Modeling effects of age at and time since delivery on subsequent risk of cancer

We describe a simple model for examining the temporal effects of childbirth on cancer risk, considering data on uniparous and nulliparous women, from either a cohort or case-control study design. For uniparous women, the expression for risk includes terms for age at delivery and time since delivery. With a suitable definition of the effect of uniparity, no terms relating to delivery are needed for nulliparous women. If the pure age effect is assumed to be the same in all women, the effects of age at delivery and time since delivery are both estimable, despite the linear dependence involving attained age in uniparous women. Omitting terms for time since delivery and considering the heterogeneity of age-specific effects of uniparity provides a valid test for the effect of time since delivery, although risk estimates are biased. Tests based on linear interaction terms for age at delivery and attained age, as applied in recent case-control studies, are not appropriate for investigating the effect of time since delivery. We show how our basic model may be applied to the analysis of case-control data from a Norwegian study of breast cancer. We then compare these results with those from other models.