Statistica Sinica 23 (2013), 1505-1521

A COPULA-MODEL BASED SEMIPARAMETRIC

INTERACTION TEST

UNDER THE CASE-CONTROL DESIGN

Hong Zhang$^1$, Jing Qin$^2$, Maria Landi$^{2}$, Neil Caporaso$^{2}$ and Kai Yu$^{2}$

$^1$Fudan University and $^2$National Institutes of Health

Abstract: It is important to study the interaction between risk factors in molecular epidemiology studies. To improve the power for the detection of interaction, some statistical testing procedures have been proposed in the literature by incorporating certain assumptions on the underlying joint distribution of two risk factors. For example, the well known case-only test used in genetic epidemiology studies is derived under the assumption of independence between the two risk factors. However, such testing procedures could have detrimental effects on both false positive and false negative rates when assumptions are not met. We propose a parametric copula function to model the joint distribution while leaving the marginal distributions for the two risk factors unspecified. A unified approach is proposed to estimate/test the interaction effect. This approach is very flexible and can be applied to study the interaction between risk factors that are continuous or discrete. A simulation study finds that the proposed test is generally more powerful than the traditional robust test derived under the standard logistic regression, and without specifying the relationship between the two risk factors. The performance of the proposed approach is comparable with the case-only test when the two risk factors are indeed independent in the control population. Unlike the case-only test, the proposed test can still maintain the type I error rate when the independence assumption is not valid. The application of the proposed procedure is demonstrated through two cancer epidemiology studies.

Key words and phrases: Case-only design, gene-environment interaction, gene-gene interaction, pseudo likelihood.