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Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk (2014)

Chapter: Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues

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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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Suggested Citation:"Chapter 7 - Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues." National Academies of Sciences, Engineering, and Medicine. 2014. Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk. Washington, DC: The National Academies Press. doi: 10.17226/22297.
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65 C h a p t e r 7 This chapter examines the research question, How does the timing of lead-vehicle closing kinematics in relation to off- road glances influence crash risk? The previous chapters have demonstrated, in line with existing results (e.g., Klauer et al. 2006, 2010), that the performance of activities requiring eyes off the forward path is associated with significantly increased risk for crashes and near crashes. Moreover, it was shown that the timing of off-path glances within the time window preced- ing the crash strongly determines the risk level. In particular, for a time window aligned to the precipitating event (PE), off- path glances around the PE appear to be the most risky. For a time window aligned to the crash point or minimum time to collision, the risk was highest for glances occurring within 3 seconds to 1 second before the crash/minTTC. To better understand why the timing of glances matters for crash risk, a more detailed analysis of the timing relations between, on the one hand, the driver’s visual behavior and reactions and, on the other, visual cues and situation kinematics was conducted. This analysis also aimed to determine to what extent these timing relations distinguish crashes from near crashes. This addresses the general hypothesis that the simultane- ous occurrence of Eyes off Path and an unexpected event plays a key role in the causation of rear-end crashes, which— as mentioned in Chapter 1, Background—was a key motiva- tion for the present research. In line with this hypothesis, Tijerina et al. (2004), in a study on eyeglance behavior during car following, found that drivers in normal following situa- tions generally did not take their eyes off the road unless the range rate was near zero (i.e., the distance between the vehi- cles is not closing). They also found that distance or time headway was generally not taken into account when deciding on an off-road glance. Thus, drivers’ decisions on whether to take the eyes off the road seem to be largely based on expecta- tions of whether or not the lead vehicle will brake in the next few seconds. However, driver expectations are sometimes vio- lated. If the lead vehicle brakes during the off-path glance and the driver has not adopted a sufficient headway, the situation may end up in a crash. Tijerina et al. suggested that this may be the key mechanism explaining why inattention is the lead- ing factor contributing to rear-end crashes. One objective of the present analysis was to investigate to what extent this “inopportune glance due to expectation vio- lation” mechanism applied to the rear-end crashes in the present data set. A further key issue concerns what factors made the critical difference in situations when the driver suc- cessfully escaped collision (i.e., near crashes). One important aspect concerns the timing of glances in relation to brake lights. Experimental studies have found that brake light onsets reliably trigger reactions in vehicle-following situations (e.g., Lieberman et al. 2007). If these results gener- alize to real-world driving, it would be expected that missed brake light onsets are associated with crashes and near crashes. More specifically, brake light onsets occurring during off-road glances should be more prevalent for crashes and near crashes compared with baselines. Thus, one objective of the present analysis was to investigate whether this hypothesis was sup- ported by the present data. Furthermore, if brake light onsets are used by drivers to predict that the lead vehicle will soon brake, drivers should generally be reluctant to take their eyes off the road if the brake light onset occurs at a moment when they have their eyes on the road (assuming the brake lights are salient enough to be detected). Thus, brake light onsets were also analyzed in relation to subsequent off-path glances. Another key objective of the present analysis was to analyze the kinematic situation (e.g., speed, headway, and time to col- lision) at the start and end of the last glance before the crash/ near crash. According to the inopportune glance mechanism hypothesized above, the kinematics for crashes and near crashes should be similar to normal driving (i.e., the matched baselines) at the beginning of the last glance but more critical when looking back. A further question of interest is whether the drivers who crashed adopted a smaller initial headway than those who successfully escaped or if the key difference between crashes and near crashes relates more to how the Timing of Eyes off Path Relative to Situation Kinematics and Visual Cues

66 criticality of the situation developed while looking away. Fur- thermore, to what extent did the duration of the last glance influence the event outcome? Did the situation develop into a crash rather than a near crash mainly because the driver was looking away for a long time period, or was it rather the rate at which the situation changed during the glance away that produced the crash? This latter question is of fundamental importance for answering the key question addressed by the present project: What characterizes safe glances? A final objective was to analyze driver reactions after look- ing back the last time before the crash or near crash. Are such reactions triggered mainly by brake lights or by the perceived kinematics of the driving situation (i.e., the optical expan- sion, looming, of the lead vehicle)? Can differences in driver reactions further explain why an event develops into a crash rather than a near crash? It was also investigated how last- second driver reactions in critical rear-end situations could be modeled to enable computer simulation of these phenom- ena. A specific analysis was also carried out on drivers’ reac- tions when they were talking/listening on a cell phone. As reported in Chapter 4, this activity was associated with a reduced risk of a crash/near crash, that is, a protective effect. Similar results have been found in previous studies (Olson et al. 2009; Hickman et al. 2010), but the basic mechanism behind this effect is still not well understood. This analysis specifically aimed to investigate whether the protective effect of talking/listening on a cell phone could be explained in terms of differences in driver reactions relative to situation kinematics. 7.1 Method Glance annotation. This analysis used the same Eyes-on-Path signal as the previous analyses, further described in Section 2.9. Kinematics. Due to the limited quality of the radar data, the headway and closing distances were calculated on the basis of optical variables manually annotated from the forward video, as further described in Section 2.9. It should be noted that the time to collision (TTC) was estimated directly from the opti- cal angle Theta (q) subtended by the lead vehicle at the camera in terms of Tau (t), that is, q divided by its time derivative q-dot (Lee 1976). Optically, q and q-dot characterize the looming (optical expansion) of the lead vehicle. An advantage of using the optically (rather than the physically) specified TTC is that this is the type of information that humans pre- sumably use to perceive and control the situation kinematics in driving and other forms of locomotion, although it is debated exactly what optical information is used for different types of tasks (e.g., Flach et al. 2004). One consequence is that TTC here refers to the TTC for the camera rather than the sub- ject vehicle’s front bumper. Since TTC goes to infinity at zero relative velocity (e.g., at constant distance in normal following situations), its inverse 1/TTC (referred to as invTTC) was used in the analysis. Event Selection This analysis included crashes, near crashes, and matched baselines. Since the analysis focused specifically on glance tim- ing, events that did not include an off-path glance were excluded. As described in Section 2.9 for the matched base- lines, the optical angle (q) was only annotated for approxi- mately 10 seconds before the reference point (i.e., the point corresponding to the crash point and minTTC for crashes and near crashes, respectively) and 5 seconds after. Since the exact duration of the precrash annotations varied somewhat, a time window of 8 seconds before the reference point was used in the present analysis. Only events in which the lead vehicle was continuously present within a time window of 8 seconds to 1 second before the crash/minTTC were included in the analy- sis. Thus, the analysis focused on “pure” vehicle-following or approach situations, excluding cut-in and lane-change sce- narios in which the lead vehicle appeared or changed in the last second, leading to a discontinuous optical angle signal. The main reason for excluding these events was that they rep- resented very different kinematic situations which would have made the analysis substantially more complicated. However, it is important to keep this in mind when interpreting the results. In addition, the optical angle annotation was sometimes miss- ing because of other reasons, such as reduced visibility (e.g., heavy rain, fog, or darkness) or limited video quality. As described in Section 2.6, the total data set used in this proj- ect consisted of 46 crashes, 211 near crashes, and 257 matched baselines. In total, 5 crashes, 34 near crashes, and 25 matched baselines were excluded because of missing or insufficient annotation of optical angle according to the criteria above. This led to a basic data set of 41 crashes, 177 near crashes, and 232 matched baselines used as the starting point for all analysis in this chapter. In addition, some further cases were excluded due to constraints in the specific analyses, as further described below. 7.2 results Timing of Glances Relative to Brake Lights First, the analysis considers the timing of brake light onsets in relation to off-road glances. In this analysis, only those events that contained at least one brake light onset were included. This led to a data set containing 35 crashes, 156 near crashes, and 75 matched baselines. The results are shown in Table 7.1. First, the prevalence of co-occurrences of brake light onsets and Eyes off Path were compared between crashes, near crashes, and matched baselines. Brake light onsets co-occurred with an

67 off-path glance in 23% of the crashes, 34% of near crashes, and 31% of matched baselines. This comparison thus includes co-occurrence of Eyes off Path with any brake light onset in the 8-second time window. Table 7.1 also gives the numbers and percentages of co-occurrences of eyes off path and the last brake light onset in the time window, which are generally simi- lar to those obtained for co-occurrence with any brake light onset. These results indicate that co-occurrences of eyes off path and brake light onsets were about as prevalent for the matched baselines as for the near crashes and slightly less prev- alent for crashes. Thus, drivers who crashed or nearly crashed were not more likely to have looked away at the last brake light onset than baseline drivers. This indicates that whether drivers missed brake light onsets by looking away did not play any significant role in the development of the crashes and near crashes in the present sample. Given that the majority of drivers had their eyes on the road when the brake light illuminated, to what extent did drivers then look away from the forward path? If drivers reliably interpret brake light onset as a sign of a potential threat, then one would expect to see very few cases where the driver looked away after having seen a brake light onset, particularly in the baselines. Similarly, drivers generally do not look away when they see the lead vehicle closing (Tijerina et al. 2004). How- ever, the results show (Table 7.1) that situations in which the driver looked away after a last brake light onset when the eyes were on the forward path are indeed common and occur in almost half of the crashes, and in about 30% of near crashes and matched baselines. Figure 7.1 shows two examples of time-series plots for crashes in which the driver looked toward the forward path at the last brake light onset and but then looked away. Taken together, these results suggest that brake lights have a negligible effect on driver behavior in real-world driving situ- ations. In the majority of crashes, near crashes, and matched baselines, the driver looked forward at the moment when the lead vehicle’s brake lights illuminated for the last time. However, this did not prevent the crashes and near crashes, Table 7.1. Analysis of the Timing of Off-Path Glances Relative to Brake Light Onsets (BLOs) Event Type Total Number of Valid Events Number of Events With Brake Light Onset (N BLO) Number of Events With BLO When Any BLO Occurred During Eyes off Path (EOP) (% of N BLO) Number of Events With BLO When the Last BLO Occurred During EOP (% of N BLO) Number of Events With BLO When Driver Looked Away After Seeing Last BLO (% of N BLO) Crashes 41 35 (85%) 8 (23%) 8 (23%) 17 (49%) Near crashes 177 156 (88%) 53 (34%) 48 (31%) 43 (28%) Matched baseline 232 75 (32%) 23 (31%) 21 (28%) 23 (31%) Figure 7.1. Examples of time-series plots for two crash events (event IDs 10631463 and 10631469 for left and right plots, respectively) in which the drivers eventually looked away despite having the eyes on the road at the last brake light onset.

