Nonparametric estimation of relative mortality functions

The standardized mortality ratio (SMR), which is the ratio of the number of deaths from a particular disease observed in a study cohort to the number expected from national vital statistics, has a long history of use in epidemiology. Separate SMRs computed according to discrete intervals of time since initial exposure, time on study, age or calendar year are used to examine effects of these variables on relative mortality. Applying some recent ideas of Andersen et al. (Biometrics 1985; 41: 921-932), we discuss refinements of this procedure that yield a nonparametric estimate of the SMR as a function of one time-varying factor while at the same time adjusting for the effects of other factors in a regression equation. The method is utilized to study relative lung cancer mortality as a function of years since initial employment in cohorts of 8014 Montana smelter workers and 679 Welsh nickel refinery workers. Suggestions are made for approximating the relative mortality function using only data for cases and matched controls sampled from the full cohort.