Case-only (or case-series, case-control without controls) design is
based on a sample consisting of cases only. It is an efficient approach
to test for gene-environment or gene-gene interaction in disease
etiology, when there is a strong reason to believe that particular
assumptions are fulfilled.
Concerning a test for gene-environment interaction it is necessary to
assume that the genetic type and the exposure occur independently in
the population. A test for gene-gene interaction is reasonable to
perform assuming that the frequencies of genetic variants are
independent in the population or, equivalently, that the genes/SNPs under study are in linkage equilibrium.
Here, we accept that the genetic interaction between two genetic
factors (e.g. genes, SNPs, alleles) is present if the joint effect of
two factors on a disease differs from the additive combination of
independent effects from both of them. The joint effect of two genetic
factors is the effect due to the presence of both of them. The
independent effect of one of the factors is its effect on a disease in
the absence of the other factor. Sometimes the term "epistasis" is used
instead of genetic interaction in the literature. The same definition
is valid for the gene-environment interaction, where one of the genetic
factors is replaced by the exposure. From now on only the gene-gene
interaction is addressed.
If the data satisfy the assumptions discussed above, then the so called
case-only test for genetic interaction can be performed by using a
-test of independence between genotypes (with four degrees of freedom)
or between alleles (with one degree of freedom) as well as logistic
regression models. Notably, the case-only analysis leads sometimes to a
more valid estimation of interaction than the corresponding
case-control analysis, i.e. case-only based tests possess a higher
power, see e.g. (Cordell, 2009), (Gatto et al., 2004), (Piegorsch et
al., 1994), (Yang et al., 1999).
INTERSNP suggests several tests to check for the gene-gene interaction,
where the genetic factors are chosen to be a pair of SNPs (SNP-SNP
interaction). Starting from a pair of SNPs, the allelic interaction
test can be performed as well.
IMPORTANT: In our study it was observed that the LD distance between
two SNPs has to be at least 20 Mb (20000000 bp) in order to satisfy the
assumption of linkage equilibrium. The recommended LD distance is even
bigger and equals 50 Mb.