Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Genetic association tests when a nuisance parameter is not identifiable under no association

  • Kim, Wonkuk (Department of Applied Statistics, Chung-Ang University) ;
  • Kim, Yeong-Hwa (Department of Applied Statistics, Chung-Ang University)
  • Received : 2017.08.22
  • Accepted : 2017.10.03
  • Published : 2017.11.30
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Abstract

Some genetic association tests include an unidentifiable nuisance parameter under the null hypothesis of no association. When the mode of inheritance (MOI) is not specified in a case-control design, the Cochran-Armitage (CA) trend test contains an unidentifiable nuisance parameter. The transmission disequilibrium test (TDT) in a family-based association study that includes the unaffected also contains an unidentifiable nuisance parameter. The hypothesis tests that include an unidentifiable nuisance parameter are typically performed by taking a supremum of the CA tests or TDT over reasonable values of the parameter. The p-values of the supremum test statistics cannot be obtained by a normal or chi-square distribution. A common method is to use a Davies's upper bound of the p-value instead of an exact asymptotic p-value. In this paper, we provide a unified sine-cosine process expression of the CA trend test that does not specify the MOI and the TDT that includes the unaffected. We also present a closed form expression of the exact asymptotic formulas to calculate the p-values of the supremum tests when the score function can be written as a linear form in an unidentifiable parameter. We illustrate how to use the derived formulas using a pharmacogenetics case-control dataset and an attention deficit hyperactivity disorder family-based example.

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