# In-Depth Evaluation of Association between Crash and Hand Arthritis via Naturalistic Driving Study
## 4 Results
### Association between Arthritis and Crashes  
The relationship between arthritis and crashes was evaluated using the SHRP2 event dataset, which is based on the case-cohort epidemiological study design [19]. The crashes and control driving segments by arthritis status are shown in Table 4. As can be seen, the prevalence of arthritis among crashes (3.8%) is higher than among control driving segments (2.2%).  
The formal inference was conducted with a mixed-effect logistics regression model. Age groups and gender are included in the model to adjust for potential confounding and interaction effects. The random-effect model was implemented in R using the \"lme4\" package. The outputs of the model are presented in Table 5. Both age and arthritis are significantly associated with crash risk. The age variable included three groups: young (18-35), middle-aged (35-64), and senior (65+). After adjusting for the age and sex factors, severe arthritis is significantly associated with an increased crash risk with an OR of \(\exp(0.69)=1.99\). That is, drivers with arthritis were twice as likely to be involved in a crash than drivers without arthritis.  
Arthritis was shown to not have any interaction with age. The variable representing the interaction between arthritis and the senior age group had a \(p\)-value of 0.44. The variable representing the interaction between arthritis and the middle-aged group had  
\begin{table}
\begin{tabular}{l c c c} \hline  & **Arthritis** & **No Arthritis** & **Total** \\ \hline Crashes & 62 (3.8\%) & 1565 (96.2\%) & 1627 (100\%) \\ Control Driving Segments & 400 (2.2\%) & 17,394 (97.8\%) & 17,794 (100\%) \\ Total & 462 & 18,359 & 19,421 \\ \hline \end{tabular}
\end{table}
Table 4: Arthritis and Crash Frequency.  
\begin{table}
\begin{tabular}{l c} \hline
**Crash Type** & **Total** \\ \hline Animal-related & 3.54\% \\ Backing into traffic & 1.14\% \\ Backing, fixed object & 4.52\% \\ Opposite direction (head-on or sideswipe) & 0.16\% \\ Other & 5.72\% \\ Pedal cyclist-related & 0.16\% \\ Pedestrian-related & 0.16\% \\ Rear-end, striking & 6.48\% \\ Rear-end, struck & 6.32\% \\ Road departure (end) & 7.14\% \\ Road departure (left or right) & 59.75\% \\ Sideswipe, same direction (left or right) & 0.98\% \\ Straight crossing path & 0.93\% \\ Turn across path & 1.42\% \\ Turn into path (opposite direction) & 1.03\% \\ Turn into path (same direction) & 0.54\% \\ Total crashes & 414 \\ \hline \end{tabular}
\end{table}
Table 3: Crash Types and Severity for Drivers with Arthritis.  
\begin{table}
\begin{tabular}{l c c c} \hline  & **Coefficient Estimates** & **Odds Ratio** & \(p\)**-Value** \\ \hline Intercept & 2.68 & - & \textless{}0.001 \\ Arthritis & 0.69 & 1.99 & \textless{}0.001 \\ Middle-aged vs. Young & 0.41 & 1.51 & \textless{}0.001 \\ Senior vs. Young & 0.17 & 1.19 & 0.048 \\ Male vs. Female & 0.06 & 1.06 & 0.422 \\ \hline \end{tabular}
\end{table}
Table 5: Random-effect Model for Crash Risk.  
a \(p\)-value of 0.83. This indicates that there is no interaction between arthritis and the age of the driver variables, and thus, a random-effect model is sufficient for distinguishing the effects of arthritis on crash risk from the driver age.