Method for recovering data on unreported low-severity crashes

Objective: Many low-severity crashes are not reported due to sampling criteria, introducing missing not at random (MNAR) bias. If not addressed, MNAR bias can lead to inaccurate safety analyses. This paper illustrates a statistical method to address such bias. Methods: We defined a custom probability distribution for the observed data as a product of an exponential population distribution and a logistic reporting function. We used modern Bayesian probabilistic programming techniques. Results: Using simulated data, we verified the correctness of the procedure. Applying it to real crash data, we estimated the {\Delta}v distribution for passenger vehicles involved in personal damage-only (PDO) rear-end crashes. We found that about 77% of cases are unreported. Conclusions: The method preserves the original data and it accounts well for uncertainty from both modeling assumptions and input data. It can improve safety assessments and it applies broadly to other MNAR cases.