Abstract
Epidemiologists often compare the observed number of deaths in a cohort with the expected number of deaths, obtained by multiplying person-time accrued in the cohort by mortality rates for a reference population (ideally, a reference that represents the mortality rate in the cohort in the absence of exposure). However, if exposure is hazardous (or salutary), this calculation will not consistently estimate the number of deaths expected in the absence of exposure because exposure will have affected the distribution of person-time observed in the study cohort. While problems with interpretation of this standard calculation of expected counts were discussed more than 2 decades ago, these discussions had little impact on epidemiologic practice. The logic of counterfactuals may help clarify this topic as we revisit these issues. In this paper, we describe a simple way to consistently estimate the expected number of deaths in such settings, and we illustrate the approach using data from a cohort study of mortality among underground miners.