Association tests for traits with variable age at onset

This paper is concerned with testing association between marker genotypes and traits with variable age at onset. Two methods are proposed, one which makes use of both age-at-ascertainment and age-at-onset information, and one which may be applied when only age-at-ascertainment information is available. (Here, by age-at-ascertainment, is meant the subject's age when presence of onset and age at onset are determined; for subjects who have died or are otherwise censored before ascertainment, the censoring time should be used instead). Adjustment for confounding due to population stratification is carried out by conditioning on observed traits and parental genotypes, or, if complete parental genotypes are not available, by conditioning on observed traits and the minimal sufficient statistics under the null hypothesis for the parental genotypes. Proportional hazards regression models and logistic regression models are used to motivate the methods, but correct type I error rates result even if the models are not correct. An illustrative example is described.