Nonrandom sampling in human genetics: skewness and kurtosis

Area of Science:

• Statistics
• Genetic Epidemiology

Background:

• Multivariate normal samples from truncated spaces violate standard normality assumptions.
• This impacts the reliability of sample observations and derived estimates.

Purpose of the Study:

• To analytically derive skewness and kurtosis for components of multivariate normal samples under nonrandom sampling.
• To assess the validity of normality tests in such scenarios.
• To discuss implications for commingling analysis in genetic epidemiology.

Main Methods:

• Analytical derivation of skewness and kurtosis for each component.
• Analysis under a broad class of nonrandom sampling schemes.
• Evaluation of normality test validity.

Main Results:

• Distortions in skewness and kurtosis due to nonrandomness are generally negligible.
• Significant distortions are observed only for the component defining the sampling region.
• Standard normality tests remain valid for non-selected variables.

Conclusions:

• Nonrandom sampling introduces minimal bias in skewness and kurtosis for most components.
• Commingling analysis in genetic epidemiology should analyze relative classes separately when using nonrandomly ascertained probands.
• Pooled sample analyses may introduce unspecified bias in test procedures.