# 7 Wellek Ziegler

The Wellek Ziegler test, as defined by Ueki and Cordell (2012), is based on the Pearson product-moment correlation coefficient, r, and is inspired by tests proposed by Wellek and Ziegler (2009).

## 7.1 Options

The options that are specific to the Wellek Ziegler test are:

Option Description
-wz perform the Wellek Ziegler test
-wz-thcc t p-value threshold for case/control test
-wz-thco t p-value threshold for case only test
-wz-th t p-value threshold for either test
-wz-cc-only perform the case/control test only
-wz-co-only perform the case only test only
-wz-so suppress results of test

CASSI performs both the case only test and case/control test for each pair of tested SNPs by default. SNPs that are too close for the case only test, as definded by the -gap option, are not tested. 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 -wz-th option. The default value for both thresholds is 0.0001.

For other basic options see section 3.2.

## 7.2 Output File

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

SNP1 CHR1 ID1 BP1 SNP2 CHR2 ID2 BP2 WZ_CASE_R WZ_CASE_VAR WZ_CTRL_R WZ_CTRL_VAR WZ_CC_CHISQ WZ_CC_P WZ_CO_CHISQ WZ_CO_P
117 0 rs1076866 1588987 934 0 rs4547126 5543590 -0.102088 0.00080134 0.0818521 0.0011718 17.1473 3.45901e-05 13.0057 0.000310544
174 0 rs7343521 2112789 948 0 rs1083841 5601579 0.131803 0.00111305 0.0109372 0.0010405 6.78342 0.00920083 15.6074 7.79475e-05
174 0 rs7343521 2112789 949 0 rs1227893 5603609 0.138261 0.00112451 0.0221176 0.00105799 6.18069 0.0129152 16.9996 3.73873e-05
177 0 rs3741208 2126350 918 0 rs7934354 5522482 -0.121458 0.000872938 0.0162084 0.00101684 10.0287 0.00154121 16.8992 3.94175e-05
198 0 rs1228842 2352598 899 0 rs1727848 5490415 -0.0628705 0.000910977 0.117571 0.00102275 16.8375 4.07198e-05 4.33896 0.0372496
...


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 Wellek Ziegler 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. See Ueki and Cordell (2012).

WZ_CASE_R is the Pearson product-moment correlation coefficient for association in the cases.

WZ_CASE_VAR is the variance of WZ_CASE_R.

WZ_CTRL_R is the Pearson product-moment correlation coefficient for association in the controls.

WZ_CTRL_VAR is the variance of WZ_CTRL_R.

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

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

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

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