In randomised controlled trials, the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it. We compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model, and quantify the bias due to omitting baseline prognostic factors. Causal estimates are found directly by maximising a novel partial likelihood; based on a structural proportional hazards model; and based on a "corrected dataset" derived after fitting a rank preserving structural failure time model. Where necessary, we extend these methods to incorporate baseline covariates. Comparisons use simulated data and a real data example. Analysing the simulated data, all three methods were found to be accurate when an important covariate was included in the proportional hazards model (maximum bias 5.4%). However, failure to adjust for this prognostic factor meant that causal treatment effects were underestimated (maximum bias 11.4%) because estimators were based on a misspecified marginal proportional hazards model. Analysing the real data example, adjusting causal estimators was found to be important to correct for residual imbalances in prognostic factors present between trial arms after randomisation. Our results show that methods of estimating causal treatment effects for time to event outcomes should be extended to incorporate covariates, so providing an informative compliment to the corresponding intention-to-treat analysis.