  Epidemiologic studies and clinical trials with a survival outcome are often
challenged by immortal time (IMT), a period of follow-up during which the
survival outcome cannot occur because of the observed later treatment
initiation. It has been well recognized that failing to properly accommodate
IMT leads to biased estimation and misleading inference. Accordingly, a series
of statistical methods have been developed, from the simplest by including or
excluding IMT to various weightings and the more recent sequential methods. Our
literature review suggests that the existing developments are often
"scattered", and there is a lack of comprehensive review and direct comparison.
To fill this knowledge gap and better introduce this important topic especially
to biomedical researchers, we provide this review to comprehensively describe
the available methods, discuss their advantages and disadvantages, and equally
important, directly compare their performance via simulation and the analysis
of the Stanford heart transplant data. The key observation is that the
time-varying treatment modeling and sequential trial methods tend to provide
unbiased estimation, while the other methods may result in substantial bias. We
also provide an in-depth discussion on the interconnections with causal
inference.
