Nonrandom sampling in human genetics: skewness and kurtosis

When a multivariate normal sample is chosen from a truncated space of one of its components one can no longer make use of the normality assumption for the sample observations or for the estimates derived from them. In this paper, skewness and kurtosis for each component are derived analytically under a broad class of nonrandom sampling. It is shown that the distortions in skewness and kurtosis produced by nonrandomness are negligible, except those for the component with respect to which the selection of sampling regions is based. The usual tests of normality from sample values of skewness and kurtosis measures remain valid under nonrandom sampling, except for the selection variable. The implications of these analytical results in the context of commingling analysis in genetic epidemiology are discussed. It is recommended that when samples of families are obtained through nonrandomly ascertained probands, a commingling analysis should treat each relative class separately, since such analyses based on the pooled sample of individuals may involve unspecified bias in the levels of the test procedure.