The person-years approach to analyzing mortality data from occupational cohorts was introduced in the midtwentieth century. It cross-classifies all observed deaths and observation times into cells, computes the number of expected deaths for each cell based on referenced mortality rates, and then examines the ratio of total number of observed deaths to total number of expected deaths (the standardized mortality ratio). The maximum likelihood method of statistical inference was developed in the early twentieth century. However, only recently has it been applied to the analysis of occupational cohort data. When so applied, it provides estimates of measures of association between exposures and disease by maximizing the probability of the observed data. This paper shows how recent developments in the use of this tool justify and extend the person-years approach. In particular, problems with the standardized mortality ratio cited in the literature are shown to result from reliance on assumptions that are inappropriate for the data at hand. Methods for testing these assumptions are described. The discussion is illustrated with examples from occupational cohort studies of lung cancer.