Regression models using parametric pseudo‐observations

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.