Case-control designs are fundamental in epidemiology for the efficient study of rare outcomes. Although instrumental variable (IV) methods have been extended to this setting to address unmeasured confounding, they typically rely on the exclusion restriction assumption, which may be violated when the IV candidates directly affect the outcome through pathways independent of the exposure. In this paper, we propose a novel instrumented difference-in-differences (iDiD) approach tailored to case-control designs. Grounded in structural mean modeling, the proposed method accommodates IV candidates that have time-invariant direct effect on the outcome. When retrospective case-control datasets are collected, the candidate can still be used as a valid instrument on the trend scale when selection bias induced by retrospective sampling is efficiently taken into account. We assess finite-sample performance of this method through extensive simulations, then apply it to evaluate the risk of serious infection of biologic treatments for psoriasis, using French national claim database.
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