Fay, Pfeiffer, Cronin, Le, and Feuer (Statistics in Medicine 2003; 22; 1837-1848) developed a formula to calculate the age-conditional probability of developing a disease for the first time (ACPDvD) for a hypothetical cohort. The novelty of the formula of Fay et al (2003) is that one need not know the rates of first incidence of disease per person-years alive and disease-free, but may input the rates of first incidence per person-years alive only. Similarly the formula uses rates of death from disease and death from other causes per person-years alive. The rates per person-years alive are much easier to estimate than per person-years alive and disease-free. Fay et al (2003) used simple piecewise constant models for all three rate functions which have constant rates within each age group. In this paper, we detail a method for estimating rate functions which does not have jumps at the beginning of age groupings, and need not be constant within age groupings. We call this method the mid-age group joinpoint (MAJ) model for the rates. The drawback of the MAJ model is that numerical integration must be used to estimate the resulting ACPDvD. To increase computational speed, we offer a piecewise approximation to the MAJ model, which we call the piecewise mid-age group joinpoint (PMAJ) model. The PMAJ model for the rates input into the formula for ACPDvD described in Fay et al (2003) is the current method used in the freely available DevCan software made available by the National Cancer Institute.