  This paper provides guidance for researchers with some mathematical
background on the conduct of time-to-event analysis in observational studies
based on intensity (hazard) models. Discussions of basic concepts like time
axis, event definition and censoring are given. Hazard models are introduced,
with special emphasis on the Cox proportional hazards regression model. We
provide check lists that may be useful both when fitting the model and
assessing its goodness of fit and when interpreting the results. Special
attention is paid to how to avoid problems with immortal time bias by
introducing time-dependent covariates. We discuss prediction based on hazard
models and difficulties when attempting to draw proper causal conclusions from
such models. Finally, we present a series of examples where the methods and
check lists are exemplified. Computational details and implementation using the
freely available R software are documented in Supplementary Material. The paper
was prepared as part of the STRATOS initiative.
