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Annual Proceedings / Association for the Advancement of Automotive Medicine logoLink to Annual Proceedings / Association for the Advancement of Automotive Medicine
. 2007;51:363–379.

A Weighted Logistic Regression Analysis for Predicting the Odds of Head/Face and Neck Injuries During Rollover Crashes

Jingwen Hu 1, Clifford C Chou 1, King H Yang 1, Albert I King 1
PMCID: PMC3217522  PMID: 18184502

Abstract

A weighted logistic regression with careful selection of crash, vehicle, occupant and injury data and sequentially adjusting the covariants, was used to investigate the predictors of the odds of head/face and neck (HFN) injuries during rollovers. The results show that unbelted occupants have statistically significant higher HFN injury risks than belted occupants. Age, number of quarter-turns, rollover initiation type, maximum lateral deformation adjacent to the occupant, A-pillar and B-pillar deformation are significant predictors of HFN injury odds for belted occupants. Age, rollover leading side and windshield header deformation are significant predictors of HFN injury odds for unbelted occupants. The results also show that the significant predictors are different between head/face (HF) and neck injury odds, indicating the injury mechanisms of HF and neck injuries are different.

Rollovers are generally multi-directional and include both linear and rotational accelerations, resulting in more complex vehicle and occupant kinematics than those seen in frontal and side crashes. Moreover, rollovers can be initiated by various types of road conditions, induce multiple contacts between the occupants and interior, and lead to complicated vehicle deformations, all of which make it very difficult to investigate the injury mechanisms associated with rollovers.

For the past decade, many field data analyses have been conducted to investigate the injury mechanisms and the main factors affecting injury risks during rollovers. Rollover leading side [Parenteau et al. 2000; Parenteau et al. 2001; Digges et al. 2005a], number of quarter-turns [Parenteau et al. 2000; Padmanaban et al. 2002], number of potential roof impacts [Digges et al. 2005b], rollover initiation type [Parenteau et al. 2003], occupant headroom reduction [Rains et al. 1995], average roof deformation [Friedman et al. 1998], seatbelt usage [Parenteau et al. 2000; Padmanaban et al. 2002; Digges et al. 2005b], occupant ejection status [Parenteau et al. 2000; Digges et al. 2005b], occupant age and gender [Padmanaban et al. 2005c; Conroy et al. 2006] have all been reported to be associated with occupant injury risks. Unfortunately, many research results were contradictory. For example, Rains et al. (1995) reported that pre-crash headroom is an important indicator of the risk to head injuries. However, Padmanaban et al. (2005c) found that the relationship between the pre-crash headroom and occupant injury risk was not statistically significant.

The following reasons may account for the discrepancies in the previous studies:

  1. Data selection: Rollovers are complex and chaotic in nature. To investigate the influence of a specific factor, a relatively large sample size is needed to achieve statistically significant results. An early study, using only 21 rollover crashes [Lund et al. 1999], had, in our opinion, too small a sample size to identify any meaningful association between influential factors and injury risk. Furthermore, cases selected for analysis should be sampled randomly to represent the whole population of rollover cases. With this criterion, the study using 273 NASS-CDS rollover crashes with only 6+ inches of roof deformation identified by NHTSA [Nash et al. 2005] was not appropriate for the investigation of the relationship between roof deformation and injury risk.

  2. Data processing: Most previous field data analyses were presented as single values without any confidence intervals or levels of statistical significance. While statistical methods cannot generate new relationships, they can be used to provide a better estimate of the strength of the relationships between risk factors and outcomes. In addition, some previous studies presented only special rollover cases that supported the authors’ hypotheses [Nash et al. 2005]. This approach can be very misleading since different cases generate entirely different results.

  3. Covariant control: Although many factors have been reported to be associated with injury risk during rollovers, few have controlled these factors carefully to avoid any influence from internal correlations among them. For example, the number of quarter-turns and average roof deformation both have been reported to correlate with injury risks. However, the average roof deformation and the number of quarter-turns both have been reported to increase with increasing crash severity [Rains et al. 1995; Piziali et al. 1998; Digges et al. 2003]. Therefore, to separate the effects of these two factors, special statistical methods have to be used to adjust or control one of the factors when studying the other. Most previous analyses did not treat this issue carefully.