68 indicating that the drivers generally ignored this predictive information. Moreover, a significant proportion of these driv- ers even looked away from the road just after having seen the brake lights illuminate. This tendency to look away after pre- sumably having seen a brake light onset was stronger for crashes than for near crashes and matched baselines. This last finding, that drivers who crashed more often looked forward at the last brake light onset, and also often looked away after having seen the brake lights illuminate, is somewhat dif- ficult to interpret. One possibility is that this is a side effect of the kinematic conditions that typically lead to rear-end crashes. Chapter 9, Conclusions and Recommendations, returns to this issue, but first, the following section considers the timing of glances in relation to situation kinematics. 7.3 timing of the Last Glance relative to Situation Kinematics This section reports on the analysis of situation kinematics relative to the last glance. The last glance was defined as the last glance away from the forward path initiated before the reference point (the crash point for crashes, the minimum TTC for near crashes, and a random point for the matched baselines). Thus, the end of the last glance could sometimes occur after the reference point, that is, outside the -8-to- 0-seconds time window. In this analysis, some events were excluded over and above those excluded due to missing optical angle information (described above)—for several possible reasons. The main reason for exclusion was that no off-path glances occurred within the 8-second time window. In total, there were 6 such crashes, 34 near crashes, and 51 matched baselines. Since some of these cases were already excluded due to missing optical angle, this led to the exclusion of an additional 4 crashes, 29 near crashes, and 46 matched baselines. Another reason for excluding events was that the last glance began before the start of the 8-second time window, which only affected measures related to the glance onset. The end of the last glance was searched for outside the time window and thus, last glance end data were only missing if the glance did not end within an additional 5 seconds after the 8-second time window (this happened in only a single case, a near crash). The number of excluded events due to missing optical angle and missing/incomplete glances is summarized in Table 7.2. Data could also be missing in other signals, which affected the total number of data points used in each of the specific analyses below. The total number of valid events used in the analyses is indicated in each subplot. For the different kinematic variables investigated, t-tests were used to test for statistically significant differences at last glance (LG) start and LG end as well as between the event types. The planned comparisons of main interest were as follows: • Crashes versus near crashes at LG start (two-sample t-test); • Crashes and near crashes versus matched baselines at LG start (paired sample t-test); • LG start versus LG end for crashes (paired sample t-test); • LG start versus LG end for near crashes (paired sample t-test); and • Crashes versus near crashes at LG end (two-sample t-test). A significance level of a = 0.05 was used in all tests. Relative Velocity Figure 7.2 plots the relative velocity (range rate) between the subject vehicle and the lead vehicle at the start and end of the last glance way from the forward path. At LG start, the mean values for crashes and near crashes were not significantly dif- ferent. However, the relative velocity was significantly higher (more negative) for crashes and near crashes compared with the matched baselines [t(133) = -4.99, p < 0.001]. In the majority of cases for all event types, the relative velocity at the start of the last glance is close to zero (thus indicating a normal following situation in which the subject vehicle and lead vehi- cle are traveling with roughly equal velocities). However, the negative tails indicate the presence of cases in which the sub- ject vehicle was already closing in on the lead vehicle at LG start. This seems to be more common for crashes and near crashes but also occurs in the matched baselines. Video inspec- tion revealed that these matched baseline cases typically involve Table 7.2. Summary of Exclusion of Events for Analysis of Last Glance Timing Event Type Original Number of Events Cases Excluded Due to Missing Optical Angle Additional Cases Excluded Due to Lack of Off-Path Glances Additional Cases Missing LG Starts Additional Cases Missing LG Ends Remaining Number of LG Starts Remaining Number of LG Ends Crashes 46 5 4 1 0 36 37 Near crashes 211 34 29 5 1 143 147 Matched baselines 257 25 46 8 0 178 186 Note: LG = last glance.

69 situations in which the subject vehicle closes in rapidly on the lead vehicle, but at a larger distance than in crash and near-crash situations. The distributions of relative velocity at LG end indicate a strong average change in relative speed during the last glance away, both for crashes [t(35) = 8.54, p << 0.001] and near crashes [t(141) = 10.77, p << 0.001]. While the change was slightly larger for crashes, the difference from the near crashes was minor and not statistically significant. Thus, the shift in relative velocity during the LG does not seem to influence whether the event develops into a crash or near crash. Time Headway Figure 7.3 plots the initial time headway (THW) at the begin- ning and end of the last glance. The distributions of time Figure 7.2. Relative velocity at the beginning and end of the last glance by event type. Figure 7.3. Time headway at beginning and end of the last glance by event type.

70 headway when the drivers looked away are very similar for all three event types (with no statistically significant differences between the means). This again indicates, in line with Tijerina et al. (2004), that the situation at the beginning of the last glance generally represented a normal following situation, in which the driver judged it safe to take his or her eyes off the road. It can be noted that drivers generally adopted relatively small headways when looking away, and this did not differ between the event types. It can also be noted that crashes with initial headways above 2 seconds were very rare. For both crashes and near crashes, the time headway was significantly reduced when looking back [t(28) = 4.04, p < 0.001 and t(129) = 6.41, p << 0.001]. In contrast with the results for relative velocity, the time headway when looking back was significantly smaller for crashes than for near crashes [t(165) = -2.87, p = 0.005]. This indicates that for the majority of the crashes and near crashes, a large portion of the initial safety margin was consumed during the last glance, where the reduction was significantly larger for crashes than for near crashes. Figure 7.4 plots the THW at LG start against the duration of the last glance. Although there is some indication of lon- ger adopted time headways for the extreme glance durations (>2 seconds), the minimum tolerance margin adopted by the driver is still often very small. Thus, again in line with Tijerina et al. (2004), drivers apparently do not generally take time headway into account when deciding on how long to look away from the road. It can also be noted that the few crashes for headways larger than 2 seconds only occurred for the extreme glances longer than 4 seconds. Thus, most events occurred at short headways with relatively short glances. Inverse Time to Collision The inverse time to collision (invTTC) at the beginning and end of the last glance is plotted in Figure 7.5. At the LG start, it can be observed that, for the majority of all drivers, the last glance begins when invTTC is near zero (i.e., the situation is still not critical, at least kinematically). The invTTC distribu- tion for the matched baselines at both LG start and LG end is relatively narrow and symmetrical around zero. For crashes and near crashes, the distributions at LG start shift slightly toward the positive side, where the means for both crashes and near crashes are close to invTTC = 0.1. There was no significant difference between the crashes and near crashes for invTTC at LG start. However, the difference between matched baselines and crashes and near crashes combined was statistically signifi- cant [t(141) = 3.91, p < 0.001]. In line with the results on rela- tive velocity above, this indicates that at least some crash/near crash–involved drivers looked away at a moment when the gap between the vehicles was already closing. At the LG end, invTTC had generally changed significantly, both for crashes and near crashes [t(35) = 5.97, p << 0.001 and t(140) = 14.1, p << 0.001, respectively]. Furthermore, the invTTC at LG end was significantly larger for crashes than for near crashes [t(180) = 3.47, p < 0.001]. This indicates that the situation when looking back was on average more critical for the crashes than the near crashes. Summary Taken together, the results reported in this section support the initial general hypothesis that many rear-end crashes occur because of an unexpected closing of the lead vehicle Figure 7.4. Time headway at the start of the last glance versus the last glance duration.

