## Abstract

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 ?(x) of the rate of onset at age x. The function ?(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 s 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 s = 1, but ascertainment bias means that p > 1/2 and s ? 1 in the sample. The maximum attained by ?(x) allows us to estimate a range for the product ps, 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. © 2007 by Astin Bulletin. All rights reserved.

Original language | English |
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Pages (from-to) | 429-452 |

Number of pages | 24 |

Journal | ASTIN Bulletin: The Journal of the IAA |

Volume | 37 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 2007 |

## Keywords

- Ascertainment bias
- Early-onset Alzheimer's disease
- Nelson-Aalen estimate
- Presenilin-1 gene
- Rate of onset