  4. Sampling weights: A weighting factor is generally provided for each case in crash databases, such as the NASS-CDS database. In the previous studies, the two frequently used strategies were: (1) analyzing the unweighted data by simply ignoring the weighting features altogether, or (2) analyzing weighted frequencies as if they were obtained from a dataset without any weighting features. Both strategies are inadequate for the prediction of rollover injuries. Using the unweighted data can lead to biased estimates, especially when the sampling weights vary significantly from one case to the other. On the other hand, although applying the simple frequency weights can predict unbiased estimates, it would underestimate the standard errors, which in turn would cause every test to be significant, because the sample size is considered as large as the population.

The objectives of this study were then to (1) develop a set of procedures which can address the aforementioned problems in field data analysis, and (2) to investigate factors affecting the likelihood of head/face and neck (HFN) injuries using this new procedure in analysis of accident data of rollover crashes.

METHODS

Eleven years of data were obtained from the NASS-CDS database for rollover crashes between 1995 and 2005, allowing for a relatively large sample size to be analyzed. As mentioned earlier, a sampling weight was provided for each case in this database, so that all the results presented in this study were based on weighted data unless otherwise noted.

CRASH SELECTION

A subset of the crash data was selected to eliminate the factors which could influence the injury mechanism or risk but were hard to control during statistical analysis. For example, rollovers involving impacts with another vehicle or fixed object (e.g. a tree or wall) prior to or after rollover were excluded. Digges and Eigen (2005b) reported that these impacts could induce higher injury risks caused by a totally different injury mechanism. NASS-CDS database coded the rollover initiation type into ten categories: trip-over, flip-over, turn-over, climb-over, fall-over, bounce-over, collision with another vehicle, other rollover type, end-over-end, and unknown. The last four categories of rollovers were excluded from our dataset. Vehicle model year was not controlled in the current study. Therefore, in the current dataset the oldest vehicle model year was 1966, and the newest vehicle model year was 2006. Overall, 98% of the case vehicles were manufactured after 1980 and 81% of the case vehicles were made after 1990.

OCCUPANT AND INJURY SELECTION

Because injury mechanisms of ejected occupants were too random to yield meaningful results, only non-ejected (without partial ejection) occupants were selected. Furthermore, only front seat occupants older than 12 years of age were analyzed in this study. Cases with unknown seatbelt usage were deleted from the dataset. Only HFN injuries were considered in this study, because HFN injuries of non-ejected occupants (without partial ejection) were generally induced by contacts between the roof and the head [Bedewi et al. 2003; Hu et al. 2005]. Injuries to other body regions may be caused by different mechanisms and are thus beyond the scope of this study. Injured occupants considered in this study had AIS 3 to 6 head/face (HF) injuries and/or AIS 3 to 6 neck injuries.

ROOF DEFORMATION

In this study, roof deformation was defined as the maximum deformation level in roof components (such as the roof, roof side rail, A/B pillar, and windshield header) local to the vicinity of the occupant’s head. Therefore, two occupants in the same car may experience two different roof deformation values, because roof deformation in this study is defined as the vehicle deformation specific to the occupant studied, not the average roof deformation measured for the entire vehicle. Using this method, we can reduce the internal correlation between the roof deformation and other factors (e.g. impact severity). The NASS-CDS database [NASS-CDS 1997] codes the magnitude of deformation by seven levels as shown in Table 1. The maximum vertical and lateral deformations adjacent to the occupant, as well as the resultant deformations of specific components were obtained and defined as covariants in the analysis.

Table 1.

NASS-CDS coded magnitude of deformation

Code Magnitude of deformation
0 <3cm
1 ≥3cm but <8cm
2 ≥8cm but <15cm
3 ≥15cm but <30cm
4 ≥30cm but <46cm
5 ≥46cm but <61cm
6 ≥61cm
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STATISTICAL METHODS

