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Case-only analysis

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 chi-square- -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.

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