71 while the driver is looking away from the forward path. When the last glance is initiated, the situation is generally still kine- matically similar to a normal following situation and the driver considers it safe to look away. However, in a few cases, the driver looked away when the lead vehicle was already clos- ing. In general, drivers do not seem to adapt their headway based on the expected duration of the glance to be initiated. The time headway when looking away is on average relatively short and does not differ between crashes, near crashes, and baselines. When the driver looks back, the situation has gen- erally turned critical for crashes and near crashes. Crashes are clearly distinguished from near crashes by a higher criticality at LG end, as reflected by significantly shorter time headways and larger invTTC. However, this analysis does not tell to what extent this higher criticality when looking back is due to the duration of the last glance and to what extent it relates to the rate at which the kinematics changed during the glance. This question is addressed next. 7.4 Mismatch Mechanisms: Last Glance Duration Versus invttC Change rate For two kinematically identical rear-end scenarios, the LG duration could make the difference between a crash and a near crash; the longer the glance, the more time the criticality (e.g., invTTC) of the situation has to develop. Conversely, for two off-path glances of the same duration, the rate at which the criticality changes during the glances determines the crit- icality when looking back at the road. To analyze the relative contribution of these two factors to crash and near-crash risk, a multivariate logistic regression analysis was carried out for last glance (LG) duration and invTTC change rate. The invTTC change rate was computed as the slope of a linear function fitted to the invTTC data dur- ing the last glance (by means of the MATLAB robustfit func- tion), as illustrated in Figure 7.6. Figure 7.7 plots the distribution of LG duration and invTTC change rate for the three event types. It can be observed that Figure 7.5. Inverse time to collision (invTTC) at the onset and offset of the last glance by event type. Figure 7.6. Illustration of the calculation of invTTC change rate (c) as the slope of a linear function fitted to the invTTC data during the last glance off the forward path (event ID 10631432).

72 the mean LG duration and invTTC change rate are both higher for crashes than for near crashes although the distribu- tions overlap considerably. The multivariate logistic regression analysis assesses the effect of last glance duration and the invTTC change rate on the likelihood of a crash/near crash relative to the matched baselines. It should be kept in mind that this analysis excludes cases with no off-path glances. Hence, the models presented here represent the crash/near-crash likelihood only for cases in which the driver looked away at least once in the 8 seconds before the crash/minTTC. Due to the relatively large number of missing cases in the matched crash/near crash and matched baselines pairs, a mixed effect model, rather than conditional logistic regression model, was used. Table 7.3 summarizes the AIC criteria for six estimated models. The models are discussed in order, beginning at the bottom of the table. The first model is a null model that includes only the intercept. The second model includes only the LG duration (LGD), and the third includes only the invTTC change rate (CR). The fourth model includes a linear combination of LGD and CR, while the fifth model includes the interaction. The final model includes the linear combina- tion of CR and LG and the interaction term. The results show that all models are superior to the null model, but that LGD does not improve predictions beyond the effect of CR. The linear combination of CR and LG was not significantly better than the model including only CR. However, the model that includes the interaction LGD and CR was substantially better than the others. The obtained dif- ference in AIC of 14 between this and linear combination was relatively large. As a rule of thumb, models that have an AIC that is 10 units higher than the others can safely be removed from consideration (Burnham and Anderson 2004). The full model that included both the individual contributions of LGD and CR along with the interaction term had a slightly lower AIC (Delta AIC = 2.65). However, the difference was relatively small. Based on this analysis, it may be concluded that invTTC change rate during the last glance had a strong effect on crash/ near-crash risk while the individual effect of the glance dura- tion was much weaker. Moreover, invTTC change rate and glance duration interacted strongly—to the degree that addi- tional contribution of the individual invTTC rate and LG dura- tion factors is marginal. What the present analysis essentially Table 7.3. General Results from Multivariate Regression Analysis of the Effect of Last Glance Duration (LGD) and invTTC Change Rate (CR) on Crash/Near-Crash Risk Model AICc Delta AICc LGD.CR.LGD X CR 226.12 2.65 LGD X CR 228.77 14.08 CR.LG 242.85 1.72 CR 244.57 206.61 LGD 451.18 265.38 Null model 716.56 Figure 7.7. Distribution of last glance duration (left) and invTTC change rate (right) for the three event types.

73 shows is that, given that the driver looks away from the road within the 8 seconds before the crash, the risk that the event develops into a crash or near crash is mainly determined by the interaction of invTTC change rate and last glance duration. To gain further insight into this interaction between LG duration and the invTTC change rate during the last glance, the two variables were plotted against each other, as shown in Figure 7.8. It can be observed that the crashes, near crashes, and matched baselines are relatively well separated in this state space. In particular, the majority of the crashes and a subset of the near crashes are approximately linearly orga- nized with a negative slope. This is clearly the source of the strong interaction in the logistic regression analysis above. The key implication of this result is that the majority of the rear-end crashes in the present sample can be characterized in terms of a particular combination of LG duration and invTTC change rate. For a short glance away from the road, the change rate needs to be higher for a crash to occur. Con- versely, for a long glance, a lower change rate is sufficient to produce a crash. If the required combination of glance dura- tion and change rate is not present, the situation normally results in a near crash, as indicated by the large cluster of near crashes below the hypothetical boundary in Figure 7.8. However, a number of crashes do not fit this pattern. In particular, several crashes with low change rates cluster with the matched baselines and a significant portion of the near crashes. Moreover, some cases have moderate to high change rates but very short LG durations that tile up vertically to the left in the figure. To better understand the characteristics of these different clusters of crashes, the forward video record- ings for each crash were inspected together with correspond- ing time-series plots of glances and kinematics. This analysis suggests that the present crashes can be roughly divided into three main categories, also indicated in Figure 7.8 and further described below. Category 1: Inopportune Glance These crashes are the prototypical cases for the general mech- anism suggested by Tijerina et al. (2004) and constitute the bulk (about 60%) of the crashes in the subset analyzed here. In these cases, the driver does not expect the lead vehicle to brake and thus looks away from the road while the situation is not yet critical (when invTTC is close to zero). During the glance away, the lead vehicle initiates braking. The level of criticality the driver faces when looking back depends on the interaction between the duration of the glance and the rate at which the situation develops, yielding the linear organization with a negative slope in Figure 7.8. Inspection of videos and time-series plots indicated that the driver typically looked away just before the invTTC started to Figure 7.8. Last glance duration versus invTTC change rate. The ovals mark the three main categories of crashes identified through video inspection. The cases marked by squares are described in the text. The dashed line represents the hypothetical boundary for safe glances.

74 grow above zero. There was most often a strong violation of expectations; these events often occurred at junctions when the principal other vehicle (POV) would normally continue ahead but instead stopped suddenly and unexpectedly. The last glance was in some cases preceded by other glances that may have impaired the detection of visual cues that could have predicted the lead vehicle’s action. When the driver looked back the second-to-last time (i.e., at the end of the glance pre- ceding the last glance), the invTTC was generally close to zero or negative (in the latter case the lead vehicle accelerated away, which may have further enhanced the false expectation). The lead vehicle’s brake lights were often salient and, as indicated by the analysis in Table 7.1, often illuminated while the driver looked forward. However, as also shown above, these brake light onsets generally failed to influence the driver’s decision to take his or her eyes off the road. In the upper left region of Figure 7.8 (short glances, high change rate), there is some overlap with Category 2, in which the driver looked away when invTTC had already risen significantly above zero (see below). The cases at the lower right end of Category 1 of Fig- ure 7.8 (extreme LG duration, low change rate) are typically low-speed scenarios in which the driver looks away for an extensive period while the vehicle is moving very slowly toward a stationary POV (e.g., in stop-and-go traffic). An example of a representative Category 1 crash is given in Figure 7.9. This case is also marked in Figure 7.8. Category 2: Looking Away in an Already Critical Situation These cases represent situations in which the driver looks away at a point when the situation is already critical—that is, the vehicles are already closing and the invTTC has already risen significantly above zero. This typically involves a very brief glance (around 0.5 second) before the gaze is presum- ably redirected to the road by the strong looming cues. These cases constitute about 20% of the cases in Figure 7.8 (as men- tioned above, some of these cases overlap with Category 1). Based on the video inspection, there seem to be several potential reasons (which sometimes combine) for why the last glance was initiated even though the POV was closing. These include • Reduced visibility due to rain, darkness, or glare; • A fast approach while time sharing, leading to a small angu- lar rate (q-dot) when looking back before the last glance; • Intense visual time sharing with a short gap between the second-to-last and the last glance; and • A search for escape: The driver knows that he or she is on a collision course and looks to the sides/mirrors for an escape path. An example of a Category 2 crash is given in Figure 7.10. Category 3: Looking Away and Back Again Before the Situation Has Turned Critical Here the driver looks away and back again before the situation has turned critical, leading to a small change rate during the last glance and varying glance durations. Here the off-path glance(s) most likely did not interfere with the reaction to the event (although it may possibly have affected the detection of available predictive cues). Thus, these events can be regarded as functionally similar to crashes in which the drivers did not Figure 7.9. Example of a Category 1 crash (event ID 19147492). Figure 7.10. Example of a Category 2 crash (event ID 19147617).

