The statistical analysis is considered of observations on non-negative variables subject to censoring on the right. That is, for each individual we may observe either the value of the random variable or that exceeds some given value, not necessarily the same for all individuals. Such data arise commonly in medical, actuarial and industrial contexts. For simplicity, call a failure time. Further it is assumed that there is available for each individual a vector of explanatory variables which may influence . Possible approaches to the analysis are reviewed. Primarily the paper deals with a model in which the age-specific failure rate (hazard function) has the form
where is an arbitrary unknown function, are unknown parameters and is the vector of explanatory variables. A modified likelihood function is obtained for inference about by arguing conditionally on the observed failure times. From this likelihood tests and confidence regions are obtained. In the special case of a two-sample problem with proportional hazards, the test of the null hypothesis of zero difference reduces to a generalization to censored data of the most efficient two-sample rank test for exponential distributions. A number of generalizations are considered and the relation with stochastic models discussed.
Discussion of the paper by 15 contributors is included togeher with the author’s reply.