Diagnostic plots for departures from proportional hazards in cohort study data

The assumption of proportional hazards is routinely made in the analysis of cohort studies, whether a simple SMR calculation or a full survival analysis is used. In this paper, we introduce simple plots for checking the validity of the assumption. The plots are of two kinds. The first, which has been used previously for survival data, makes use of the fact that the individual integrated hazards are distributed as unit exponential varieties under proportional hazards, and involves plotting their estimates against expected exponential order statistics. The second displays the evolution of relative risk as a function of time, and in this case, a choice of time scale must be made for the plots. A score test for proportional hazards is also derived, and the methods are illustrated by data on cancer mortality among the employees of a South Wales nickel refinery.