  One of the most common ways researchers compare survival outcomes across
treatments when confounding is present is using Cox regression. This model is
limited by its underlying assumption of proportional hazards; in some cases,
substantial violations may occur. Here we present and compare approaches which
attempt to address this issue, including Cox models with time-varying hazard
ratios; parametric accelerated failure time models; Kaplan-Meier curves; and
pseudo-observations. To adjust for differences between treatment groups, we use
Inverse Probability of Treatment Weighting based on the propensity score. We
examine clinically meaningful outcome measures that can be computed and
directly compared across each method, namely, survival probability at time T,
median survival, and restricted mean survival. We conduct simulation studies
under a range of scenarios, and determine the biases, coverages, and standard
errors of the Average Treatment Effects for each method. We then apply these
approaches to two published observational studies of survival after cancer
treatment. The first examines chemotherapy in sarcoma, where survival is very
similar initially, but after two years the chemotherapy group shows a benefit.
The other study is a comparison of surgical techniques for kidney cancer, where
survival differences are attenuated over time.
