Survival Analysis

Abstract

There are many situations in law that require estimation of the time to failure, e.g., how long someone will live or something will last. The event of failure may be anything—death, filing a claim after exposure to a carcinogen, peeling of defective paint on house sidings, or termination of an at-will relationship. If there are comparable populations in which all or almost all members have already failed, the probabilities of survivorship and death at various ages can be estimated directly from data and presented in the form of a life table. The classical life table tracks an initial cohort of people year by year from birth, showing in each year how many people die and how many survive, until the entire cohort has died. If there are no comparable populations with complete survival data, the problem of estimation is more difficult. The average life of those who have already failed would seriously underestimate the average life of those still surviving. An estimate of the likelihood of early failure is still possible; but at later times, to take account of the fact that many in the population have not yet failed, one must assume that the force of mortality has a certain mathematical form or model as a function of time and estimate the model’s parameters from the data. The future rate of mortality is then extrapolated from the model.