Stoppage: an issue for segregation analysis

Segregation analysis assumes that the observed family-size distribution (FSD), i.e., distribution of number of offspring among nuclear families, is independent of the segregation ratio p. However, for certain serious diseases with early onset and diagnosis (e.g., autism), parents may change their original desired family size, based on having one or more affected children, thus violating that assumption. Here we investigate "stoppage," the situation in which such parents have fewer children than originally planned. Following 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 that under "random" ascertainment, the presence of stoppage does not bias estimates of p. However, for other ascertainment 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 estimates 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.