PROPORTIONAL HAZARDS MODEL - A REVIEW

The proportional hazards model was introduced in 1972 by D. R. Cox in order to estimate the effects of different covariates influencing the times to the failures of a system. The model has been used rather extensively in biomedicine and, recently, interest in its application in reliability engineering has increased. The main purpose of this expository paper is to review the existing literature on the proportional hazards model. At first, the characteristics of the method are explained and its importance in reliability analysis is presented. Subsequently, methods for estimating parameters, along with the small and large sample properties of the estimators, are briefly discussed. Afterwards, work carried out so far on topics such as the effects of interaction, omission, measurement error, misclassification, monotonicity, multicolinearity and time dependency of covariates on the estimator are summarized. Some goodness-of-fit tests, especially those based on graphical methods, are described. We also describe some possible extensions of this model considered so far and available computer programs and packages for estimating the parameters of this model. Finally, some areas for further research are also discussed.