The rank-ordered logit (rologit) model was recently introduced as a robust approach for analysing continuous outcomes, with the linear exposure effect estimated by scaling the rank-based log-odds estimate. Here we extend the application of the rologit model to continuous outcomes with ties and ordinal outcomes treated as imperfectly-observed continuous outcomes. By identifying the functional relationship between survival times and continuous outcomes, we explicitly establish the equivalence between the rologit and Cox models to justify the use of the Breslow, Efron and perturbation methods in the analysis of continuous outcomes with ties. Using simulation, we found all three methods perform well with few ties. Although an increasing extent of ties increased the bias of the log-odds and linear effect estimates and resulted in reduced power, which was somewhat worse when the model was mis-specified, the perturbation method maintained a type I error around 5%, while the Efron method became conservative with heavy ties but outperformed Breslow. In general, the perturbation method had the highest power, followed by the Efron and then the Breslow method. We applied our approach to three real-life datasets, demonstrating a seamless analytical workflow that uses stratification for confounder adjustment in studies of continuous and ordinal outcomes.