75 look away at all within the 8-second window (these were excluded in the present analysis, as explained above). Video inspection revealed that Category 3 events typically involved a strong violation of expectation (e.g., the lead vehi- cle stops late at yellow light, or a traffic queue builds in front of the POV in an unexpected location). The driver’s reaction to the closing vehicle does not appear to be markedly delayed. Rather, an insufficient safety margin and/or a strong lead- vehicle deceleration rate seem to be key mechanisms behind these crashes. Moreover, the effectiveness of the avoidance maneuver may be a key factor separating crashes from near crashes in these events. A more detailed quantitative analysis is needed before any safe conclusions may be drawn. An exam- ple of a Category 3 crash is given in Figure 7.11. Summary The analysis in this section demonstrates that the majority of the rear-end crashes in the present subset are well explained by the general hypothesis stated above (based on Tijerina et al. 2004). These Category 1 crashes can be explained in terms of the co-occurrence of an off-path glance and a change in situ- ation kinematics (normally the lead vehicle initiating braking) that strongly violated the driver’s expectations. In line with Tijerina et al., the situation was generally kinematically non- critical at the moment when the driver looked away and then changed rapidly just after the driver looked away. Crashes in this category are generally distinguished from near crashes by the combination of last glance duration and the rate at which the situation changes during the glance away (here oper- ationalized as invTTC change rate). Thus, these crashes hap- pen largely due to a “perfect mismatch” between the visual attention to the forward roadway and the kinematics of the traffic situation, in line with the general mismatch model of driver inattention suggested by Engström, Monk et al. (2013). For a given glance duration, a certain minimum change rate is needed to produce a crash. Conversely, for a given change rate, the glance has to be sufficiently long for a crash to happen. This leads to the strong interaction between last glance dura- tion and invTTC change rate in influencing crash/near-crash risk observed in the multivariate logistic regression analysis. However, a number of crashes did not entirely fit this pat- tern. Category 2 crashes are characterized by the driver look- ing away for the last time at a moment when the situation was already kinematically critical (i.e., the distance between the two vehicles was already closing at LG start). This indicates that other factors than off-path glances affected the driver’s ability to detect the hazard. Video inspection suggested that, in particular, reduced visibility might be a key factor in this type of crash. This seems to be in line with the finding in Chapter 3 (Figure 3.6) that visual obstructions (in particular sunlight, precipitation, curve/hill, and broken or inappropri- ately cleaned windshield) are overrepresented in crashes. However, a more detailed and systematic analysis of these fac- tors is needed before any safe conclusions may be drawn. Finally, in the Category 3 crashes, drivers looked back before the situation had turned critical, and thus, the last glance did not directly contribute to the crash. In these crashes, an insuf- ficient safety margin (headway) in combination with a strong violation of expectation seems to be the key mechanism that led to the crash. This analysis thus provides one answer to what constitutes safer glances: As long as the combination of glance duration and change rate remains in the safe region under the hypo- thetical boundary indicated in Figure 7.8, the situation nor- mally does not result in Category 1 crashes. Minimizing the duration of off-path glances is naturally one way to achieve this. However, the present data show, in line with previous studies, that excessive glance durations are infrequent, even in crashes. The extreme glance durations (>4 seconds) in the present sample typically occurred at close to zero speed in stop-and-go situations. Of the crashes in Category 1, 50% occurred for glances shorter than 2 seconds, combined with a high change rate (there are also a number of similar cases in Category 2). Thus, an efficient strategy to protect oneself from Category 1 crashes is to ensure that the headway when looking away is sufficient while, at the same time, avoiding extreme glance durations. As can be observed in Figures 7.3 and 7.4, rear-end crashes with a time headway above 2 sec- onds at LG start were rare, and the average headway adopted at LG start was generally small, also in the baseline events. Therefore, a shift toward a more defensive driving style with larger adopted headways would have a very strong potential for preventing these types of crashes. Note that this strategy Figure 7.11. Example of a Category 3 crash (event ID 19147493).

76 does not apply to cut-in scenarios, which were excluded from the present analysis. What determines the location of the critical boundary for the Category 1 crashes? First, it is largely determined by vehi- cle’s braking capacity (given road surface conditions). The single crash not included in any of the categories in Figure 7.8 followed the general pattern of a Category 1 event. The invTTC consumed during the last glance would normally not have been sufficient to produce a crash; however, video inspection as well as the video annotation revealed that the driver was skidding with brake lockup (due to wet road surface), so the stopping distance was longer than usual. With a normal stop- ping distance, this crash would have ended up a near crash (like the other events that surround it). Thus, improvements in vehicle braking systems and roads that reduce stopping dis- tances would shift the boundary upward (i.e., requiring a greater change rate for a given last glance duration to produce a crash). Second, the boundary also depends on what the driver does after looking back to the forward path the last time. For exam- ple, did drivers that successfully avoided the crash react faster to the impending hazard after looking back than those who crashed? This topic is addressed in the following section. 7.5 What triggers Drivers’ responses after the Last Glance? So far, the focus has been on what happens before and during the final off-road glance, and how this differs between crashes, near crashes, and normal driving. A main insight has been that in many crashes (Category 1 in Figure 7.8) the amount of change in situation kinematics during the final off-path glance (as determined by the interaction between glance duration and kinematics change rate) seems to be a main factor separating these crashes from near crashes. However, there could also be differences between near crashes and crashes in what hap- pened after the final glance, a possibility that applies to all three categories of crashes in Figure 7.8. Investigating this possibility seems relevant, not the least for the crashes in Category 3, for which the analyses so far in this chapter have not shed any light on potential causes (other than some preliminary suggestions based on video inspection). This section looks specifically at the question of when drivers reacted to the rear-end situation, with the aim of answering the following questions: • When, in relation to the situation kinematics, did drivers react? Were there differences between near crashes and crashes in this respect? • Do POV brake lights predict timing of SV driver reaction? One tool used to answer these questions will be parameter- fitting and comparison of reaction timing models. The test of these models is in itself an additional aim here, since it is envi- sioned that they can be useful in future analyses. For example, they may be used in Monte Carlo simulations to extrapolate from the findings in this chapter by studying a wide range of hypothetical rear-end situations, or to address “what if” ques- tions about the SHRP 2 events. Throughout this section, driver reaction point refers to the manual annotation of “the first visible reaction of the SV driver to the POV [such as a] body movement, a change in facial expression, etc.” This point of driver reaction does not necessarily coincide exactly with the initiation of an evasive braking or steering maneuver; it was adopted here due to dif- ficulties in identifying the exact point of maneuver onset, partially caused by the lack of reliable data on pedal use (see Section 2.9). From manual inspection of the driver reaction point annotations, it is clear that in a great majority of cases this annotation is followed within some tenths of a second by signs of subject-vehicle deceleration (although there are some exceptions to this rule). The inclusion criteria adopted here (see Table 7.4) targeted the same type of scenarios as described above in this chapter, but they were stricter to allow parameter-fitting of models in the time plane. Matched baseline events were not included at all, since they did not have any annotated driver reaction points. The difference in exclusion rate between crashes and near crashes was mainly due to three criteria: (1) greater prevalence of events with >8 seconds driving with Eyes on Path before reaction among near crashes than crashes (Criterion 2), (2) lack of optical data all the way up to the point of extrapolated colli- sion (see next section) in 21 near-crash events (Criterion 3), and (3) a manual effort to inspect the quality of GPS speed data in crashes without CAN speed data, allowing inclusion of three crash events that would otherwise have been programmatically excluded (Criterion 4). Driver Reaction Timing, Situation Kinematics, and Brake Lights Figure 7.12 provides a first look at the extracted data, repre- senting each event as a vertical gray line. Each event line starts on the x-axis, at the event’s invTTC at end of last off-path glance (here and below denoted invTTCELG); passes through a black cross, showing the time from end of last glance to annotated driver reaction point; and ends at a blue dot, show- ing the time when a collision would have occurred, assuming the driver did not react at all and, in practice, defined as a constant SV speed from the annotated driver reaction point (same approach as in Chapter 8).

77 First, consider the actual driver reaction points (the black crosses). For both crashes and near crashes, two approximate regimes of behavior are discernible in this figure, to the left and right of an invTTCELG = 0.2 s-1 threshold: 1. A clear majority of the long times to reaction >1 second occurred for invTTCELG < 0.2 s-1 (seven out of eight for crashes; 27 out of 28 for near crashes). This is consistent with the observation in the previous section that in some events, more specifically those in Category 3 of Figure 7.8, the driver did not find anything to react to at the end of the last off-path glance. Indeed, all the crashes in Category 3 of Figure 7.8 have invTTCELG < 0.2 s-1. As a shorthand through- out this section, events with invTTCELG < 0.2 s-1 will be Table 7.4. Exclusion of Crashes and Near Crashes for the Analysis of Driver Reaction Timing Exclusion Criterion Crashes Excluded (% of total 46) Near Crashes Excluded (% of total 211) 1. No annotated reaction before collision 5a (11%) 0 2. Time from last off-path glance to reaction >8 seconds, or no off-path glances in event 3 (7%) 35 (17%) 3. Optical data not complete from end of last glance to extrapolated point of collision 3 (7%) 32 (15%) 4. No usable CAN or GPS SVspeed data (missing or with apparent synchronization issues) 1 (2%) 14 (7%) 5. Annotated reaction with driver’s eyes still off-path 0 9 (4%) 6. Other apparent problems with the optical angle data 0 3 (1%) 7. Annotated reaction after minimum distance point 0 1 (<1%) Total number of excluded events 12 (26%) 94 (45%) Total number of included events 34 117 a In four of these five crash events, the driver’s eyes were still off-path at collision. Figure 7.12. Inverse TTC at end of last glance (invTTCELG) versus time from end of last glance to the driver reaction point and to extrapolated collision. Threshold invTTCELG = 0.2 s1 is shown as a vertical dashed line; the regression line, fitted to reactions in crash events with invTTCELG > 0.2 s1, is shown as a red line in both panels. Eyes-off-threat crashes correspond to Categories 1 and 2 in Figure 7.8; eyes-on-threat crashes correspond to Category 3. -0.5 0 0.5 1 1.5 0 1 2 3 4 5 6 7 8 invTTC at end of last off-path glance (1/s) Ti m e fro m en d of la st of f-p at h gla nc e (s) Crashes (n = 34) -0.5 0 0.5 1 1.5 0 1 2 3 4 5 6 7 8 invTTC at end of last off-path glance (1/s) Ti m e fro m en d of la st of f-p at h gla nc e (s) Near-crashes (n = 117) Driver reaction Non-reaction collision Crash reaction regression Ey es -o n- th re at Ey es -o ff- th re at Ey es -o n- th re at Ey es -o ff- th re at

