Survival Analysis: A Primer

In this article, I will discuss life tables and Kaplan–Meier estimators, which are similar to life tables. Then I turn to proportional-hazards models, aka “Cox models.” Along the way, I will look at the efficacy of screening for lung cancer, the impact of negative religious feelings on survival, and the efficacy of hormone replacement therapy. What conclusions should be drawn about statistical practice? Proportional-hazards models are frequently used to analyze data from randomized controlled trials. This is a mistake. Randomization does not justify the models, which are rarely informative. Simpler analytic methods should be used first. With observational studies, the models would help us disentangle causal relations if the assumptions behind the models could be justified. Justifying those assumptions, however, is fraught with difficulty.