Nonlinear models of injury risk and implications in intervention targeting for thoracic injury mitigation

Field data analyses often use either parametric or nonparametric means to describe the relationship between risk and various predictor variables. This study sought to evaluate a hybrid approach using semiconstrained multivariate nonlinear spline-based analysis.

Data were compiled from NASS-CDS years 1998-2015, selecting belted occupants age 16+ in collisions with a principal direction of force (PDOF) from 10 o'clock to 2 o'clock. Outcome measures included the incidence of Maximum Abbreviated Injury Scale (MAIS) 3+ injury in general and Abbreviated Injury Scale (AIS) 3+ rib fracture injury. Multivariate logistic regression models were fit controlling for PDOF, ΔV, vehicle model year, collision year, occupant age, occupant body mass index (BMI), and other select factors. Within the logistic regression models, each of the continuous variables was modeled with a 4-knot spline. These were compared to models treating ΔV and BMI linearly.

A total of 29,667 occupants were observed from the query, representing approximately 13,608,398 occupants when weighted. Sixty percent of the AIS 3+ rib fracture cases occurred at ΔVs at or below 40 km/h. The median age for cases without AIS 3+ rib fracture was 34 years old. The median age for cases with AIS 3+ rib fracture was 62 years old. When modeled via nonlinear spline, the risk of MAIS 3+ injury in general and AIS 3+ rib fracture injury specifically exhibited a relationship with ΔV similar in shape to that observed in the linear model. In both cases, the spline model exhibited greater risk prediction over ΔVs from 25 to 50 km/h compared to the linear model (20-33% greater risk at ΔVs below 40 km/h) and less risk than the linear model at greater ΔVs. BMI exhibited a nonlinear, nonmonotonic relationship with both injury types studied. The risk tended to be a minimum at BMIs of 22-24 kg/m², with an increase in risk at both higher and lower BMIs. For AIS 3+ rib fracture, the risk for a person with a BMI of 18 was approximately equal to the risk for a person with a BMI of 30, both being approximately 40% greater than the risk associated with a BMI of 24.

Nonlinear multivariate regression methods have the potential to convey information about the risk-predictor relationship that cannot be captured through traditional linear modeling. These results suggest that traditional linear logistic regression models may underestimate the risk of AIS 3+ rib fracture injury in the ΔV range where they most frequently occur (below 50 km/h). Due to its nonmonotonic effect, traditional linear models may underestimate injury risk at both high and low BMIs.