78 referred to as eyes-on-threat events, in line with the conclu- sion above in this chapter that in the Category 3 crashes, the rear-end threat arose after the last off-path glance. 2. A clear majority of all short times to reaction, ≤1 second, occurred for invTTCELG > 0.2 s-1 (25 out of 26 for crashes; 82 out of 89 for near crashes), suggesting situations in which a threat arose sometime before the end of the off- path glance, such that the driver found something to react to more or less immediately after the glance. Consistent with this idea, all the crashes in Categories 1 and 2 of Fig- ure 7.8 have invTTCELG > 0.2 s-1; throughout this section, events with invTTCELG > 0.2 s-1 will be referred to as eyes- off-threat events. For these events, there are significant decreases in time to reaction with increasing invTTCELG for both crashes [r = -0.52; t(24) = 2.96; p = 0.007; regres- sion line shown in both panels of Figure 7.12] and near crashes [r = -0.25; t(81) = 2.30; p = 0.024; regression line not shown in Figure 7.12]. Given the aims of this section, it is interesting to note that for eyes-off-threat near crashes (i.e., the near crashes with invTTCELG < 0.2 s-1), driver reaction points seem to group below the regression line for eyes-off-threat crashes (the red line in both panels of Figure 7.12). To verify this impression, deviations from this regression line were compared between crashes and near crashes; they were found to have signifi- cantly different averages [t(107) = -4.020; p = 0.0001], with near-crashing drivers reacting, on average, 0.19 seconds faster than what is predicted by the regression line for crashes. Next, consider the blue dots, showing the time after end of last off-path glance, of nonreaction collisions. This time dura- tion can be regarded as a crude estimate of situation urgency at end of last off-path glance, and there are two observations to be made here. First, the times to nonreaction collision seem shorter in crashes than in near crashes. If so, this would mean that not only was invTTCELG at end of last glance higher, on average, for crashes than for near crashes (as shown in Fig- ure 7.5), but also for a given invTTCELG the situation grew worse faster for crashes (e.g., due to larger POV decelerations). As a crude test of this possibility, times to nonreaction colli- sion in the invTTCELG interval [0.4, 0.7] s-1 (where there is a reasonable coverage of both crashes and near crashes) were compared and found to be lower for crashes (1.4 seconds) than for near crashes (1.7 seconds), but this difference is not statistically significant [t(48) = -1.268; p = 0.21]. A similar test for the eyes-on-threat crashes (with invTTCELG < 0.2 s-1) also comes up nonsignificant [average times to extrapolated colli- sion are 4.9 seconds for crashes and 4.7 seconds for near crashes; t(40) = 0.188; p = 0.85]. Second, it should be noted that in most crash events, there are time margins after the observed reaction point within which reaction could have occurred and still precede a collision, in some cases up to 2 seconds. This observation—as well as the observation of only one nonreaction collision with Eyes on Path among the 46 crashes in the total data set (see Table 7.4)— suggests that if a driver looks forward, he or she will generally react (at least in the sense of a first visible reaction) to a rear- end threat before the actual crash. This makes a very strong case for the hypothesis that situation kinematics (e.g., medi- ated by visual looming) have an effect on the timing of driver reactions. The analysis in Table 7.1 indicated that drivers in crashes and near crashes generally tended to ignore the onset of brake lights as a cue that the lead vehicle was likely to become a threat in the near future. Nonetheless, it is still possible that lead-vehicle brake lights influenced driver reactions once the situation became critical (i.e., after the end of the last glance). However, in most crashes (74%) and near crashes (79%), POV brake lights were on all the way from end of last glance to the driver reaction point, so it is clear from Figure 7.12 that, in general, drivers did not react within some fixed, situation- independent reaction time to the sight of already illuminated brake lights. Figure 7.13 shows driver reaction points in the (rather few) events in which one or more brake light onsets occurred between end of last glance and the driver reaction point; the figure also shows when in time the last brake light onset occurred (the start of the red lines). One interesting pos- sibility regarding the difference between crashes and near crashes starting at invTTCELG < 0.2 s-1 (i.e., the eyes-on-threat events, corresponding to Category 3 of Figure 7.8) would have been that near-crashing drivers in these events were more suc- cessful than crashing drivers at responding to brake light onsets. However, the data shown in Figure 7.13 do not provide any strong support for this idea. Among the five eyes-on- threat crashes, driver reaction came within 1 second after brake light onset in one case (20%). For near crashes, the same figure was seven cases out of 20 (35%), a difference that was not sta- tistically significant (p = 0.47; Fisher’s exact test). In the other crashes and near crashes shown in Figure 7.13, reaction came any time up to 6 or 7 seconds after the last brake light onset. This leaves the general impression that brake light onsets had rather little to do with the timing of driver reactions in the present crashes and near crashes. Thus, so far the results indicate that brake lights had a lim- ited effect on reaction timing but that reactions were instead strongly related to kinematics, at least in the sense that driver reaction occurred (with only one exception) before the actual crash, and typically with quite some time margin left to when a nonreacting driver would have crashed. Figure 7.14 pro- vides further insight into the relationship between kinematics and reactions, by showing both invTTC at end of last glance (on the x-axis) and invTTC at the driver reaction point, referred to here as invTTCR (on the y-axis). A diagonal y = x line is shown; a reaction on this line implies an event in which

79 Figure 7.13. As in Figure 7.12, but showing only events with one or more brake light onsets between end of last glance and the driver reaction point. The red stripes begin at the time of last brake light onset and, for clarity, end at the driver reaction point (regardless of whether or not the brake lights remained illuminated up to this point). -0.5 0 0.5 1 1.5 0 1 2 3 4 5 6 7 8 invTTC at end of last off-path glance (1/s) Ti m e fro m en d of la st o ff- pa th g lan ce (s ) Crashes (n = 5) -0.5 0 0.5 1 1.5 0 1 2 3 4 5 6 7 8 invTTC at end of last off-path glance (1/s) Ti m e fro m en d of la st o ff- pa th g lan ce (s ) Near-crashes (n = 21) Figure 7.14. invTTC at end of last off-path glance (invTTCELG) versus invTTC at the driver reaction point (invTTCR), for crashes and near crashes. Four red rings show driver reactions in the four near crashes when the driver talked/listened on cell phone (right panel): one cell phone event (at invTTCR ≈ 0.5) was included in the other analyses of this section; the other three were originally excluded (see Table 7.4) due to time to reaction over 8 seconds (one case), or to no optical cues available at the end of the last off-path glance (two cases; at invTTCELG = 0 since both were clear eyes-on-road Category 3 events). -0.5 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 invTTC at end of last off-path glance (1/s) in vT TC at dr iv er r ea ct io n (1/ s) Crashes (n = 34) -0.5 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 invTTC at end of last off-path glance (1/s) in vT TC at dr iv er r ea ct io n (1/ s) Near-crashes (n = 117) R ea ct io ns o cc ur a bo ve in vT TC th re sh ol d R ea ct io ns o cc ur ab ov e in v TT C th re sh ol d

