Several models of a population survival curve composed of two piecewise exponential distributions are developed. In one formulation the hazard rate changes at a point that is an unobservable random variable that varies between individuals. The population hazard function may decrease with age even when all individuals' hazards are increasing. In a second formulation, the population hazard function is modeled directly. Several models are fit to the survival history of a cohort of 5751 highly inbred male Drosophila melanogaster and the British coal mining disaster data.
Bibliographical noteFunding Information:
IIRis research was supported in part by NIH Grants POI-AGOS761, (/al-AG10328, NCI-AI05073, KO4-HDOO638, ROI-HS07772, and POl-DC00133 and a grant from the Minnesota Supercomputer Institute. We are grateful to Brad Carlin for supplying serjeral useful references.