I have taken the survival analysis class a few years ago, and we have learned both Kaplan-Meier estiamtes for survival curves, and the log-rank test for inferencing the difference of hazard rate between 2 groups.
That being said, I can use software (such as proc lifetest in SAS or survival package in R) to do KM estimates or log-rank test seaprately.
My question is though, what is the theoretical link between these 2? Is there any connection in between? e.g., is the test statsitic of (stratified) log-rank test based on the KM-estimate?
The reason I am asking is because, recently I see in a document (for confidential purpose I could not mention from where), that a stratified log-rank test is based on KM method, but I do not understand why, as the document did not give any further detail exept referring to the literature by Kaplan and Meier back in 1958 (Nonparametric estimation from incomplete observations).
I checked the referred literature (KM 1958) but it only layed out the deriation of KM estimates, without mentioning anything about log-rank test.
Could someone help?