Hazard ratios from proportional hazards models are hard for clinicians to interpret, while accelerated failure time models require distributional assumptions. Quantile regression (QR) survival models give easily interpreted results without distributional assumptions. However, to our knowledge, there is no QR model that handles arbitrary censoring and/or truncation. We introduce a QR model that does. Regression coefficients are estimated by maximizing a non-parametric approximation to the likelihood. Simulation results were good for right-skewed right censored data, a common case in survival analysis. Results were also good for interval censored data with 100% censoring, allowing estimation of the median when a continuous variable has been categorized into bins and the original continuous data are not available. Our method is flexible because it assumes no distribution and handles complex censoring and truncation. More importantly, it has the potential to replace hazard ratios with differences and rates of change in clinically-relevant units that are easily interpreted by clinicians. Arming clinicians with such results will lead to better patient care and advances in medicine.