FLAME: a model for duration-dependent risk accumulation in episodic temporal exposures

Emerging technologies enable continuous monitoring of temporal exposures to disease risk factors, leading to complex exposure processes characterized by subject-specific numbers and durations of exposure episodes. A key scientific question is how the number and duration of such episodes influence disease risk. Existing methods typically rely on scalar summaries or time-indexed representations and are not naturally suited to model duration-dependent risk accumulation at the episode level. We introduce the FLexible Accumulation ModEl (FLAME), a semiparametric model for risk accumulation at the level of individual exposure episodes, with duration as the primary driver of risk. FLAME is motivated by and applied to quantifying the association between the duration of intraoperative hypotension and acute kidney injury (AKI) following cardiac surgery. The estimated risk accumulation function reveals that, although 60 one-minute hypotensive episodes are associated with an AKI probability of 0.24, a single sustained 60-minute episode increases that probability to 0.33, representing a 38% increase despite identical total duration. These findings provide actionable insights for intraoperative hemodynamic management and demonstrate the importance of accounting for episodic exposure patterns. While motivated by cardiac surgery, FLAME is broadly applicable to other settings involving high-resolution temporal exposures. An R package, flameRisk, is provided to facilitate the application of the method in practice.