JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1155 10.6339/24-JDS1155 Data Science Reviews Bibliographical Connections for Semiparametric Analysis in Case-Control Studies on Gene-Environment Interactions WangTianying1 LiuJianxuanjliu193@syr.edu2∗ WuAijing2 Department of Statistics, Colorado State University, Fort Collins, CO, USA Department of Mathematics, Syracuse University, Syracuse, NY, USA Corresponding author. Email: jliu193@syr.edu. 202516102024233454469 Supplementary Material

The code that implements Algorithm 1 in Section 3.3 is provided in the Supplementary Materials

30620242392024 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

Analyzing the gene-environment interaction (GEI) is crucial for understanding the etiology of many complex traits. Among various types of study designs, case-control studies are popular for analyzing gene-environment interactions due to their efficiency in collecting covariate information. Extensive literature explores efficient estimation under various assumptions made about the relationship between genetic and environmental variables. In this paper, we comprehensively review the methods based on or related to the retrospective likelihood, including the methods based on the hypothetical population concept, which has been largely overlooked in GEI research in the past decade. Furthermore, we establish the methodological connection between these two groups of methods by deriving a new estimator from both the retrospective likelihood and the hypothetical population perspectives. The validity of the derivation is demonstrated through numerical studies.

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