Genetic association tests when a nuisance parameter is not identifiable under no association
- Authors
- Kim, Wonkuk; Kim, Yeong-Hwa
- Issue Date
- Nov-2017
- Publisher
- KOREAN STATISTICAL SOC
- Keywords
- Cochran-Armitage trend test; Rice's formula; sine-cosine process; transmission disequilibrium test; unidentifiable parameter
- Citation
- COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS, v.24, no.06, pp 663 - 671
- Pages
- 9
- Journal Title
- COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS
- Volume
- 24
- Number
- 06
- Start Page
- 663
- End Page
- 671
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/3744
- DOI
- 10.29220/CSAM.2017.24.6.663
- ISSN
- 2287-7843
2383-4757
- 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 C A 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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Collections - College of Business & Economics > Department of Applied Statistics > 1. Journal Articles
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