Chakraborty R, Hanis C L
Genet Epidemiol. 1987;4(2):87-101. doi: 10.1002/gepi.1370040204.
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.
当从多元正态样本的一个分量的截断空间中选取样本时，就不能再对样本观测值或从它们得出的估计值使用正态性假设。在本文中，在一类广泛的非随机抽样下，通过解析方法得出了每个分量的偏度和峰度。结果表明，非随机性产生的偏度和峰度的扭曲可以忽略不计，但对于基于其选择抽样区域的那个分量除外。除了选择变量外，从偏度和峰度测量的样本值进行的通常的正态性检验在非随机抽样下仍然有效。讨论了这些分析结果在遗传流行病学混合分析背景下的意义。建议当通过非随机确定的先证者获得家庭样本时，混合分析应分别处理每个亲属类别，因为基于个体合并样本的此类分析可能在检验程序水平上涉及未指明的偏差。
