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A common concern in non-inferiority (NI) trials is that non adherence due, for example, to poor study conduct can make treatment arms artificially similar. Because intention to treat analyses can be anti-conservative in this situation, per protocol analyses are sometimes recommended. However, such advice does not consider the estimands framework, nor the risk of bias from per protocol analyses. We therefore sought to update the above guidance using the estimands framework, and compare estimators to improve on the performance of per protocol analyses. We argue the main threat to validity of NI trials is the occurrence of trial specific intercurrent events (IEs), that is, IEs which occur in a trial setting, but would not occur in practice. To guard against erroneous conclusions of non inferiority, we suggest an estimand using a hypothetical strategy for trial specific IEs should be employed, with handling of other non trial specific IEs chosen based on clinical considerations. We provide an overview of estimators that could be used to estimate a hypothetical estimand, including inverse probability weighting (IPW), and two instrumental variable approaches (one using an informative Bayesian prior on the effect of standard treatment, and one using a treatment by covariate interaction as an instrument). We compare them, using simulation in the setting of all or nothing compliance in two active treatment arms, and conclude both IPW and the instrumental variable method using a Bayesian prior are potentially useful approaches, with the choice between them depending on which assumptions are most plausible for a given trial.