Simulation enhanced distributed lag models for mortality displacement

Distributed lag models (DLM) are attractive methods for dealing with mortality displacement, however their estimates can have substantial bias when the data is generated by a multi-state model. In particular DLMs are not valid for mortality displacement. Alternative methods are scarce and lack feasibility and validation. We investigate the breakdown of DLM in three state models by means of simulation and propose simulation enhanced distributed lag models (SEDLM) to overcome the defects. The new method provides simultaneous estimates of the net effect (entry) and the displacement effect (exit). These have improved performance over the singular estimate from a regular DLM. SEDLM entry estimates have negligible bias and their variance is reduced. The exit estimates are unbiased and their variance is one order of magnitude lower with respect to the entry estimates. Applying SEDLM to the original Chicago data, the 95% highest posterior density intervals for both entry and exit contain 0, providing neither evidence for a 'displacement effect' nor for a 'net effect'.