Survival analysis where covariates are unavailable for censored data I am looking at the time required by judges to reach decisions. Each judge assesses a number of applicants and can either approve or not approve the application. The case is finalized when the judge renders his report, which may be some time after the hearing. A number of cases were still open at the end of the study period.
I want to estimate the average time required for cases to move through the system. In addition, I would like to see if cases that are refused take longer than cases that are approved. (Judges seem to spend longer writing up the reports of those they eventually fail to approve, or  seek extra documentation).
Obviously, I don't know if the cases that were still open when the study ended would have been approved or not, so the covariate (approve/don't approve) is censored along with the data.
Is there anything I can do about this? 
 A: If I understand you, this is pretty standard survival analysis/event history analysis right-censoring stuff; Kaplan-Meyer, discrete-time hazard models etc. all estimate "whether and when" an event occurs while accounting for right-censoring of event occurrence (i.e your case case approval) by incorporating the shrinkage of the sample at risk of event over time due to both event occurrence and due to censoring.
The Wikipedia article gives a decent intro. And you might check out Singer, J. D. and Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press, New York, NY, which goes into detail on discrete-time event history models, and has a decent enough section on Cox proportional-hazards models.
A: @jsk has the key in their comment to @Alexis' answer. The appropriate type of survival analysis to use in this case is Competing Risks. You have three possible outcomes: a) accepted, b) rejected, and c) right-censored.
The key is that accepted/rejected is not a single covariate but rather are two competing risks. This is pretty easy in most statistical software. For example, in R's survival package, you simply code the event as a factor with levels censored, accepted, and rejected. (censored must be the first level, other levels are assumed to be competing risks.)
