We present a novel approach for the flexible modeling of exposure-lag-response associations, i.e., time-to-event data where multiple past exposures are cumulatively associated with the hazard after a certain temporal delay. Our method is based on piece-wise exponential models and allows estimation of a wide variety of effects, including potentially smooth and time-varying effects as well as cumulative effects with leads and lags, taking advantage of the advanced inference methods that have

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... tly been developed for generalized additive mixed models.