We develop a statistical model for estimating cystic fibrosis (CF) incidence among infants born in the U.S.A. that accounts for under-diagnosis due to death prior to diagnosis and we apply it to the Cystic Fibrosis Foundation Patient Registry data for the years 1989 to 1991. The resulting estimate of incidence relative to live births among whites is 1:3419 while that among non-whites is 1:12,163. As a by-product of the modelling approach, estimates of the underlying average diagnosis age given survival to diagnosis are 4⋅09 years for whites and 4⋅55 years for non-whites, but this difference was not statistically significant and appears to demonstrate that diagnosis efforts may be approximately the same for whites and non-whites. Also, as another by-product of the modelling approach, CF mortality was estimated as more severe for females than males and marginally more severe for non-whites than whites. A variety of statistical methods underlie achievement of these results, including semi-parametric maximum likelihood, survival analysis, multiple imputation and bootstrap techniques.