Epidemiologists often compare the observed number of deaths in a cohort to the expected number 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 then this calculation will not consistently estimate the number of deaths expected in the absence of exposure. This is because exposure will have affected the distribution of person-time observed in the study cohort.Methods
This talk describes a simple way to consistently estimate the expected number of deaths and illustrates the approach using data from a cohort study of mortality among underground miners. In addition, the talk considers use of these simple counterfactual-based methods for calculation of years of life lost and demonstrate how this clarifies interpretation of results.Results
In a cohort of 3254 white male miners followed from 1960 through 2005, the observed number of deaths was 2428. A standard SMR calculation yields an estimate of 1693 expected deaths (SMR=1.4;95% CI: 1.4, 1.5). The proposed counterfactual approach yields 2167 expected deaths (CMR=1.1; 95% CI: 1.1, 1.2). However, the effect of the exposure is reflected by evidence of life shortening.Conclusions
The proposed approach yields more interpretable estimates of excess deaths and years of life lost.