Noncompliance often complicates estimation of treatment efficacy from randomized trials. Under random noncompliance, per protocol analyses or even simple regression adjustments for noncompliance, could be adequate for causal inference, but special methods are needed when noncompliance is related to risk. For survival data, Robins and Tsiatis introduced the semi-parametric structural Causal Accelerated Life Model (CALM) which allows time-dependent departures from randomized treatment in either arm and relates each observed event time to a potential event time that would have been observed if the control treatment had been given throughout the trial. Alternatively, Loeys and Goetghebeur developed a structural Proportional Hazards (C-Prophet) model for when there is all-or-nothing noncompliance in the treatment arm only. Whitebiet al. proposed a ‘complier average causal effect’ method for Proportional Hazards estimation which allows time-dependent departures from randomized treatment in the active arm. A time-invariant version of this estimator (CHARM) consists of a simple adjustment to the Intention-to-Treat hazard ratio estimate. We used simulation studies mimicking a randomized controlled trial of active treatment versus control with censored time-to-event data, and under both random and non-random time-dependent noncompliance, to evaluate performance of these methods in terms of 95 per cent confidence interval coverage, bias and root mean square errors (RMSE). All methods performed well in terms of bias, even the C-Prophet used after treating time-varying compliance as all-or-nothing. Coverage of the latter method, as implemented in Stata, was too low. The CALM method performed best in terms of bias and coverage but had the largest RMSE. Copyright © 2010 John Wiley & Sons, Ltd.