For many diseases, it seems that the age at onset is genetically influenced. Therefore, the age-at-onset data are often collected in order to map the disease gene(s). The ages are often (right) censored or truncated, and therefore, many standard techniques for linkage analysis cannot be used. In this paper, we present a correlated frailty model for censored survival data of siblings. The model is used for testing heritability for the age at onset and linkage between the loci and the gene(s) that influence(s) the survival time. The model is applied to interval-censored migraine twin data. Heritability (obtained from the frailties rather than actual onset times) was estimated as 0.42; this value was highly significant. The highest lod score, a score of 1.9, was found at the end of chromosome 19.