  We consider cross-sectional genetic association studies (common and rare
variants) where non-genetic information is available, or feasible to obtain for
$N$ individuals, but where it is infeasible to genotype all $N$ individuals. We
consider continuously measurable Gaussian traits (phenotypes). Genotyping $n<N$
extreme phenotype individuals can yield better power to detect
phenotype-genotype associations, as compared to randomly selecting $n$
individuals. We define a person as having an extreme phenotype if the observed
phenotype is above a specified threshold or below a specified thresholds. We
consider a model where these thresholds can be tailored to each individual. The
classical extreme sampling design is to set equal thresholds for all
individuals. We introduce a design ($z$-extreme sampling) where personalized
thresholds are defined based on the residuals of a regression model including
only non-genetic (fully available) information. We derive score tests for the
situation where only $n$ extremes are analyzed (complete case analysis), and
for the situation where the non-genetic information on $N-n$ non-extremes is
included in the analysis (all case analysis). For the classical design, all
case analysis is generally more powerful than complete case analysis. For the
$z$-extreme sample, we show that all case and complete case tests are equally
powerful. Simulations and data analysis also show that $z$-extreme sampling is
at least as powerful as the classical extreme sampling design and the classical
design is shown to be at times less powerful than random sampling. The method
of dichotomizing extreme phenotypes is also discussed.
