Supplementary Material for: An Analytic Solution to the Computation of Power and Sample Size for Genetic Association Studies under a Pleiotropic Mode of Inheritance
2017
Our motivation here is to calculate the power of 3 statistical tests
used when there are genetic traits that operate under a pleiotropic mode
of inheritance and when qualitative phenotypes are defined by use of
thresholds for the multiple quantitative phenotypes. Specifically, we
formulate a multivariate function that provides the probability that an
individual has a vector of specific quantitative trait values
conditional on having a risk locus genotype, and we apply thresholds to
define qualitative phenotypes (affected, unaffected) and compute
penetrances and conditional genotype frequencies based on the
multivariate function. We extend the analytic power and
minimum-sample-size-necessary (MSSN) formulas for 2 categorical
data-based tests (genotype, linear trend test [LTT]) of genetic
association to the pleiotropic model. We further compare the MSSN of the
genotype test and the LTT with that of a multivariate ANOVA (Pillai).
We approximate the MSSN for statistics by linear models using a
factorial design and ANOVA. With ANOVA decomposition, we determine which
factors most significantly change the power/MSSN for all statistics.
Finally, we determine which test statistics have the smallest MSSN. In
this work, MSSN calculations are for 2 traits (bivariate distributions)
only (for illustrative purposes). We note that the calculations may be
extended to address any number of traits. Our key findings are that the
genotype test usually has lower MSSN requirements than the LTT. More
inclusive thresholds (top/bottom 25% vs. top/bottom 10%) have higher
sample size requirements. The Pillai test has a much larger MSSN than
both the genotype test and the LTT, as a result of sample selection.
With these formulas, researchers can specify how many subjects they must
collect to localize genes for pleiotropic phenotypes.
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