S-Space Graduate School of Public Health (보건대학원) Dept. of Public Health (보건학과) Theses (Master's Degree_보건학과)
Adjusting Bias of Wald Test for Smooth Components and Their Interactions in Generalized Additive Model
일반화가법모형의 평활요소 및 교호작용의 편의 보정 기법에 대한 연구
- 보건대학원 보건학과
- Issue Date
- 서울대학교 보건대학원
- Generalized additive model (GAM); Smooth function; Extended Wald-type test; Genome-environment wide interaction studies (GEWIS); SOX9
- 학위논문 (석사)-- 서울대학교 보건대학원 보건학과, 2017. 8. 원성호.
- Generalized additive model (GAM) uses covariates based on smooth functions and can easily predict non-linear relationship between response variables and covariates. However, in spite of its flexibility, it has been known that p-values for its Wald and likelihood ratio tests do not preserve the nominal significance levels. S. N. Wood (2013) found that Wald statistics follow the mixture of weighted chi-square distribution and it has been often utilized for statistical inference. However, its performance was not carefully investigated and I found that it can lead to inflated results in certain scenarios. In my thesis, I extended his method and the proposed method was evaluated with simulation data for various hypothesis tests such as joint test for two or more smooth functions or interactions. With extensive simulations, I confirmed that the proposed method generally performs better than Woods method. Furthermore, the proposed method was applied to the gene-by-smoking interaction association analyses. Four SOX9-associated SNPs were known to be associated with lung functions, and their interaction effect with pack-years was evaluated with Korean cohort data. Interaction test between pack-years and SNPs with linear mixed effects model was not significant but a generalized linear mixed model resulted in significant interaction, which reveals that GAM is useful for covariates with nonlinear relationships with response variables. In conclusion, GAM is useful for modeling non-linear relationship and the proposed method enables valid statistical inferences.