How are the chi-squared statistics from the SAS PROC CASECONTROL correlated?

SAS PROC CASECONTROL produces 3 flavors of chi-squared statistics. We suspect that the statistics are highly correlated. To get a handle on this question we construct populations and sample them 40 times at each of 19 different values of OR and 8 values of disease allele frequency for each of 3 kinds of models, "recessive", "dominant", and "additive". In each population, the penetrance for subjects homozygous with the non-disease allele is always 0.05

Histogram of all 6 off-diagonal elements in 19*8*3=456 cor matrices

Recessive model: Graphs of color coded correlations among data sets at each combination of minor allele frequency and OR, cor less than 0.6 implies red, cor=1 implies blue N=5,000, n=2,000, pen.0=0.05, no.sets=40

Dominant model: Graphs of color coded correlations among data sets at each combination of minor allele frequency and OR, cor less than 0.6 implies red, cor=1 implies blue N=5,000, n=2,000, pen.0=0.05, no.sets=40

Additive model: Graphs of color coded correlations among data sets at each combination of minor allele frequency and OR, cor less than 0.6 implies red, cor=1 implies blue N=5,000, n=2,000, pen.0=0.05, no.sets=40

Graphical diagnostics for the recessive models

Graphical diagnostics for the dominant models

Graphical diagnostics for the additive models

Possible next steps on this project.