Weighted logistic regression analyses were conducted to evaluate the association between selected predictors and the odds of receiving HFN injuries. The predictors selected for this study included occupant factors (age, gender, height, weight, and seatbelt usage), crash factors (rollover initiation type, rollover leading side, and the number of quarter-turns), and vehicle factors (different component deformations in different directions). For belted occupants, additional statistical analyses were conducted to investigate any potential difference between significant HF and neck injury predictors. For each regression analysis, covariants were introduced sequentially in the order of the occupant factors, crash factors, and finally the vehicle factors. Consequently, the odds ratios calculated for the crash factors were based on results after adjusting the occupant factors. Likewise, the odds ratios predicted for the vehicle factors were based on results after adjusting both the occupant and crash factors. This sequence was used to account for the fact that each occupant may be in any type of a vehicle, which may be involved in one of several types of rollovers. Therefore, to properly evaluate the relationship between vehicle factors and injury risks, effects from occupant and crash factors have to be eliminated first. Statistically adjusting the occupant and crash factors is a way of constraining them first, so that vehicle factors can be evaluated more objectively. As for the occupant and crash factors, we did not think it was necessary to adjust the vehicle deformations for them, because occupant and crash factors should be evaluated regardless of which vehicles are involved. Most of the analyses in this study were performed using SUDAAN 9.0 (RTI International, Research Triangle Park, NC), in which Taylor series linearization was used to adjust the standard errors and significance levels of weighted data for complex samples involving stratification and clustering. For comparing the different methods of handling the sampling weights, some of the analyses were performed using SPSS 15.0. The significance level of 0.05 was used to test statistical significance.

RESULTS

The final study cohort consisted of 3,256 occupants (of which 204 (124 belted) occupants had serious HFN injuries, 146 (82 belted) occupants had serious HF injuries, and 76 (58 belted) had serious neck injuries), representing a total of 1,652,233 occupants (of which 17,549 occupants had serious HFN injuries, 11,138 occupants had serious HF injuries, and 7,420 occupants had serious neck injuries) who were involved in rollover crashes in the US (Table 2). Large differences existed between the weighted and unweighted data. In particular, the percentage for one to four quarter-turns was lower while that for five or more quarter-turns was higher in the unweighted data. Additionally, the percentages for rollover associated head, face, and neck injuries were higher in unweighted data. These differences indicated that NASS-CDS database sampled more rollover cases with more quarter-turns and serious injuries, based on their sampling algorithm.

Table 2.

Characteristics of study cohort

Characteristic Unweighted Weighted
Total 3,256 1,652,233
Male 1,995 (61.3%) 1,047,350 (63.4%)
Belt usage Belted 2,175 (67.1%) 1,253,001 (76.0%)
Lap belt only 106 (3.3%) 51,426 (3.1%)
Unbelted 960 (29.6%) 344,597 (20.9%)
Near-side rollover 1,728 (53.1%) 841,564 (50.9%)
Number of quarter-turns 1–4 2,230 (68.5%) 1,312,351 (79.4%)
5–8 880 (27.0%) 313,619 (19.0%)
9–12 122 (3.7%) 23,577 (1.4%)
13+ 24 (0.7%) 2,687 (0.2%)
Occupants with serious neck injuries 76 (2.3%) 7,420 (0.4%)
Occupants with serious HF injuries 146 (4.5%) 11,138 (0.7%)
Occupants with serious HFN injuries 204 (6.3%) 17,549 (1.1%)
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Table 3 shows the results of three weighted logistic regression analyses using only occupant factors as the covariants for all the sampled occupants, the belted occupants, and the unbelted occupants, respectively. HFN injury odds for unbelted occupants were 3.02 (95% CI 1.52–6.00) times that of belted occupants. Occupants with lap belt only were 1.22 (95% CI 0.30–5.00) times more likely to sustain HFN injuries than occupants with three-point seatbelts, but this finding was not statistically significant. Age was a statistically significant predictor of the odds of HFN injuries for both belted and unbelted occupants, but the weight and height of occupants were not. The injury odds ratios of female to male were 2.50 (95% CI 0.92–6.78) for belted occupants and 0.45 (95% CI 0.18–1.10) for unbelted occupants, which indicated that the seatbelt was somehow more effective in protecting males as compared to females. However, this finding was not statistically significant (0.05<p<0.10).

Table 3.

