A Nelson-aalen Estimate of the Incidence Rates of Early-onset Alzheimer's Disease Associated with the Presenilin-1 Gene

We analyse, in a probabilistic setting, Newcombe's (1981) life table method of estimating rates of onset of high-penetrance single-gene disorders, and extend this to a counting process model for individual life histories, including movement between risk groups arising from genetic testing and onset in relatives. A key result is that estimates of rates of onset at any age x must be conditioned only on information available when subjects were age x, even though their later life histories might be available to the investigator. This determines the data that must be included in pedigrees. We derive a Nelson-Aalen-type estimate of a function of the rate of onset, and show that when all that is known is that the persons in the study inherited a mutation with probability 1/2, the function estimated is bounded. In practice, the treatment of censored observations or the methods of ascertainment might cause the estimate to exceed this bound, which results in infinite estimates of the rate of onset but might be a useful diagnostic check on the presence of these features. We summarise the literature on mutations in the Presenilin-1 (PSEN-1) gene, associated with early-onset Alzheimer's disease (EOAD), and from published pedigrees we estimate rates of onset of EOAD.