Method for recovering data on unreported low-severity crashes

Many low-severity crashes with no injuries are not reported in crash databases due to specific sampling criteria. If this sampling bias is not addressed, safety assessment analyses could yield inaccurate results. Unreported cases in crash databases are an example of missing not at random (MNAR) data. Recognizing and addressing MNAR data can be difficult; it requires domain expertise and clear assumptions to build accurate statistical models to recover the complete sample. Previous studies have often created ad-hoc procedures with arbitrary or implicit assumptions. These procedures are not directly adaptable to different use cases, do not account well for uncertainty from the biased data and the modelling choices, and are harder to critique due to the multiple steps involved, which can sometimes be intricate. This paper illustrates a method to address MNAR data while maintaining the set of observations intact. Based on principles of probability and clear modeling assumptions, the method is implemented using modern Bayesian probabilistic programming techniques. We include two examples: in the first, we used simulated data to demonstrate that the procedure is correct; in the second, we used crash data to estimate the complete distribution of Δv for passenger vehicles involved in personal damage-only (PDO) rear-end crashes. We estimated that about 77% of data on these vehicles is missing. The method can be used as a preliminary step in safety benefit analyses---for example, to accurately estimate baseline conditions for safety benefit estimation. This method is not restricted to the traffic safety domain but can be tailored to any use case involving systematic sampling bias. The code has been made publicly available.