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 approach 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, but our method is general. It facilitates the use of retrospective data from the multitude of cross-sectional and longitudinal studies worldwide that collect and potentially could collect event data. Copyright © 2012 John Wiley & Sons, Ltd.