A note on pseudo-observations and left-truncation

Pseudo-observations have been introduced as a way to perform regression analysis of a mean value parameter related to a right-censored time-to-event outcome, such as the survival probability or the restricted mean survival time. Since the introduction of the approach there have been several extensions from the original setting. However, the proper definition and performance of pseudo-observations under left-truncation has not yet been addressed. Here, we look at two types of pseudo-observations under right-censoring and left-truncation. We explored their performance in a simulation study and applied them to data on diabetes patients with left-truncation.