Challenges to case-only analysis for interaction detection using polygenic risk scores: model assumptions and biases in large biobanks

Understanding gene-environment and gene-gene interactions is important for studying complex diseases. Case-only analysis has been proposed to improve power for detecting interactions. However, case-only analysis relies on key assumptions, including correct specification of the disease risk model and marginal independence between variables. In this study, we systematically investigate the challenges of case-only analysis using polygenic risk scores (PRS) as genetic variables in large biobanks. Through simulations, we demonstrate that the false positive control of PRS-based case-only analysis depends on the log-linear disease risk model and weak main effects, and that it is prone to false positives under other commonly used disease risk models. We then conduct case-only analyses for breast cancer, prostate cancer, class 3 obesity, and short stature in the UK Biobank, using PRS derived from non-overlapping chromosome sets (e.g. even-numbered and odd-numbered chromosomes) that are unlikely to interact with each other. The resulting case-only regression estimates consistently show negative shifts compared to population-based estimates, suggesting false positives driven by collider bias due to model misspecification. Furthermore, correlations between chromosome set-specific PRS, likely driven by assortative mating or population stratification, suggest additional sources of confounding. Our results underscore the challenges of applying PRS-based case-only analysis in large biobank settings and highlight the need for caution when interpreting case-only results.