HFN Injury odds ratios for occupant factors

Predictors All Belted Unbelted
p Odds ratio (95% CI) p Odds ratio (95% CI) p Odds ratio (95% CI)
Age 0.002 1.03 (1.01–1.05) 0.038 1.03 (1.00–1.05) 0.001 1.05 (1.02–1.08)
Gender 0.677 1.20 (0.51–2.85) 0.074 2.50 (0.92–6.78) 0.078 0.45 (0.18–1.10)
Weight 0.089 1.02 (1.00–1.04) 0.207 1.02 (0.99–1.05) 0.353 1.01 (0.99–1.04)
Height 0.930 1.00 (0.96–1.04) 0.695 1.01 (0.96–1.06) 0.977 1.00 (0.95–1.05)
Belt usage Overall 0.007 – – – – –
Unbelted – 3.02 (1.52–6.00) – – – –
Lap belt only – 1.22 (0.30–5.00) – – – –
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Table 4 shows the HFN injury odds ratios of crash factors after statistically adjusting for occupant factors. It was found that the number of quarter-turns was a statistically significant predictor of the HFN injury odds for the belted occupants, but not for the unbelted occupants. The injury odds were 1.24 (95%CI 1.10–1.40) times for the belted and 1.14 (95%CI 0.92–1.42) times for the unbelted occupants for each additional increasing number of quarter-turns. The rollover leading side was found to be a significant factor affecting HFN injury odds for the unbelted occupants, but not for the belted occupants. Far-side unbelted occupants were 2.52 (95%CI 1.00–7.08) times more likely to sustain HFN injuries than near-side unbelted occupants. On the contrary, the rollover initiation type was a statistically significant predictor of the HFN injury odds for the belted occupants, but not for the unbelted occupants. Because trip-over was reported as the major rollover initiation type [Parenteau et al. 2000; Parenteau et al. 2003; Hu et al. 2005], the injury odds of other rollover intitiation types were compared to those of trip-overs. For belted occupants, the injury odds for turn-over were found to be significantly lower, while climb-over had significantly higher injury odds than trip-over.

Table 4.

HFN injury odds ratios for crash factors after adjusted for occupant factors

Predictors Belted Unbelted
p Odds ratio (95% CI) p Odds ratio (95% CI)
Number of quarter-turns 0.000 1.24 (1.10–1.40) 0.227 1.14 (0.92–1.42)
Rollover leading side 0.425 0.74 (0.36–1.54) 0.050 2.52 (1.00–7.08)
Rollover initiation type Overall 0.043 – 0.320 –
Trip-over – 1 – 1
Bounce-over – 0.97 (0.22–4.29) – 0.40 (0.11–1.48)
Flip-over – 0.74 (0.28–1.97) – 0.98 (0.26–3.66)
Turn-over – 0.06 (0.01–0.47) – 0.76 (0.12–4.73)
Climb-over – 7.39 (1.76–30.99) – 0.50 (0.08–3.29)
Fall-over – 2.05 (0.65–6.45) – 0.26 (0.08–0.91)
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After statistically adjusting for occupant and crash factors, the maximum vertical deformation adjacent to the occupant became a statistically insignificant predictor of HFN injury odds for both the belted (p=0.259) and unbelted (p=0.431) occupants, while the maximum lateral deformation adjacent to the occupant was significant (p=0.039) for belted occupants but not significant (p=0.444) for unbelted occupants (Table 5). The HFN injury odds were 1.60 (96% CI 1.02–2.50) times for belted occupants for each additional increase of maximum lateral deformation level. Breaking down the deformations into structural components revealed that A-pillar and B-pillar deformations were statistically significant predictors of HFN injury odds for belted occupants, and windshield header deformation was a statistically significant predictor for HFN injury odds in unbelted occupants. Roof and roofrail deformations were not good predictors of HFN injury odds for either the belted or unbelted occupant.

Table 5.

HFN injury odds ratios for vehicle factors after adjusted for occupant and crash factors

