I'm working with a problem where I have a progressive type I censoring. A batch of rats is censored after 7 days and another batch is censored after 14 days (the study ends after 14 days). The event is taking a rat out of the study due to a given level of weight loss. I want to model the participation times in the study (for these rats) with some acute biomarkers as regressors. I'm thinking of doing a Cox regression model. But I'm not sure if the standard Cox model is appropriate for a progressive type I censoring. Does the informative censoring (I know at the beginning of the study which rats to be censored after day 7) make any difference? How to model participation times appropriately?