In Phase II oncology trials, which have progression-free survival as an end point, it is common for some patients to receive alternative treatments before progression. For example, the reason may be that the investigator considers that there has been tumor progression, and a second line of treatment is initiated, but progressive disease is not confirmed in the centralized radiological assessment. Since this type of censoring would be informative, but usually occurs in few cases, which is the most correct management. Perhaps censoring and performing competing risk sensitivity analyses?
I’m surprised you considered censoring here. The trials are usually intent-to-treat designs and you ignore concomitant treatments. The overall inference is for the time-zero treatment policy. In an extreme case, if an initial treatment were to have the magical power of making progressions easier to spot and to treat, the initial treatment should be given credit for this. Of course when the protocol is written one tries to limit the use of concomitant therapies when ethical.
Ok. But what about an observational study in which you wish to estimate the true PFS associated to a specific therapy, if doctors switch a number of patients to a second drug before progression?
Could one code the switch as a treatment effect? Probably an additional categorical variable and exploit covariance between similar groups with a hierarchical model.
If we think it’s difficult in a randomized trial, it’s far more difficult when nothing was randomized.
As already discussed, you first need to clarify which effect you’d like to estimate, i.e. to define the estimand. If it should be treatment policy then it is easy. If it should be hypothetical (“effect if patients had not taken alternative therapy”) then just censor makes very strong and unrealistic implicit assumptions. Methods from the treatment switching and epi literature can be a starting point here, see e.g. this paper.