Nygård Johansen, M, Lundbye‐Christensen, S, Thorlund Parner, E. Regression models using parametric pseudo‐observations. Statistics in Medicine. 2020; 1– 13. https://doi.org/10.1002/sim.8586

Regression models for time-to-event data in the medical literature has predominantly been based on either parametric models or the semi-parametric Cox proportional hazards model. A completely different approach has been developed within the past 20 years using a transformation of the censored dataset and applying a generalized linear model to estimate association measures. The transformed data is known as pseudo-observations and the transformation is most commonly based on a non-parametric estimator of the cumulative incidence function; typically, the Kaplan-Meier estimator for survival data or the Aalen-Johansen estimator in the presence of competing risks.
In this article, a different approach to calculating pseudo-observations is proposed by using the idea behind the flexible parametric model for time-to-event data, where the baseline log cumulative hazard function is modeled by a spline function. This gives rise to an approach, which is fully parametric yet does not impose any distributional assumptions on the underlying time-to-event data. The parametric pseudo-observations obtained can be used in regression models to estimate absolute and relative association measures.
The article presents the results of an extensive simulation study to assess the properties of the proposed approach compared to those of the traditional pseudo-observation method. The simulations show that the proposed method can reduce the uncertainty of the final regression estimates substantially in some situations. The method is also illustrated in practice on a publicly available dataset.