Adjustment of a sparse and irregular reference rate matrix

Regional sex-specific rates of a rare disease often show conspicuous fluctuations over conventional strata of age and calendar time. In a cohort study, when such rates are used as references in the calculation of the expected number of cases, the accumulated person-time of the study cohort may somewhat haphazardly contribute to the result. For example, only the person-time observed in the strata with at least one reference case registered contnbutes to the expected number of cases. It may therefore be important to evaluate whether the regional rates seem to differ systematically from the more stable national rates. When such differences may be indicated, a fairly simple method is proposed for smoothing rates. This method aims to
produce rates that better reflect the underlying, supposedly smooth, rate pattern over age and calendar time in a population of interest. The present paper illustrates the technique by considering right-sided colon cancer incidence rates from a regional male population, which the authors use to calculate the expected number of such cases in an occupational cohort.