Three-way Table

shhs = array(c(52, 29, 898, 678, 33, 48, 923, 1722), dim=c(2,2,2))
dimnames(shhs) = list(Residence = c("Rented", "Owner"),
                      CHD = c("Yes", "No"),
                      Smoker = c("Yes", "No"))
shhs

## , , Smoker = Yes
## 
##          CHD
## Residence Yes  No
##    Rented  52 898
##    Owner   29 678
## 
## , , Smoker = No
## 
##          CHD
## Residence Yes   No
##    Rented  33  923
##    Owner   48 1722

mantelhaen.test(shhs, correct=FALSE)

## 
##  Mantel-Haenszel chi-squared test without continuity correction
## 
## data:  shhs
## Mantel-Haenszel X-squared = 2.8049, df = 1, p-value = 0.09398
## alternative hypothesis: true common odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.9537528 1.8203312
## sample estimates:
## common odds ratio 
##          1.317629

From the note of R documents for mantelhaen.test():

“The asymptotic distribution is only valid if there is no three-way interaction. In the classical 2 by 2 by K case, this is equivalent to the conditional odds ratios in each stratum being identical. Currently, no inference on homogeneity of the odds ratios is performed.”