The infinite-lived rat—An equal-age replacement process

Equal-age replacement is used to formulate the competing-risk problem in terms of a set of nonhomogenous Poisson processes whose mean value functions are the set of cumulative hazards (the integrals of the age-and cause-specific incidence rates). Cumulative hazard is estimated by a weighted count that is the sum of the reciprocals of numbers at risk at the times of occurrence of the specific risk. Occurrence data are generally insufficient to distinguish between plausible forms of the distribution function or types of nonparametric shifts with dose. More emphasis has to be given to understanding the biological mechanisms that dictate the parametric form to be fitted to the data.