Stoppage: An issue for segregation analysis

Segregation analysis assumes that the observed family-size distribution (FS D), i.e.. distribution of number of offspring among nuclear families, is in dependent of the segregation ratio p. However, for certain serious diseases with early onset and diagnosis (e.g., autism), parents may change their or iginal desired family size, based on having one or more affected children, thus violating that assumption. Here we investigate "stoppage," the situati on in which such parents have fewer children than originally planned. Follo wing Brookfield et al. [J Med Genet 25:181-185, 1988], we define a stoppage probability d that after the birth of an affected child, parents will stop having children and thus not reach their original desired family size. We first derive the full correct likelihood for a simple segregation analysis as a function of p, d, and the ascertainment probability pi. We show that p can be estimated from this likelihood if the FSD is known. Then, we show t hat under "random" ascertainment, the presence of stoppage does not bias es timates of p. However, for other ascertanment schemes, we show that is not the case. We use a simulation study to assess the magnitude of bias, and we demonstrate that ignoring the effect of stoppage can seriously bias the es timates of p when the FSD is ignored. In conclusion, stoppage, a realistic scenario for some complex diseases, can represent a serious and potentially intractable problem for segregation analysis. (C) 2001 Wiley-Liss. Inc.