Predictors Belted Unbelted
p Odds ratio (95% CI) p Odds ratio (95% CI)
Vertical deformation 0.259 1.22 (0.86–1.72) 0.431 1.22 (0.74–2.01)
Lateral deformation 0.039 1.60 (1.02–2.50) 0.444 1.23 (0.73–2.06)
Roof panel deformation 0.704 1.05 (0.80–1.39) 0.964 0.99 (0.63–1.56)
Roofrail deformation 0.152 1.19 (0.94–1.52) 0.871 0.96 (0.56–1.63)
A pillar deformation 0.031 1.53 (1.04–2.25) 0.148 1.33 (0.90–1.94)
B pillar deformation 0.007 1.42 (1.10–1.84) 0.817 1.05 (0.68–1.64)
Windshield header deformation 0.992 1.00 (0.69–1.45) 0.002 1.63 (1.20–2.22)
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To further differentiate the injury mechanisms between HF and neck injuries, two more weighted logistic regressions were conducted for belted occupants with HF and neck injuries, respectively (Table 6). It was found that the occupant age and the number of quarter-turns became significant only for neck injury odds, but not for HF injury odds. Weight became significant for the neck inury odds but not significant for the HF injury odds. Lateral deformation was statically significant (p=0.037) for predicting the HF injury odds, but not significant (p=0.159) for predicting the neck injury odds. On the contrary, vertical deformation was significant (p=0.002) for predicting the neck injury odds, but not significant (p=0.821) for predicting the HF injury odds. The HF injury odds ratio of lateral deformation was much greater than that of vertical deformation; while neck injury odds ratio of vertical deformation was much larger than that of lateral deformation.

Table 6.

Injury odds ratios when considering HF and neck injuries separately

Predictors HF Injury Neck Injury
p Odds ratio (95% CI) p Odds ratio (95% CI)
Age 0.275 1.02 (0.98–1.06) 0.018 1.04 (1.01–1.07)
Gender 0.128 2.78 (0.74–10.38) 0.529 1.64 (0.67–4.02)
Weight 0.604 0.99 (0.97–1.02) 0.013 1.03 (1.01–1.08)
Height 0.331 1.03 (0.98–1.08) 0.930 1.02 (0.93–1.07)
Number of quarter-turns 0.054 1.19 (1.00–1.42) 0.000 1.38 (1.21–1.57)
Rollover leading side 0.421 0.69 (0.28–1.70) 0.723 1.2 (0.43–3.35)
Rollover Type 0.026 – 0.527 –
Vertical deformation 0.821 1.05 (0.67–1.66) 0.002 1.64 (1.19–2.25)
Lateral deformation 0.037 1.83 (1.04–3.21) 0.159 1.27 (0.91–1.77)
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DISCUSSION

The purpose of this study was to develop a set of procedures for analyzing rollover field data to determine factors affecting HFN injury risks, which can properly handle data selection, estimate prediction, covariant control, and sampling weights. The use of a relatively large dataset, weighted logistic regression method, careful selection of crashes, occupants, injuries and local vehicle deformations, and sequentially adjusting covariants made this set of procedures suitable for finding some significant predictors of the odds of HFN injuries during rollovers. Furthermore, the important injury odds predictors found in this study can be used to control, investigate, and/or evaluate further experimental and numerical studies to explore the detailed HFN injury mechanisms associated with rollover crashes.

WEIGHTED LOGISTIC REGRESSION

Only a limited number of previous studies have used statistical methods to analyze the field data. For example, Conroy et al. (2006) used logistic regression to determine potential risk factors for serious injury odds in rollovers based on combined unweighted NASS-CDS and Crash Injury Research and Engineering Network (CIREN) data. However, to the best of our knowledge, weighted logistic regression was never used, because of the difficulties in handling the sampling weights. With general statistical software packages, such as SPSS and SAS, frequency weights are normally used when the weighting factor is available. This can result in treating the sample size as the population size. As a result, most statistical tests would yield significant results. One remedy for this problem is to transfer the frequency weight to normalized weight (or proportional weight), which is defined as dividing the individual frequency weight by the sum of the frequency weights of the whole dataset. By doing so, one can get unbiased estimates and correct significance levels, if the effect of clustering in sample design is not important. However, the sampling weights calculation of NASS-CDS database involved in stratification and clustering, hence special statistical module such as Complex Samples of SPSS, or special software packages such as SUDAAN, is needed to correct the standard errors by some specific methods. To better illustrate the difference between the methods mentioned above, logistic regressions based on four different methods dealing with sampling weights were conducted for belted occupants with covariants shown in Table 7. Two online articles reported by Hendrickx (2002) and Maletta (2006) provided some important suggestions in understanding the issues related to sampling weights. For more theoretical details, the reader is referred to articles by Clogg et al. (1987) and Winship et al. (1994). It was clear that the odds ratios predicted by the unweighted data could be very different from those predicted by weighted data. On the other hand, the odds ratios are always the same for weighted data, no matter what kind of weights is being used. Results shown in Table 7 demonstrate that unweighted data would lead to biased estimates. In terms of the significance level, the results from all the four methods are different. Since the estimates from unweighted data were biased, the predicted significance levels were also biased. It was apparent that the frequency weights severely over-estimated the significance levels, while the significance levels predicted by normalized weights and SUDAAN were comparable. It is also worth noting that with unweighted data vertical deformation was a very good predictor for the odds of HFN injuries, which is very different from the results from SUDAAN. NASS-CDS database intended to sample more cases with larger vehicle deformation and serious injuries, so unweighted data can overestimate the influence of vehicle deformations. It should also be mentioned that the intent of Table 7 was to compare the results of different weighting methods and not to find the odds ratio for a specific predictor. Therefore, the sequence of covariants was not controlled. Thus, the odds ratios predicted here should not be compared with the results reported in the previous tables.