80 invTTC was the same at end of last glance and reaction. As in Figure 7.12, there are signs of qualitative differences between eyes-on-threat and eyes-off-threat events, and there are traces of the same 0.2 s-1 threshold for invTTCR. In the figure, both of these thresholds are shown, as one vertical and one hori- zontal line. 1. To the left of the vertical line in the figure—that is, for the eyes-on-threat events (with invTTCELG < 0.2 s-1)—there is a vertical gap from the diagonal y = x line up to the hori- zontal line, above which almost all reactions occur, with some variability. This signifies that in both crashes and near crashes, reactions generally did not occur before the kinematics had evolved to at least a level of 0.2 s-1 invTTC. Specifically, for these crashes and near crashes, average invTTCR was 0.49 s-1 and 0.45 s-1, respectively, a non- significant difference [t(40) = 0.479; p = 0.63]. 2. To the right of the vertical line—that is, for the eyes-off- threat events (with invTTCELG > 0.2 s-1)—driver reactions are present directly from the diagonal y = x line, again with variability, creating a diagonal band of points in the plot both for crashes and near crashes. This band seems to have a larger vertical spread for crashes than for near crashes. Indeed, the average of invTTCR - invTTCELG—that is, the height of reactions over the y = x line—was significantly larger [t(107) = 6.182 < p 0.0001] for crashes (0.32 s-1 average increase) than for near crashes (0.13 s-1 average increase). In other words, even for comparable situation kinematics at end of last glance, crashing drivers reacted, on average, at a point in time with more severe kinematics than near-crashing drivers. Another way of formulating this last result is that, on aver- age, in eyes-off-threat events, the situation changed more for the worse in crashes than in near crashes during the time interval from end of last glance to the driver reaction point. This is analogous to what was found in the previous section regarding changes in kinematics during the last off-path glance, and again both time (here, time to reaction) and kine- matics change rate could play a role. Here, it has already been observed, in relation to Figure 7.12, that for eyes-off-threat events, driver reactions were, on average, significantly slower in crashes than in near crashes and that there was a possible nonsignificant trend of times to extrapolated collision being shorter in crashes than in near crashes (implying a faster kine- matics change rate). Both of these observations align with the observed difference in total change in invTTC from end of last glance to the driver reaction point. Driver Reactions When Talking/ Listening on a Cell Phone Several naturalistic driving studies have found cell phone conversation to have a protective effect (Olson et al. 2009; Hickman et al. 2010). The present study found an even stronger protective effect, with an odds ratio for Talking/ Listening on Cell Phone of 0.1 (see Chapter 4). To investigate to what extent this effect is related to changes in driver reac- tions induced by phone conversation, the four near-crash events in which the driver was coded as Talking/Listening on Cell Phone are plotted in the right panel of Figure 7.14 along with the other events in which the driver was not in a phone conversation. (As described in Chapter 4, there were no crashes in the present sample coded as Talking/Listening on Cell Phone.) First, it may be noted that all four talking/listening near crashes are of the eyes-on-threat type (i.e., Category 3). Sec- ond, as can be observed in Figure 7.14, there are no indica- tions that the cell phone conversation affects reactions to the rear-end threat; these drivers react at about the same kine- matic severities as the other nearly crashing drivers. Average invTTCR for the four talking/listening drivers was 0.38 s-1, which is actually lower than the average 0.45 s-1 for the other eyes-on-threat near crashes. However, the difference was nonsignificant [t(35) = -0.708; p = 0.48]. Underlying Mechanisms and Model-Fitting Driver reactions in the SHRP 2 crashes and near crashes are strongly associated with situation kinematics. Reactions are almost never observed for invTTC below 0.2 s-1, but above this threshold, reactions almost always occur before collision. In practice this means that at progressively higher invTTCELG, the reactions are progressively faster. A candidate mechanism that could account for this set of observations is called evidence accumulation. In psychology and neuroscience, some models assume that overt actions are triggered once evidence for their suitability has accumulated to a threshold (also known as diffusion or race models). These models have been found to account well for reaction-time dis- tributions in a wide variety of tasks (Gold and Shadlen 2007; Ratcliff and Van Dongen 2011), including brake reactions to expected activations of lead-vehicle brake lights (Ratcliff and Strayer 2013). Potential neural correlates of such processes have also been identified (Gold and Shadlen 2007; Purcell et al. 2010). Markkula (2014) hypothesized that timing of brake responses in driving could be driven by accumulation of the various cues that signal the possible need for decel- eration (e.g., contextual, augmenting, and primary cues, in the terminology of Tijerina et al. 2004). Here, using the same type of accumulator as Markkula (2014) and, for simplicity, assuming accumulation of invTTC, driver reaction could be hypothesized to occur when an activation A(t) ≥ 0, changing over time as ( ) ( ) ( )= − + εinvTTC (7.1)dA t dt t M t

81 has risen above a threshold At. Here invTTC is used, but inverse Tau could equally be used. (Here, these two are the same; see above in this section. Also see, for example, Flach et al. 2004, Kiefer et al. 2005, and Fajen 2007 for alternative visual cues to consider.) Markkula (2014) suggested that the model parameter M could be regarded as the sum of the influence from all other cues (e.g., contextual cues) and that it therefore could be affected by factors such as attention or expectancy. e(t) is a noise term (e.g., normally distributed) that relates to inherent variability in underlying neural activ- ity. For a given parameterization of the model as formulated above: • No reactions will be generated as long as invTTC is suffi- ciently below M [sufficiently below given the variability of e(t)]; and • Above M, larger values of invTTC will cause activation to reach threshold faster. In other words, qualitatively, the model is completely in line with what has been observed here. To test these ideas in practice, the model in Equation 7.1 was parameter-fitted to the crash and near-crash data sepa- rately, by means of a genetic algorithm (GA) optimizing parameters to minimize DRMS, the root mean square deviation between observed and predicted times of reaction (Wahde 2008). e(t) = 0 to allow this type of deterministic simulation and model-fitting (rather than, for example, maximum likeli- hood model-fitting). This approach can provide a first idea of the usefulness of the model, but perfect fits should not be expected. A deterministic model with one shared parameter- ization for all events cannot at all account for natural variabil- ity in reaction times [nonzero e(t)] or for variations between events in driver attention or expectancy (varying M). For each event, the model was fed the invTTC history start- ing from end of last glance. To allow meaningful fitting of model reactions occurring later than the observed reactions, the effect of driver avoidance maneuvering on invTTC was removed, as mentioned above, by assuming a constant SV vehicle speed after the annotated point of driver reaction. To reduce the risk of obtaining local optima, each optimization was repeated three times, with 500 GA generations in each repetition, and reasonable optimization convergence was sub- jectively verified by inspection of model-fit time histories. Figure 7.14 shows the fit of the model to the crash and near-crash data, together with the coefficients of determina- tion R2, interpretable as the amount of variance explained by the model, computed as ∑ ∑ ( ) ( )= − = − − − 1 12 , , 2 , 2R SS SS T T T T E T i model i observedi i observed observedi where Ti,observed are the observed times to reaction, with average T – observed, and Ti,model are the corresponding model predictions. Negative values for R2 thus imply that the model produces larger prediction errors than what would be obtained for a fixed prediction Ti,model = T – observed for all events. Figure 7.15 shows that for both crashes and near crashes, the accumulator model is rather successful at predicting times to reaction (R2 = 0.95 and R2 = 0.93, respectively, root mean square error of predicted reaction timing DRMS ≈ 0.4 second) when considering the entire sets of data, in which the vari- ability is dominated by the long times to reaction of the eyes- on-threat crashes. If singling out only the shorter times to reaction of the eyes-off-threat crashes (invTTCELG > 0.2 s-1; bottom left panel of Figure 7.15), the coefficient of determina- tion is more modest (R2 = 0.24), but note that it is comparable to what was obtained for the linear correlation in Figure 7.12 (R2 = 0.27). This can be interpreted as the model indeed pro- viding a possible underlying mechanism behind that linear correlation, but not having any further explanatory power beyond it (and, as mentioned above, no means of accounting for, for example, variations in attention or expectancy). When fitting the model only to the eyes-off-threat events, a slightly better fit, with DRMS = 0.24 seconds and R2 = 0.28, was obtained. For the eyes-off-threat near crashes, the linear correlation in Figure 7.12, was, although statistically significant, even weaker than for the crashes (R2 = 0.06). As is clear from Fig- ure 7.14 (bottom right panel), this weak correlation was not recreated by the accumulator model. Also, fitting only to the invTTCELG > 0.2 s-1 subset yielded an improved model fit, DRMS = 0.20 seconds, though still with a negative coefficient of determination (R2 = -0.04). That the accumulator model was less able to fit the times to reaction in eyes-off-threat near crashes than in eyes-off-threat crashes could imply there were some differences in mecha- nisms between these crashes and near crashes which the model doesn’t cover. Another possibility might be that a type of selec- tion bias comes into play, making any signs of evidence accu- mulation difficult to discern. Driver reactions in the crash events did not seem tightly constrained by the need to lead to collisions to be included in the data set (as discussed in relation to Figure 7.12). However, reaction timing in near crashes was constrained both from above (must be early enough to avoid crash) and from below (must be late enough to generate a near crash). In other words, the SHRP 2 vehicles may have been involved in many driving events with similar kinematics to the near-crash events, but those did not register as near crashes because the driver happened to react slightly faster (in the terms of the model, due to favorable e, or a lower M), or they registered as a crash because of a slightly later reaction. If so, this could mean that variability in observed near-crash driver reactions may be dictated more by the kinematic constraints of near-crash-detecting triggers and crash-avoidance feasibility, than by actual driver behavior phenomena.

82 As a contrast to the accumulator model, another two- parameter model was also fitted that predicts a driver reac- tion and a fixed reaction-time delay TR after passing an invTTC threshold. At long times to reaction, this model closely approximates the accumulator model (with M as the invTTC threshold, and accumulation to At as a delay). As could therefore be expected, this simpler model also worked well for the eyes-on-threat events, with long times to reaction (overall DRMS = 0.38 seconds and R2 = 0.94 for crashes; DRMS = 0.43 seconds and R2 = 0.94 for near crashes). However, for the shorter times to reaction of the eyes-off-threat events, this model will almost always predict a time to reaction of TR, yielding poor fits (DRMS = 0.29 seconds and R2 = -0.04 for crashes; DRMS = 0.33 seconds and R2 = -1.74 for near crashes) and reinforcing the idea that something akin to evidence accumulation is needed to explain the effect of situation kinematics on times to reaction in eyes-off-threat events. Finally, consider the parameter values obtained for the accu- mulator model when fitted to crashes and near crashes. The mere observation that the parameter values differ does not provide much information, since M and At are to some extent redundant (a higher M can be partially compensated for by a lower At, and vice versa). Therefore, analogously to what was done for the linear correlation in Figure 7.12, Figure 7.16 shows the results of applying the accumulator model obtained for near crashes to the crash events. For the eyes-off-threat crashes, Figure 7.15. Fits of the accumulator model to observed reactions, in crashes and near crashes. The top two panels show full sets of data used for model-fitting. The bottom two graphs provide a zoomed-in view of the events with invTTC at end of the last glance > 0.2 s1. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Crashes (n = 34) M = 0.080; At = 0.228 RMS = 0.35 s; R 2 = 0.95 Observed time to reaction (s) Pr ed ic te d tim e to re ac tio n (s) 0 2 4 6 8 10 0 2 4 6 8 10 Near-crashes (n = 117) M = 0.271; At = 0.044 RMS = 0.45 s; R 2 = 0.93 Observed time to reaction (s) Pr ed ic te d tim e to re ac tio n (s) -0.5 0 0.5 1 1.5 -0.5 0 0.5 1 1.5 Crashes with invTTCELG > 0.2 s -1 (n = 26) M = 0.080; At = 0.228 RMS = 0.25 s; R 2 = 0.24 Observed time to reaction (s) Pr ed ic te d tim e to re ac tio n (s) -0.5 0 0.5 1 1.5 2 2.5 -0.5 0 0.5 1 1.5 2 2.5 Near-crashes with invTTCELG > 0.2 s -1 (n = 83) M = 0.271; At = 0.044 RMS = 0.36 s; R 2 = -2.28 Observed time to reaction (s) Pr ed ic te d tim e to re ac tio n (s)

