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Despite extensive safety assessments of drugs prior to their introduction to the market, certain adverse drug reactions (ADRs) remain undetected. The primary objective of pharmacovigilance is to identify these ADRs (i.e., signals). In addition to traditional spontaneous reporting systems (SRSs), electronic health (EHC) data is being used for signal detection as well. Unlike SRS, EHC data is longitudinal and thus requires assumptions about the patient's drug exposure history and its impact on ADR occurrences over time, which many current methods do implicitly. We propose an exposure model framework that explicitly models the longitudinal relationship between the drug and the ADR. By considering multiple such models simultaneously, we can detect signals that might be missed by other approaches. The parameters of these models are estimated using maximum likelihood, and the Bayesian Information Criterion (BIC) is employed to select the most suitable model. Since BIC is connected to the posterior distribution, it servers the dual purpose of identifying the best-fitting model and determining the presence of a signal by evaluating the posterior probability of the null model. We evaluate the effectiveness of this framework through a simulation study, for which we develop an EHC data simulator. Additionally, we conduct a case study applying our approach to four drug-ADR pairs using an EHC dataset comprising over 1.2 million insured individuals. Both the method and the EHC data simulator code are publicly accessible as part of the R package https://github.com/bips-hb/expard., Comment: 40 pages, 7 figures