Onset distributions of age dependent zero-one events. Estimation from population data

Distributions associated with ages at onset of the first episode of an all-or-none phenomenon are often referred as “age of onset distributions”. At least two kinds of such distributions have to be distinguished: (i) the incidence (or ‘crude’) onset distribution giving the probability that a newborn individual will actually experience onset before age x, and (ii) the waiting time onset distribution representing an individual's chance of having onset before age x, supposing he lives so long. Theoretical bases for derivation of these probability functions are similar to those in competing risks (Section 2). Using nonparametric approach, the onset distributions can be expressed in terms of multiple decrement life tables. The techniques for constructing these tables usually involve data on both deaths among those who have not, and those who have experienced onset. Our methods (Sections 3–5) do not require these data; they are based on a population life table together with incidence and prevalence data for event under consideration.