Multistage modeling of leukemia in benzene workers: a simple approach to fitting the 2-stage clonal expansion model

A simple SAS software program (SAS Institute, Inc., Cary, North Carolina) was developed for fitting an exact formulation of the 2-stage clonal expansion model accommodating piecewise constant exposures and left and right censoring of observations. Data on leukemia mortality and occupational exposure to benzene among rubber hydrochloride production workers in Ohio (1940-1996) were analyzed by using this approach. A model in which benzene exposure increased clonal expansion fit these data well; little evidence of an association between benzene exposure and initiation of leukemia was found. The estimated exposure-response association increased in magnitude with age at exposure and decreased with time since exposure. This analysis shows that the 2-stage clonal expansion model can be readily fit to epidemiologic cohort data by using a simple SAS program. The illustrative analyses of leukemia mortality among rubber hydrochloride workers suggest that the effect of benzene on leukemia risk is due to an exposure-induced increase in the proliferation of initiated cells.