Proc freq data = filtered_data;
tables K * X * Y / cmh;
* the order of K, X, and Y appearing on the line is important!;
run; CMH Test
Cochran-Mantel-Haenszel Test
The CMH procedure tests for conditional independence in partial contingency tables for a 2 x 2 x K design. However, it can be generalized to tables of X x Y x K dimensions.
CMH in SAS
The cmh test is calculated in SAS using the PROC FREQ procedure. By default, it outputs the chi square statistic, degrees of freedom and p-value for each of the three alternative hypothesis: general association, row means differ, and nonzero correlation. It is up to the statistical analyst or statistician to know which result is appropriate for their analysis.
When the design of the contingency table is 2 x 2 x K (i.e, X == 2 levels, Y == 2 levels, K >= 2 levels), the Mantel-Haenszel Common Odds Ratio (odds ratio estimate, 95% CI, P-value) and the Breslow-Day Test for Homogeneity of the Odds Ratios (chi-square statistic, degrees of freedom, P-value) are also output.
Below is the syntax to conduct a CMH analysis in SAS:
References
SAS documentation (Specification): https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.3/statug/statug_freq_examples07.htm
SAS documentation (Theoretical Basis + Formulas): https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/procstat/procstat_freq_details92.htm