Hazard functions, or hazards, are fundamental to survival analysis and clinical trial research. They are related to the mortality curves used by actuaries. A person's mortality curve at age t years is the probability of dying in the next year, given that the person has reached t years of age. Hazards take a limit as the future time period approaches zero: the hazard at time t is the probability of `death' or `failure' in the next instant.

Human life hazards generally have a bathtub shape: vulnerability is higher after birth. Humans who survive the first year of life have decreased hazard. The hazard then rises during the middle-age years.

An interesting non-health example of hazard arises in the sport of cricket - where `time' is the score of the cricketer. If several recorded innings on a particular cricketer are available then his or her hazard can be estimated. Innings that are incomplete due to rain or lack of partners, known as `not out' scores, correspond to being `censored from the right' in survival analysis jargon.

This figure is the estimated hazard of S.R. (Steve) Waugh - a former captain of the Australian men's team who holds the record for the most international matches, or `tests'. The following aspects of S.R. Waugh's batting are apparent from the estimated hazard:

Reference: Cai, T., Hyndman, R.J. and Wand, M.P. (2002). Mixed model-based hazard estimation. Journal of Computational and Graphical Statistics, 11, 784-798.

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