83 with short times to reaction, the model fitted to near crashes predicted faster reactions than the model fitted to crashes, and the average difference of 0.22 seconds is well in line with the 0.19 seconds difference observed in relation to Figure 7.12. For the eyes-on-threat crashes, with longer times to reaction, pre- diction deviations went in both directions, adding up to the near-crash model predicting, on average, 0.01-second shorter times to reaction. This is in line with the apparent lack of dif- ference in reaction timing between eyes-on-threat crashes and near crashes observed in Figure 7.14. Summary In conclusion, it has been shown that driver reactions in the SHRP 2 crashes and near crashes were not notably affected by POV brake lights but were instead strongly coupled to situa- tion kinematics. It was found that the categories of crashes in Figure 7.8 could be neatly separated by a threshold of invTT- CELG at end of last off-path glance: the eyes-off-threat crashes (Categories 1 and 2) all had invTTCELG > 0.2 s-1, and the eyes- on-threat crashes (Category 3) all had invTTCELG < 0.2 s-1. For eyes-on-threat events (both crashes and near crashes), very few reactions occurred before reaching an invTTC of at least 0.2 s-1. This means the reaction could occur an arbitrarily long time after the last off-path glance. In contrast, for eyes-off- threat events (again, both crashes and near crashes), the driver reactions almost always came within a second, and almost always before the crash, in practice implying that reactions were faster in situations with high invTTCELG. It has been explained that an accumulator model of reac- tion timing, accumulating invTTC once invTTC has reached a minimum threshold, would, qualitatively, predict exactly these observations (no reactions below an invTTC threshold, and progressively faster reactions above it). In actual model- fitting to the observed reactions, a simple two-parameter accumulator was found to account acceptably well for reac- tion variability in crash events (both eyes-off-threat and eyes- on-threat) and in eyes-on-threat near-crash events, but not in eyes-off-threat near crashes. This could possibly relate to issues of selection bias, which make model-fitting to this type of naturalistic data challenging in general. There are clear signs that, for eyes-off-threat events, near- crashing drivers reacted, on average, about 0.2 second faster than crashing drivers, and there are possible indications that the crash events in this regime also evolved to higher severity faster than comparable near crashes. This implies that causa- tion of eyes-off-threat crashes could be further understood as involving (a) kinematics that changed faster than in similar near crashes after the end of the last off-path glance (not sta- tistically proven here), and (b) drivers that for some reason had slower reactions (statistically significant). These slower driver reactions could be a result of natural variability in reac- tion timing, such that slightly slower reactions happened to lead to crashes, and slightly faster reactions did not. However, the descriptive data analysis (Chapter 3) identifies a number of factors that were overrepresented in crashes, such as young age, rain, and visual obstructions—factors that could be hypothesized to be associated with slower reactions in critical situations. Another factor that could be expected to influence driver reactions is the degree to which the driver’s expectancy was violated (Green 2000); it is possible that crashes on aver- age involved situations in which the driver was more certain that the lead vehicle would not brake, leading to a longer time to reaction. Finally, one aspect which has not been considered in the analyses presented here is the possibility of drivers acquiring some information about the impending rear-end situation via peripheral vision (Lamble et al. 1999; Markkula, 2014). This could be needed to convincingly explain some of the very short and even zero times to reaction occurring in some eyes-off-threat events, especially in near crashes. For the eyes-on-threat crashes, the analyses in this section did not identify any specific differences from comparable near crashes that could serve as clues regarding crash causation. No clear signs were found of slower reactions from crashing driv- ers or of situation kinematics evolving faster in crashes than in near crashes. Moreover, drivers involved in cell phone conver- sation did not respond at higher invTTC (looming) values than the other near-crash-involved drivers. Overall, these results suggest that what separates eyes-on-threat crashes Figure 7.16. Comparison of fits of crash data for the crash model (gray crosses, same as in top left panel of Figure 7.15) and the near- crash model (blue crosses, same parameters as in top right panel of Figure 7.15). 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Crashes (n = 34) M = 0.271; At = 0.044 RMS = 0.42 s; R 2 = 0.93 Observed time to reaction (s) Pr ed ic te d tim e to re ac tio n (s)

84 from comparable near crashes may be related to failures to apply crash-avoidance braking or steering maneuvers after the point of driver reaction. This could involve differences in the time from observed driver reaction (such as studied here) to initiation of actual maneuvering, but also differences in factors such as actual maneuvering capacity of the vehicle on the road (e.g., relating to vehicle brakes, road surface friction), space available for lateral maneuvering, or the extent to which the drivers used the full maneuvering capacities of the vehicle. 7.6 Conclusions The present analysis has yielded several novel insights on the role of glance timing relative to external events in rear-end crashes. The main conclusions are summarized and discussed below. Conclusion 1: Brake Lights Have a Limited Impact on Driver Behavior in Rear-End Situations The present results indicate that the timing relationship between brake light onsets and off-path glances does not have any impact on whether the situation develops into a safety- critical event. In fact, co-occurrences between Eyes off Path and brake light onsets were less prevalent in crashes com- pared with near crashes and matched baselines. Moreover, brake light onsets occurring while the driver looked forward were generally ignored and do not seem to have influenced the willingness of the driver to take his or her eyes off the road. Finally, as further discussed below, there was no indica- tion that drivers reacted to brake light onsets after looking back to the road for the last time. One possible explanation for why many drivers in the pres- ent sample seem to have ignored brake light onsets is based on the notion that their predictive value could be limited. Brake light onsets are very common in noncritical situations; as indi- cated in Table 7.1, 32% of the matched baselines in the present sample included brake light onsets. Thus, the great majority of brake light onsets that drivers are exposed to are not associated with any real threat. This may lead to a “cry-wolf” effect such that evidence from brake lights is taken more lightly than, for example, the detection of a closing lead vehicle. In the present crashes and near crashes, strong expectations that the lead vehi- cle would not brake may thus have overridden the relatively weak evidence from the brake light onset that the lead vehicle might become a threat in the near future. Drivers about to crash were more likely than near-crash and baseline drivers to look ahead when the brake lights illuminated, and also more likely to look away in the next moment. One possible explanation for this somewhat coun- terintuitive finding is that the phenomenon occurs as an indirect consequence of the way rear-end crashes typically happen. As described above (and further discussed below), a large portion of rear-end crashes (Category 1) occur because of a particular combination of glance duration and the rate at which the criticality changes (measured here in terms of invTTC change rate). For this to happen, the driver must often look away precisely at the wrong moment, that is, just after the invTTC has started to rise. Since the last brake light onset often occurs just before the rise in invTTC, it will often also occur at a moment when the driver looks ahead. Fig- ure 7.1 provided two examples, and there were many similar cases among the Category 1 crashes. It should be noted that this does not mean that drivers never use brake lights as a cue for initiating braking. On the contrary, early responses to brake lights may have been a key reason that many potentially critical scenarios did not end up as crashes and near crashes in the present sample. However, as suggested by the cry-wolf effect described above, strong expec- tations induced by other cues and/or a strong motivation to engage in a secondary task may easily override evidence from brake light onset that the lead vehicle is about to close. An issue that has not been systematically addressed in the present analysis is the saliency of the brake lights. Here it was generally assumed that the brake light onset was perceived when the driver was looking ahead and missed when looking away. However, this may not always be the case since detec- tion also depends on the saliency of the brake lights, which may be strongly reduced, for example, due to strong sunlight. As mentioned above, video inspection of the Category 1 crashes indicated that the driver often looked away despite a very salient brake light onset. However, a more systematic analysis is needed to better understand the role of brake light saliency in this context. Conclusion 2: Most Rear-End Crashes Are Characterized by a Mismatch Between Duration of the Last Glance and the Change Rate of the Situation Kinematics The present analysis revealed, for the first time, how the driv- er’s visual behavior and the situation kinematics interact to produce rear-end crashes, yielding a distinct pattern that characterizes the majority of crashes in the present sample (i.e., those belonging to Category 1 in Figure 7.8, and exem- plified in Figures 7.9 and 7.12). These crashes happen because of a rapid change in situation kinematics, often occurring just after the driver has taken his or her eyes off the road. The crash mechanism is constrained by the fact that drivers nor- mally do not take their eyes off the forward roadway if they detect that the lead vehicle is closing (Tijerina et al. 2004). Thus, the kinematic situation is perceived as normal when the driver looks away but has turned critical when the driver looks back. This can thus be understood in terms of a mis- match model of driver inattention (Engström, Monk et al.

