Adjusting for observational secondary treatments in estimating the effects of randomized treatments

In randomized clinical trials, for example, on cancer patients, it is not uncommon that patients may voluntarily initiate a secondary treatment postrandomization, which needs to be properly adjusted for in estimating the 'true' effects of randomized treatments.As an alternative to the approach based on a marginal structural Cox model (MSCM) in Zhang and Wang [(2012).Estimating treatment effects from a randomized trial in the presence of a secondary treatment. Biostatistics13, 625.636], we propose methods that treat the time to start a secondary treatment as a dependent censoring process, which is handled separately from the usual censoring such as the loss to follow-up.Two estimators are proposed, both based on the idea of inversely weighting by the probability of having not started a secondary treatment yet.The second estimator focuses on improving efficiency of inference by a robust covariate-adjustment that does not require any additional assumptions.The proposed methods are evaluated and compared with the MSCM-based method in terms of bias and variance tradeoff using simulations and application to a cancer clinical trial.