We give up-to-date methods for estimating the age-specific incidence of a disease and for estimating the effect of risk factors. We recommend taking age as the basic time scale of the analysis; then, the hazard function can be interpreted as the age-specific incidence of the disease. This choice raises a delayed entry problem. We present three methods: the person-years method; the smoothed Nelson-Aalen estimator, and the penalized likelihood approach. When explanatory variables are available, the Poisson model and the Cox model with delayed entry may be used for estimating relative risks; the penalized likelihood approach can also be used. We apply these methods to estimate the age-specific incidence of dementia using data from a large cohort study, Paquid. This 5-year study followed a random initial sample of 3675 subjects with 190 incident cases of dementia. We compare the estimates based on the three possible methods. The estimated incidences computed separately for men and women cross and it is verified that a non-proportional hazards model for gender holds; women below 75 have a lower risk than men while women above 75 have a higher risk.