How do I calculate correlation rate and kappa statistic between two (ordinal) categorical variables in R?

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How do I calculate correlation rate and kappa statistic between two (ordinal) categorical variables (clinical stage and pathologic stage) as in the table in the provided article? https://link.springer.com/article/10.1007/s11605-018-3777-y

Table of correlation rate

This is what I did in R and got results but I am not sure if it is correct:

library(polycor)
library(irr)

polychor(my_dataset$clinical_T, my_dataset$pathologic_T)  # calculating overall correlation between clinical stage and pathologic stage

Tstage <- cbind(my_dataset$clinical_T, my_dataset$pathologic_T) 
kappa2(Tstage) # calculating cohen's kappa
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