Joint effects on cancer risk of age at childbirth, time since birth and attained age: circumventing the problem of collinearity.

In previous studies of female cancer risk, we introduced a new method for circumventing the problem of collinearity in age-adjusted analysis of the joint effects of age at birth and time since birth. The basic idea was to estimate the pure age effect considering nulliparous women, assuming that the age effect is common to all women. However, risk estimates for attained age obtained in this manner may suffer from bias, in particular in small data sets, which may in turn influence risk estimates for reproductive factors among parous women. Certain factors possibly affecting cancer risk among nulliparous women only, for instance biological infertility, might also introduce bias. The purpose of this paper is to investigate the accuracy of risk estimates obtained by the joint approach, and to reveal the extent of bias in traditional separate age-adjusted analyses of age at birth or time since birth among parous women. Results are based on analyses of simulated data sets reflecting reproductive and demographic characteristics of a cohort of 1.1 million Norwegian women. Incidence rate ratios are calculated in Poisson regression analyses of person-years at risk. Our simulations show that the joint analysis in general yields unbiased risk estimates, but the number of cases must be rather high to achieve reliable results. Risk estimates from separate analyses can be seriously biased, although the amount of bias depends on the strength and direction of associations with cancer risk. With a total of 5500 cancer cases, the estimators for age at last birth and time since last birth were 13-78 per cent and 5-66 per cent more efficient in the joint than in the separate analysis, respectively. Significance levels were close to the nominal 5 per cent in the joint analysis, but about twice as high in the separate analysis. Adding an effect of biological infertility on cancer risk among nulliparous women, without taking it into account in the analyses, did not seriously affect risk estimates in the joint model.