# 4 Joint Effects

For full details of the joints effects test and the accompanying notation please refer to the manuscript by Ueki and Cordell (2012).

## 4.1 Options

The options that are specific to the joint effects test are:

Option Description
-je perform the joint effects test
-je-thcc t p-value threshold for case/control test
-je-thco t p-value threshold for case only test
-je-th t p-value threshold for either test
-je-cc-only perform the case/control test only
-je-co-only perform the case only test only
-je-cellmin m minimum cell count required in each cell to perform test
-je-so suppress results of test

CASSI performs both the case only test and case/control test for each pair of tested SNPs by default. The results of the test are recorded for the pair of SNPs if either p-value threshold is met. Both thresholds may be set simultaneously by using the -je-th option. The default value for both thresholds is 0.0001.

To avoid issues with insufficient data, a minimum number cell count is required (where cells are given by the genotype combinations, 9 for cases and 9 for controls). The default number is set to 5, but can be changed with the -je-mincell option. Setting the cell count minimum to 0 obviously gives no minimum. If there is no cell minimum and any cells are 0 then all any cells will have 0.5 added.

For other basic options see section 3.2.

## 4.2 Output File

The output file from running a joint effects SNP interaction analysis using CASSI will look something like the following:

SNP1 CHR1 ID1 BP1 SNP2 CHR2 ID2 BP2 JE_CASE_LOG_OR JE_CASE_SE JE_CTRL_LOG_OR JE_CTRL_SE JE_CC_CHISQ JE_CC_P JE_ALT_CC JE_CO_CHISQ JE_CO_P JE_ALT_CO
4 1 rs5367015 220368 558 1 rs7129551 4544990 6.34341 0.632507 3.65647 0.597288 2.00984 0.156282 N 16.0982 6.01412e-05 N
5 1 rs12363280 221980 506 1 rs1102289 4422547 4.1916 1.04833 4.15869 1.04265 0.00334286 0.953894 N 19.3086 1.11203e-05 N
5 1 rs12363280 221980 512 1 rs1083109 4447884 5.17158 0.820119 4.93334 0.742762 0.467668 0.494062 N 17.9887 2.22222e-05 N
5 1 rs12363280 221980 526 1 rs1500597 4483159 4.1916 1.04833 4.15869 1.04265 0.00334286 0.953894 N 19.3086 1.11203e-05 N
5 1 rs12363280 221980 551 1 rs1103294 4534498 4.63789 0.970636 4.36155 0.95259 0.0916524 0.762087 N 20.2653 6.74113e-06 N
...


The first line is a header labelling the columns of the results file. The SNP details for the pair of SNPs are given firstly followed by values calculated from the joint effects tests. Results are given for both the case only test and for the case/control test regardless of which p-value was significant enough to record the pair of SNPs. The case only test assumes that the two SNPs are in linkage equilibrium in the general population, so care must be taken in interpreting results with SNPs that are near one another. Therefore, SNPs that are too close, as definded by the -gap option, are not tested. See Ueki and Cordell (2012).

JE_CASE_LOG_OR is the log odds ratio for association in the cases and is given by $\inline \tilde{\lambda}_A \small$. If the alternative test is used this is given by $\inline \tilde{\mu}_A \small$.

JE_CASE_SE is the standard error of $\inline \tilde{\lambda}_A \small$ and is given by the square root of $\inline \tilde{\nu}_A \small$. If the alternative test is used the standard error for $\inline \tilde{\mu}_A \small$ is recorded, given by the square root of $\inline \tilde{\nu}_{\mu_A} \small$.

JE_CTRL_LOG_OR is the log odds ratio for association in the controls and is given by $\inline \tilde{\lambda}_N \small$. If the alternative test is used this is given by $\inline \tilde{\mu}_N \small$.

JE_CTRL_SE is the standard error of $\inline \tilde{\lambda}_N \small$ and is given by the square root of $\inline \tilde{\nu}_N \small$. If the alternative test is used the standard error for $\inline \tilde{\mu}_N \small$ is recorded, given by the square root of $\inline \tilde{\nu}_{\mu_N} \small$.

JE_CC_CHISQ is the $\inline \chi^2 \small$ test statistic with one degree of freedom for the case/control test.

JE_CC_P is the corresponding p-value for the case/control test.

JE_CC_ALT whether or not the alternative statistic was used for the case/control test.

JE_CO_CHISQ is the $\inline \chi^2 \small$ test statistic with one degree of freedom for the case only test.

JE_CO_P is the corresponding p-value for the case only test.

JE_CO_ALT whether or not the alternative statistic was used for the case only test.