  When choosing estimands and estimators in randomized clinical trials, caution
is warranted as intercurrent events, such as - due to patients who switch
treatment after disease progression, are often extreme. Statistical analyses
may then easily lure one into making large implicit extrapolations, which often
go unnoticed. We will illustrate this problem of implicit extrapolations using
a real oncology case study, with a right-censored time-to-event endpoint, in
which patients can cross over from the control to the experimental treatment
after disease progression, for ethical reasons. We resolve this by developing
an estimator for the survival risk ratio contrasting the survival probabilities
at each time t if all patients would take experimental treatment with the
survival probabilities at those times t if all patients would take control
treatment up to time t, using randomization as an instrumental variable to
avoid reliance on no unmeasured confounders assumptions. This doubly robust
estimator can handle time-varying treatment switches and right-censored
survival times. Insight into the rationale behind the estimator is provided and
the approach is demonstrated by re-analyzing the oncology trial.
