I just ran a Cox model with some covariates interacted with survival time to account for violations of the PH assumption. To do that, I needed to create a multi-episode dataset with an observation for each survival time unit per individual in the data (acutally Stata does it automatically when using the tvc() option in stcox).
So, although the number of individuals does not change, the number of observations is kind of inflated and Allison (1982) suggested that treating multiple observations of the same individual as independent might be inappropriate.
I thought I might account for that by using clustered standard errors at the person level. However, it turned out that these SEs are identical to the White standard errors, such that clustering seems to be completely irrelevant. Why is that the case in a Cox model used on multi-episode data?
P.S.: I should add that Allison (1982) described the problem for discrete time PH models, like e.g. the Prentice-Gloeckler-Model with the cloglog link (see Prentice and Gloeckler, 1978). When using clustered SEs with the cloglog model (which also requires the multi-episode dataset), I found that they were close to the White standard errors but not identical. That's why I wondered whether there is something fundamentally different going on in the multi-episode Cox model?