Peter Austin and Jason Fine (of Fine & Gray fame) have just published a nice review article in Statistics in Medicine on handling competing risks in randomized trials. They reviewed RCTs published in four top medical journals in the last three months of 2015. Of the 40 trials found with time to event outcomes, Austin & Gray determined that 31 were potentially susceptible to competing risks.
Yesterday the Advanced Analytics Centre at AstraZeneca publicly released the InformativeCensoring package for R, on GitHub. Standard survival or time to event analysis methods assume that censoring is uninformative - that is that the hazard of failure in those subjects at risk at a given time and who have not yet failed or been censored, is the same as the hazard at that time in those who have been censored (with regression modelling, this assumption is somewhat relaxed).
I recently attended a great course by Odd Aalen, Ornulf Borgan, and Hakon Gjessing, based on their book Survival and Event History Analysis: a process point of view. Among the many interesting topics covered was the issue of how to interpret changes in estimated hazard functions, and similarly, changes in hazard ratios comparing two groups of subjects.