Many late-onset diseases are caused by what appears to be a combination of a genetic predisposition to disease and environmental factors. The use of existing cohort studies provides an opportunity to infer genetic predisposition to disease on a representative sample of a study population, now that many such studies are gathering genetic nformation on the participants. One feature to using existing cohorts is that subjects may be censored prior to genetic sampling, thereby adding a layer of complexity to the analysis. We develop a statistical framework to infer parameters of a latent variables model for disease onset. The latent variables model describes the role of genetic and modifiable risk factors on the onset ages of multiple diseases, and accounts for right-censoring of disease onset ages. The framework also allows for missing genetic information by inferring a subject's unknown genotype through appropriately incorporated covariate information. The model is applied to data gathered in the Framingham Heart Study for measuring the effect of different Apo-E genotypes on the occurrence of various cardiovascular disease events.