Abstract
Treatment switching is common in randomized trials of oncology treatments. For example, control group patients may receive the experimental treatment as a subsequent therapy. One possible estimand is the effect of trial treatment if this type of switching had instead not occurred. Two-stage estimation is an established approach for estimating this estimand. We argue that other estimands of interest instead describe the effect of trial treatments if the proportion of patients who switched was different. We give precise definitions of such estimands. By motivating estimands using real-world data, decision-making in universal health care systems is facilitated. Focusing on estimation, we show that an alternative choice of secondary baseline, the time of first subsequent treatment, is easily defined, and widely applicable, and makes alternative estimands amenable to two-stage estimation. We develop methodology using propensity scores, to adjust for confounding at a secondary baseline, and a new quantile matching technique that can be used to implement any parametric form of the post-secondary baseline survival model. Our methodology was motivated by a recent immuno-oncology trial where a substantial proportion of control group patients subsequently received a form of immunotherapy.