Pseudo-observations based on the nonparametric Kaplan-Meier estimator of the survival function have been proposed as an alternative to the widely used Cox model for analyzing censored time-to-event data. Using a spline-based estimator of the survival has some potential benefits over the nonparametric approach in terms of less variability. We propose to define pseudo-observations based on a flexible parametric estimator and use these for analysis in regression models to estimate parameters related to the cumulative risk. We report the results of a simulation study that compares the empirical standard errors of estimates based on parametric and nonparametric pseudo-observations in various settings. Our simulations show that in some situations there is a substantial gain in terms of reduced variability using the proposed parametric pseudo-observations compared with the nonparametric pseudo-observations. The gain can be measured as a reduction of the empirical standard error by up to about one third; corresponding to an additional 125% larger sample size. We illustrate the use of the proposed method in a brief data example.