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12 - Proportional Hazards Regression

Published online by Cambridge University Press:  05 June 2012

Daniel Zelterman
Affiliation:
Yale University, Connecticut
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Summary

Much of the language of survival analysis dates back to the 1600s with the early Dutch traders. Ships would leave Europe on a long and dangerous journey to India and China. When they returned with spices and silk, they brought great wealth and fortune to sailors who risked their lives and bankers who invested in the ship and its crew. Along the way there were storms, pirates, even sea monsters to contend with. Sometimes traders failed to return and were never heard from again, leaving behind widows and orphans, and financial ruin for their backers. The need to spread the risks involved in these journeys gave rise to an insurance industry.

Survival analysis uses a lot of the language of life insurance. If we think of life insurance as a bet, then we also need to think of the company that is taking the other side of this bet. Actuaries are special types of statisticians who assess these risks and then set the rates for the insurance company. If an actuary overestimates the risk, the company will charge high rates and will lose customers to their competitors. If the actuary underestimates the risks, the company risks financial disaster. Many of the terms used in this chapter will be familiar to actuaries and were originally developed by them. The hazard function is a natural way to describe the risk. It leads us to a popular and effective regression method for modeling survival data.

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Publisher: Cambridge University Press
Print publication year: 2010

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