanation. Is it some sort of mathematical manipulation in which the significance of a tag-SNP is reduced to zero, to see if other SNPs are directly associated to the phenotype in question?
In GWA studies you tend to analyze your "lead" SNPs in regions where genotypes are correlated (known as linkage disequilibrium).
If you find an association between another SNP with the outcome, and this SNP is correlated with the original variant, you can perform a conditional analysis where you adjust for the original SNP in the model. This is to test if the association between the 2nd SNP is independent of the first, or whether it is just because they are correlated (in LD).
So performing a conditional analysis is just seeing if the association observed is an independent signal.
At least, this is how I have interpreted it perviously!
E.g. SNP-A is found to be associated with increased risk of type-2 diabetes (T2D).
SNP-B is later found to be associated with risk of T2D as well.
SNP-A and SNP-B are correlated.
To see if the association between SNP-B and T2D is independent of the first association, you would adjust for SNP-B in the model (a conditional analysis).
If the association between SNP-A (and/or SNP-B) and T2D is still significant then they have some independent effect on risk of T2D. If the association disappears then they are only both associated because they are correlated in the individuals.