A goodness‐of‐fit test for the polygenic threshold model: Application to pyloric stenosis

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Abstract
A new test of goodness of fit for the polygenic threshold model is proposed. This test, when applied to disorders showing different incidence rates in males and females, is designed to account for ascertainment in more detail than previously done by other investigators. This is accomplished by computing the expected distribution of nuclear families with more than one affected sib conditioned on several family‐dependent variables, including whether each family was ascertained via only affeted boys or via at least one affected girl. A direct measure of the probability of observing a data set is thereby derived. The test, when applied to data on pyloric stenosis, exposes the critical nature of the ascertainment procedures. Different levels of statistical significance are obtained when mode of ascertainment is taken into account than when the mode of ascertainment is ignored.