Table 7.

Comparison of different methods used to handle the sampling weights

Predictor Unweighted Frequency weights Normalized weights SUDAAN
p Odds ratio p Odds ratio p Odds ratio p Odds ratio
Age 0.000 1.025 0.000 1.024 0.089 1.024 0.072 1.024
Gender 0.576 1.112 0.000 1.436 0.427 1.436 0.324 1.436
Number of quarter-turns 0.416 1.03 0.000 1.141 0.150 1.141 0.107 1.141
Rollover Leading side 0.001 1.872 0.000 0.677 0.416 0.677 0.301 0.677
Vertical deformation 0.001 1.238 0.000 1.162 0.368 1.162 0.475 1.162
Lateral deformation 0.000 1.343 0.000 1.486 0.025 1.486 0.013 1.486
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HFN INJURY ODDS PREDICTORS

In this study, seatbelt usage was found to be very important for predicting the odds of HFN injuries during rollovers, which is consistent with most previous studies [Parenteau et al. 2000; Digges et al. 2003]. However, Digges et al. (1994) reported that the percentage of HARM due to head/spine injuries in roof and rail/header contacts was about twice as high for the restrained as for the unrestrained occupants, while Bedewi et al. (2003) also reported that percentage point-wise belted occupants had 4% more neck injuries than unbelted occupants. The emphasis of our study is on estimating injury risks instead of determining injury distribution, but the data obtained from those two papers are actually injury distribution, hence are not relevant to the current study. Additionally, unbelted occupants are likely to sustain a higher number of injuries in body regions other than the neck compared to belted occupants. Consequently, the ratio of neck injuries to all injuries could be lower in unbelted occupants due to a larger denominator. Thus, injury distribution and injury risk in belted versus unbelted occupants are two very different parameters and cannot be compared directly. The difference in injury odds between lap-belt-only occupants and three-point belted occupants was very small, indicating that the lap belt is almost as effective as three-point belt during rollover crashes. This is consistent with the results of some previous experimental studies [Moffatt et al. 1997]. For belted occupants, age, number of quarter-turns, rollover initiation type, maximum lateral deformation adjacent to the occupant, A-pillar and B-pillar deformation were found to be significantly associated with the HFN injury odds. And gender was marginally significant. Since the results demonstrated that different rollover initiation types can result in different levels of HFN injury risks, future studies need to use multiple experiments or numerical simulations to investigate different rollover scenarios. Using only one rollover scenario to represent all rollovers is unlikely to yield meaningful results. For unbelted occupants, age, rollover leading side, and windshield header deformations were found to be significantly associated with HFN injury odds, and gender was marginally significant. It is also worth noting that while gender was not a significant predictor of the odds of HFN injuries with an overall injury odds ratio of 1.09, the injury odds ratios were opposite (one is greater than 1.0, but the other is less than 1.0) between belted and unbelted occupants, which made the injury odds ratio for the entire sample nearly equal to 1. This interesting finding suggests that separating belted and unbelted occupants was necessary, because opposite effects for belted and unbelted occupants can be evened out when analyzing all occupants as one group. In the open literature, there is great controversy over whether there is a causal relationship between roof deformation and occupant injury risk. To date, most of the studies, including field data analyses [Padmanaban et al. 2005a; Padmanaban et al. 2005b; Padmanaban et al. 2005c; 2006] and experimental tests [Orlowski et al. 1985; Bahling et al. 1990; Moffatt et al. 2003], reported that such a relationship does not exist. It was further suggested that higher and stronger roofs and improved restraints should be analyzed as a system to improve the occupant protection during rollover [Moffatt et al. 2005]. However, several studies [Rechnitzer et al. 1998; Nash et al. 2005] insisted that this causal relationship does exist. In our current study, although the maximum vertical deformation adjacent to the occupant is not significant for either belted or unbelted occupants, the maximum lateral deformation is significant for belted occupants. A-pillar and B-pillar deformations were also significant predictors of the HFN injury odds for belted occupants. These findings indicated that deformation from the lateral side might be more crucial for predicting the odds of HFN injuries than that from the top, which was rarely mentioned in the open published literature. However, we should not conclude that there is a causal relationship between lateral deformation and HFN injury odds, since correlation did not represent causality.

