Autologistic Modeling in Benchmark Risk Analysis

Abstract

An important objective in statistical risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a pre-specified Benchmark Response (BMR) in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called Benchmark Dose Lower Limits (BMDLs). With this context, a quantitative methodology is developed to characterize vulnerability among 132 U.S. urban centers ('cities') to terrorist events, applying a place-based vulnerability index to a database of terrorist incidents and related human casualties. A centered autologistic regression model is employed to relate urban vulnerability to terrorist outcomes and also to adjust for autocorrelation in the geospatial data. Risk- analytic BMDs are then estimated from this modeling framework, wherein levels of high and low urban vulnerability to terrorism are identified. This new, translational adaptation of the risk-benchmark approach, including its ability to account for geospatial autocorrelation, is seen to operate quite flexibly in this socio-geographic setting. Further, alternative definitions for neighborhoods are considered to extend the autologistic benchmark paradigm to non-spatial settings. All 3108 counties in the contiguous 48 U.S. states are studied to identify a benchmark dose variable as the number of hazards. This is employed to benchmark billion-dollar losses across each county. County-level resilience is used as a potential characteristic for defining the neighborhood structure within the autologistic model.