title: Optimal methods for using posterior probabilities in association testing.
abstract: OBJECTIVE
  The use of haplotypes to impute the genotypes of unmeasured single nucleotide variants continues to rise in popularity. Simulation results suggest that the use of the dosage as a one-dimensional summary statistic of imputation posterior probabilities may be optimal both in terms of statistical power and computational efficiency; however, little theoretical understanding is available to explain and unify these simulation results. In our analysis, we provide a theoretical foundation for the use of the dosage as a one-dimensional summary statistic of genotype posterior probabilities from any technology.
  
  
  METHODS
  We analytically evaluate the dosage, mode and the more general set of all one-dimensional summary statistics of two-dimensional (three posterior probabilities that must sum to 1) genotype posterior probability vectors.
  
  
  RESULTS
  We prove that the dosage is an optimal one-dimensional summary statistic under a typical linear disease model and is robust to violations of this model. Simulation results confirm our theoretical findings.
  
  
  CONCLUSIONS
  Our analysis provides a strong theoretical basis for the use of the dosage as a one-dimensional summary statistic of genotype posterior probability vectors in related tests of genetic association across a wide variety of genetic disease models.
authors.affiliation: Department of Statistics, Harvard University, Cambridge, MA, USA.
authors.forename: Keli
authors.initials: K
authors.lastname: Liu
authors.forename: Alexander
authors.initials: A
authors.lastname: Luedtke
authors.forename: Nathan
authors.initials: N
authors.lastname: Tintle
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D055106:Genome-Wide Association Study / Q000706:statistics & numerical data*; D005838:Genotype; D006801:Humans; D008957:Models, Genetic; D011336:Probability
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