85 2013), in which the duration of the last glance and the invTTC change rate combine into a “perfect mismatch” that produces the crash. If one of the two constraints is not met (e.g., the glance is too short or the change rate is too low), the situation will end up in a near crash or may not turn critical at all. This mechanism results in the linear organization of Cat- egory 1 crashes in Figure 7.8. One way to look at this phe- nomenon is as the result of a natural variability in situation kinematics in vehicle-following situations and the driver’s (learned) ability to control it. The driver’s decision to take his or her eyes off the road is largely guided by expectation. Thus, long glances are very infrequent because the driving situation normally does not permit them. Similarly, very rapidly chang- ing kinematics in vehicle-following situations are also infre- quent (because the lead-vehicle drivers are also good at controlling variability). Thus, the probability of Category 1 rear-end crashes can be understood in terms of a joint prob- ability distribution of off-path glance durations and kine- matics change rates. Long off-path glances require only a low change rate for a crash to happen, while short glances require high rates. The pattern observed in Figure 7.8 emerges because long glances and fast change rates are both rare, and the points along this line represent the combinations with the highest joint probability. The present limited sample of crashes mainly contains low-severity crashes on the border of the near-crash region. With a larger sample, containing more severe cases, the crashes would be expected to be less linearly organized, featuring the more rare—and severe—combinations of long glances and fast kinematics. The present data suggest a hypothetical boundary for what characterizes safe glances (see Figure 7.8). Off-road glances and change rates below this line are unlikely to produce a crash. However, the key problem is that the variability in situ- ation kinematics is only partially controlled by the driver. One important implication of the present results is that the major- ity of Category 1 and Category 2 crashes are produced by rela- tively short glances (<2 seconds). Thus, even in the hypothetical situation in which all glances longer than 2 seconds are elimi- nated, the majority of crashes directly caused by off-path glances would remain (all other things being equal). A simple and efficient strategy for counteracting these cat- egories would be to increase headway; very few Category 1 or 2 crashes happened at initial headways (at LG start) larger than 2 seconds. Moreover, the present analysis showed that the lead vehicle often initiated braking just before the driver looked away, as indicated by the frequent occurrence of brake light onsets while the driver was still looking forward (e.g., the cases plotted in Figure 7.16). However, the driver often ignored the brake lights and looked away just before strong looming cues (indicating closing of the lead vehicle) started to appear. Thus, if the driver could be reliably alerted already at the point when the lead vehicle initiates braking (in some way other than by the lead vehicle’s brake lights, which seem to have lost their predictive value due to the cry-wolf effect), many of the critical off-path glances could likely be elimi- nated. Collision warnings enabled by V2X technology should have a great potential in this context. Although the majority of the present crashes could be explained by the mechanism just discussed, the results also pointed to other mechanisms behind rear-end crashes. In particular, in the Category 2 crashes, drivers typically failed to detect that the lead vehicle was already closing and eventually looked away from the road, thus further delaying their reac- tion. The preliminary video inspection pointed to reduced visibility as a key factor in these cases, but a more systematic analysis is needed to establish this. Finally, in a significant portion of the present crashes, grouped as Category 3 and characterized as eyes-on-threat, the off-road glance did not have anything to do with the driv- er’s reaction. These crashes are thus functionally similar to crashes in which the driver did not look away at all before the crash. Further analysis is needed to determine the key factors behind these crashes, although some initial speculations were offered above. Conclusion 3: Driver Reactions Are Coupled to the (Perceived) Situation Kinematics A key insight from the analysis of driver reactions is that reac- tions in critical situations are strongly coupled to the situa- tion kinematics. As mentioned above, this analysis further demonstrated that neither the drivers who crashed nor those ending up in near crashes appeared to have responded to brake light onsets that occurred after looking back. (Note, however, that the number of cases with a brake light onset occurring after the last glance back was relatively limited.) Rather, the present results indicate that the moment when the driver reacts is mainly determined by the presence of suffi- ciently strong optical cues indicating that the lead vehicle is closing. The analysis indicates that drivers with their eyes on the road did not react until the criticality of the situation was sufficiently high, as mediated by visual looming. The present data for crashes and near crashes indicate an invTTC (or 1/t) threshold of roughly 0.2, below which drivers did not seem to react. While both this finding and the lack of reaction to brake lights can possibly be explained in terms of selection bias (drivers ended up in these crashes and near crashes pre- cisely because they did not react earlier), a key further find- ing, not affected by selection bias, was that all but one driver did react after passing the 0.2 invTTC threshold. This last result has important consequences for how to deal with the concept of reaction time in naturalistic data. In previ- ous studies of near-crash and crash events (e.g., in simulation models), many researchers have assumed a constant, situation- independent distribution of driver reaction times to the situa- tion itself (Sugimoto and Sauer 2005; Kusano and Gabler

86 2012). The present results indicate that such an assumption is inadequate. Rather, a model of driver reactions in critical rear- end situations must account for the fact that drivers react when the situation is perceived as sufficiently critical (e.g., when looming information has accumulated above a thresh- old). In the present eyes-on-threat situations (Category 3), the reaction time largely depended on the moment when the driver looked back to the road for the last time and the way the kinematics developed, rather than on a driver-inherent reaction time. Thus, the concept of reaction time is generally meaningless in naturalistic driving analysis—except in specific types of situations (such as the current eyes-off-threat cases in Categories 1 and 2) in which the driver looks back at a moment when invTTC has risen above the critical threshold. Another key finding was that reactions in eyes-off-threat situations were generally faster for near crashes than for crashes. It is not possible to determine whether this reflects an actual difference in reaction performance between crash- and near-crash-involved drivers or just a selection bias operating on a natural variability in time to reaction; however, this result at least indicates that small differences in the time to reaction after looking back to the road sometimes determine whether the event results in a crash or a near crash. Finally, the specific analysis of reaction timing in the four near crashes in which the driver was Talking/Listening on Cell Phone did not indicate any significant difference in reaction performance to the other near crashes. If, as suggested by experimental studies (e.g., Brookhuis et al. 1991; Alm and Nilsson 1995; Strayer et al. 2003; Strayer and Drews 2004; Strayer et al. 2006), cell phone conversation induces reaction delays critical for road safety, drivers on the phone would be expected to react markedly slower (i.e., at higher invTTC) than the average near-crash driver. It is of course difficult to draw any safe conclusions on the basis of just four cases, but there is no sign of such an effect in these data. If anything, the invTTC values at which these drivers reacted were slightly lower than average. However, the general results from the reaction analysis have further implications for the generalizability of results from experimental studies on cell phone conversation to the real world. Most of these studies have used reactions to the lead-vehicle brake lights as the key performance measure. However, as demonstrated by the present analysis, drivers do not seem to react to brake lights in naturalistic rear-end situ- ations but rather to the situation kinematics, mediated by visual looming. Thus, whether the cognitive load induced by cell phone conversation delays reactions to brake lights might be irrelevant for understanding reactions to looming in real- world situations. In fact, the few experimental lead-vehicle braking studies on cognitive load in which the brake lights were turned off (Muttart et al. 2007) or using other looming stimuli (Baumann et al. 2008) have generally found a null effect of cognitive load on driver reaction performance. This does not explain the protective effect found in the present study (Section 4.1) as well as previous naturalistic driving studies. But it may at least suggest a reason why talking/listening does not increase crash risk in naturalistic rear-end crashes, as would be predicted by the experimental results. Conclusion 4: Modeling Driver Reactions on the Basis of Naturalistic Data Is Feasible Initial attempts to model driver reactions based on evidence accumulation were partly successful. First, such a model con- ceptually accounts for the general observed patterns: reactions do not occur while there is no looming (as observed in the eyes-on-threat cases), but reactions nevertheless almost always occur before crash, that is, faster in more severe situations (as observed in the eyes-off-threat cases). Thus, this type of model is clearly superior to naïve models that assume a constant reac- tion time to the situation as such, or to brake lights. The model also did a reasonably good job in capturing the fine-grained variance in eyes-off-threat cases in which the driver looks back to the road when looming cues are already present. However, the model did not capture all the variance in these reactions; this is not surprising given the multitude of factors that possi- bly influence time to reaction at this scale (e.g., visibility, the eccentricity of the off-path glances, individual variation). The proposed model is still potentially useful for simulating driver reactions in computer simulations of the phenomena investi- gated here. A particularly promising application area is what-if simulations, such as those described in Chapter 8, or the evalu- ation of active safety systems [e.g., forward collision warning (FCW) and autonomous emergency braking (AEB) systems]. Further Work While the present analysis has yielded several new insights on the relationship between the last off-path glance and situa- tion kinematics/visual cues, a fundamental question remains: Why did the driver take his or her eyes off the road at that inopportune moment in time? This decision might be gov- erned by a balance between (1) the motivation to perform a secondary task and (2) expectations on how the situation will develop. Expectations derive from the driver’s current under- standing of the situation, which, in turn, depends on the per- ception of relevant contextual cues (such as a traffic queue building up ahead or a red light). Glances away from the for- ward path very likely impair the detection of such contextual cues, leaving the driver with an inadequate understanding of the situation and possibly increasing the risk that an inop- portune glance will coincide with sudden braking by the lead vehicle. One way to address this issue is through video-based analysis using a dedicated coding scheme. See Engström, Werneke et al. (2013) for the first step in this direction.

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TRB’s second Strategic Highway Research Program (SHRP 2) Report S2-S08A-RW-1: Analysis of Naturalistic Driving Study Data: Safer Glances, Driver Inattention, and Crash Risk explores the relationship between driver inattention and crash risk in lead-vehicle precrash scenarios (corresponding to rear-end crashes).

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