DIFFERENCES BETWEEN HF AND NECK INJURY MECHANISMS

Age, weight and the number of quarter-turns were found to be the only statistically significant predictors for the odds of neck injuries. Neck injuries during rollovers are mainly bony fractures. Thus, older occupants with degenerated cervical vertebrae are more likely to sustain neck injuries. Because more than half of the head injuries during rollovers are brain injuries, HF injury odds ratio is not as sensitive to the age differences as bony fractures. The weight and number of quarter-turns were found to have more prominent influences on neck than HF injury odds. The reason for this finding is not clear, and thus needs further investigations. Our results further suggest that, HF injury odds had a stronger association with lateral deformations than vertical deformations, while neck injury odds had a stronger association with vertical deformations than lateral deformations. All the differences in association found between HF and neck injuries on vehicular factors suggest that the mechanisms for neck injuries are quite different from those for HF injuries during rollover crashes.

LIMITATIONS

The significance levels of statistical tests can be influenced greatly by sample size. Even though some factors were not statistically significant in this study, it does not mean that the effects associated with these factors can be totally ignored. On the other hand, even if some factors were statistically significant, it does not mean that they are biomechanically meaningful. Moreover, almost all the statistical analyses are subjected to the usual cautions about causal inference. Although A-pillar and B-pillar deformations were found to be significant when predicting the odds of HFN injuries, it does not mean that those deformations caused the HFN injuries. Therefore, additional experimental and numerical studies need to be performed to further validate the findings of field data analyses and to explore the fundamental injury mechanisms during specific rollover conditions. Nevertheless, this study can at least provide some useful options and directions for future research. Additionally, this study is limited by the fact that all vehicle deformations presented are static residual deformations. While it is more appropriate to use dynamic deformations for the analysis, there is no widely accepted method to transform static residual deformations into dynamic deformations. To account for the difference between a static and corresponding dynamic roof deformation, Rains et al. (1995) added 10 cm to the static roof deformation to estimate the dynamic roof deformation. Mathematically, such a linear transformation will not change the results of a logistic regression. Therefore, results presented in this study should be able to, at least to a limited extent, reflect the effects of dynamic roof deformation.

CONCLUSIONS

A weighted logistic regression method which incorporated careful selection of crash, vehicle, occupant and injury data and sequentially adjusting the covariants was developed and used to investigate the predictors of the odds of HFN injuries during rollovers. Weighted data used for this analysis could provide an unbiased estimation of injury odds ratios, and the variance was adjusted to achieve a more reasonable significance level. The results show that, in non-ejected occupants, unbelted occupants have statistically significant higher HFN injury risks than belted occupants. Thus, the injury mechanisms for these two groups of occupants need to be investigated separately. Age, the number of quarter-turns, rollover initiation type, maximum lateral deformation adjacent to the occupant, A-pillar and B-pillar deformation are significant predictors of HFN injury odds for belted occupants. Age, rollover leading side and windshield header deformation are significant predictors of HFN injury odds for unbelted occupants. This analysis also suggests that the HF and neck injuries should be analyzed separately when investigating injury mechanisms during rollovers, because significant injury predictors are different between the HF and neck injury odds.

ACKNOWLEDGEMENT

This research was supported by a URP grant from Ford Motor Company. The opinions expressed in this paper are those of the authors and do not necessarily represent the opinions of Ford Motor Company.

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