Causal inference for long-term survival in randomised trials with treatment switching: Should re-censoring be applied when estimating counterfactual survival times?

Treatment switching often has a crucial impact on estimates of effectiveness and cost-effectiveness of new oncology treatments. Rank preserving structural failure time models (RPSFTM) and two-stage estimation (TSE) methods estimate ‘counterfactual’ (i.e. had there been no switching) survival times and incorporate re-censoring to guard against informative censoring in the counterfactual dataset. However, re-censoring causes a loss of longer term survival information which is problematic when estimates of long-term survival effects are required, as is often the case for health technology assessment decision making. We present a simulation study designed to investigate applications of the RPSFTM and TSE with and without re-censoring, to determine whether re-censoring should always be recommended within adjustment analyses. We investigate a context where switching is from the control group onto the experimental treatment in scenarios with varying switch proportions, treatment effect sizes, treatment effect changes over time, survival function shapes, disease severity and switcher prognosis. Methods were assessed according to their estimation of control group restricted mean survival that would be observed in the absence of switching, up to the end of trial follow-up. We found that analyses which re-censored usually produced negative bias (i.e. under-estimating control group restricted mean survival and over-estimating the treatment effect), whereas analyses that did not re-censor consistently produced positive bias which was often smaller in magnitude than the bias associated with re-censored analyses, particularly when the treatment effect was high and the switching proportion was low. The RPSFTM with re-censoring generally resulted in increased bias compared to the other methods. We believe that analyses should be conducted with and without re-censoring, as this may provide decision-makers with useful information on where the true treatment effect is likely to lie. Incorporating re-censoring should not always represent the default approach when the objective is to estimate long-term survival times and treatment effects.