Proportional hazards models (also known as Cox models) are useful for modeling failure times or life events. They have applications in engineering, medicine, and social sciences, for example, modeling component failures, marriage, mortality, and relapse times.
The model assumes that an underlying hazard rate exists for all records which determines the probability of failure. The explanatory variables then affect the hazard rate proportionally. If records are stratified, a separate hazard rate is associated with each stratum. For example, records may be stratified by sex to assign a separate hazard rate to males and females.
The outcome is assumed to represent the amount of time elapsed before a failure. If a failure never occurs, the outcome is said to be censored. For example, if a survey asks about the subject’s age at first marriage, subjects who had never been married would be considered censored observations.
Proportional hazards models can accommodate multiple causes of failure. If multiple causes of failure are present, then a separate set of explanatory coefficients is estimated for each cause. For each cause of failure, all records with a different cause are assumed to be censored for purposes of the cause of interest. For example, deaths due to automobile accident would be treated as censored observations when estimating coefficients for deaths due to heart disease.