1.1 Dominantly Inherited Gene Mutations

Estimation of rates of onset of rare, late-onset dominantly inherited genetic disorders is complicated by: (a) probable ascertainment bias resulting from the `recruitment ' of strongly aected families into studies; and (b) inability to identify the true `at risk ' population of mutation carriers. To deal with the latter, Gui & Macdonald (2002a) proposed a non-parametric (Nelson-Aalen) estimate ̂(x) of a simple function (x) of the rate of onset at age x. (x) had a nite bound, which was an increasing function of the probability p that a child of an aected parent inherits the mutation and the life-time penetrance. However if ̂(x) exceeds this bound, it explodes to innity, and this can happen at quite low ages. We show that such `failure ' may in fact be a useful measure of ascertainment bias. Gui & Macdonald assumed that p = 1=2 and = 1, but ascertainment bias means that p> 1=2 and 6 = 1 in the sample. The maximum attained by ̂(x) allows us to estimate a range for the product p, and therefore the degree of ascertainment bias that may be present, leading to bias-corrected estimates of rates of onset. However, we nd that even classical independent censoring, prior to ascertainment, can introduce new bias. We apply these results to early-onset Alzheimer's disease associated with mutations in the Presenilin-1 gene