In a couple hours of searching, I wasn't able to find an adequate answer for this. We have a method that uses independent sets at each time point for a survival-type analysis (because the process of observation is destructive). While we've been able to show that our method (by curve fitting) is appropriate, I am having some trouble formulating precisely why Kaplan-Meier and the associated Log-Rank test are inappropriate for that scenario. Intuitively it makes sense since Kaplan-Meier is intended to follow individuals in a repeated-measures study over time. To appropriately model our case would involve censoring every single data point- most would end up being both right and left censored- which seems like might violate the assumption of non-informative censoring since censoring can't be random when 100% of individuals are censored.
Can anyone help formulate a succinct and convincing basis for rejecting utilization of Kaplan-Meier for such an application?