Event History Regression with Pseudo-Observations: Computational Approaches and an Implementation in R

Abstract

Due to tradition and ease of estimation, the vast majority of clinical and epidemiological papers with time-to-event data report hazard ratios from Cox proportional hazards regression models. Although hazard ratios are well known, they can be difficult to interpret, particularly as causal contrasts, in many settings. Nonparametric or fully parametric estimators allow for the direct estimation of more easily causally interpretable estimands such as the cumulative incidence and restricted mean survival. However, modeling these quantities as functions of covariates is limited to a few categorical covariates with nonparametric estimators, and often requires simulation or numeric integration with parametric estimators. Combining pseudo-observations based on non-parametric estimands with parametric regression on the pseudo-observations allows for the best of these two approaches and has many nice properties. In this paper, we develop a user friendly, easy to understand way of doing event history regression for the cumulative incidence and the restricted mean survival, using the pseudo-observation framework for estimation. The interface uses the well known formulation of a generalized linear model and allows for features including plotting of residuals, the use of sampling weights, and correct variance estimation.