When event data are retrospectively reported, more temporally distal events tend to get “heaped” on even multiples of reporting units. Heaping may introduce a type of attenuation bias because it causes researchers to mismatch time-varying right-hand side variables. We develop a model-based ap… proach to estimate the extent of heaping in the data, and how it affects regression parameter estimates. We use smoking cessation data as a motivating example to describe our approach, but the method more generally facilitates the use of retrospective data from the multitude of cross-sectional and longitudinal studies worldwide that already have and potentially could collect event data.