ABSTRACT
Collecting time-to-death data involves more work than recording survival to a fixed endpoint, but significant statistical benefits accrue from the small amount of additional work. In typical regression and analysis of variance applications, the error distribution is assumed to be a normal distribution. However, a normal distribution is inappropriate for most time-to-death data because they are not symmetrical around the mean. A statistical model for times-to-death specifies how various covariates influence the median time-to-death, but it does not specify the magnitude of the influence. The proportional hazards model describes the effect of a particular treatment by its influence on the hazard, the probability that a surviving individual will die during a small interval of time. The analysis of exponentially distributed data is relatively simple, and much early analysis of failure-time data was based on the exponential distribution, but the assumption of a constant hazard function is appropriate for very few biological systems.
