A Correction for Ascertainment Bias in Estimating Rates of Onset of Highly Penetrant Genetic Disorders

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 affected 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 Λ(x) of the rate of onset at age x. The function Λ(x) had a finite bound, which was an increasing function of the probability p that a child of an affected parent inherits the mutation and σ the life-time penetrance. However if (x) exceeds this bound, it explodes to infinity, 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 σ = 1, but ascertainment bias means that p > 1/2 and σ ≠1 in the sample. The maximum attained by (x) allows us to estimate a range for the product pσ, and therefore the degree of ascertainment bias that may be present, leading to bias-corrected estimates of rates of onset. However, we find 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.