# Presentation: 695184

## Analysis of Real-World Data

- Static Stability Factor
- and the Risk of Rollover
- April 11, 2001

## References

*Federal Register*, June 1, 2000
- Description of the original linear regression analysis
*Federal Register*, January 12, 2001
- Description of the updated linear regression analysis
- Comparison with logistic regression analysis

## Need to Specify

- Vehicles
- Calendar years
- States
- Crash types
- Variables
- Statistical model

## Criteria for Selecting Vehicles

- Reliable estimate of the Static Stability Factor (SSF)
- Model years 1988 and later
- Sources include:
- Vehicles tested by the agency
- Passenger cars tested by General Motors

## Vehicles Selected

- 100 vehicle model groups, including:
- 36 cars
- 30 SUVs
- 13 vans
- 21 pickup trucks

## Criteria for Selecting Calendar Years

- Vehicle Identification Numbers (VINs) for that year had been decoded and included in the State Data System (SDS)
- Wanted multiple years to maximize data available for analysis

## Calendar Years Selected

- 1994-1997 for the original linear regression analysis
- 1994-1998 for the updated linear regression analysis and the logistic regression analysis

## Criteria for Selecting States

- Part of the SDS
- Provided 1994-1998 calendar year data
- Include VIN on the crash file
- Identify rollover occurrence even if it is not the first harmful event in the crash

## States Selected

- Florida
- Maryland
- Missouri
- North Carolina
- Pennsylvania
- Utah

## Other SDS VIN States

- VIN available for fatalities only
- Kansas
- VIN added in 1998
- Georgia
- Incomplete rollover information
- New Mexico
- Ohio

## Criteria for Selecting Crashes

- Single-vehicle crashes of study vehicles
- Excluded crashes with other participants
- Pedestrian, pedalcyclist, animal, or train
- Excluded certain unusual situations
- No driver, parked vehicle, pulling a trailer, or emergency use (ambulance, fire, police, or military)

## Crashes Selected

- 241,036 single-vehicle crashes, including
-   48,996 rollovers
- This is 0.20 rollovers per single-vehicle crash, consistent with the national estimate from the General Estimates System for these calendar years and vehicle groups

## Criteria for Selecting Variables

- Variables describing purpose of study
- Rollover (yes or no)
- SSF (study values range from 1.00 to 1.53)
- Confounding factors
- Environmental and driver factors that describe how the vehicle was used
- Want variables correlated with rollover risk, including travel speed

## Variables Selected

- Rollover
- SSF
- Dichotomous variables based on:
- Environmental factors (light condition, weather, urbanization, speed limit, road grade, road curve, road condition, surface condition)
- Driver factors (sex, age, insurance coverage, alcohol/drug use)
- Number of occupants in the vehicle

## Summary of Available Data

- Six states
- Five calendar years (1994-1998)
- 100 vehicle groups with a reliable estimate of SSF
- 14 confounding variables, including
-     10 available in all six states
- 241,036 single-vehicle crashes, including
-   48,996 rollovers

## Limitations

- Pennsylvania dropped key road use variables (grade and curve) from its electronic file in 1998, so 1998 Pennsylvania data were not used here
- Some variables were not available for all six states (urbanization, road condition, insurance coverage, and number of occupants in vehicle)
- Could not be used in analysis of combined data
- Were used in logistic analysis of individual states
- Reporting practices vary by state

## Statistical Models

- Linear model of summarized data
- Logistic models of individual crashes

## Preparing Data for the Linear Model

- Limited to state-vehicle groups with at least 25 observations
- 518 state-vehicle groups used in analysis
- Percentage involvement calculated for each variable, for each state-vehicle group
- Values ranged from 0 to 1
- For example:
- Rollover risk described by rollovers per single-vehicle crash
- Urbanization described by percent of crashes on rural roads

## Specifying Linear Model Form

- Dependent variable = LOG(rollover risk)
- Rollover risk set at 0.0001 for state-vehicle groups with no rollovers so they can be included in model
- Five dummy variables used to capture state-to-state differences in reporting practices
- Missouri used as baseline case
- Linear regression of the rollover variable as a function of the summarized explanatory variables and the state dummy variables

## Fitting the Linear Model

- Each summary data point was weighted by the sample size, capped at 250 as a trade-off between two considerations
- Sample size affects reliability of estimates
- Model should fit over entire range of SSF
- Stepwise procedure used forward variable selection and a significance level of 0.15 for entry and removal from the model

## Results of the Linear Model

- Model selected six confounding factors (DARK, FAST, CURVE, MALE, YOUNG, and DRINK) and all five state dummies
- R2 = 0.88 for the model of rollover risk as a function of state, road use variables, and SSF
- SSF variable coefficient was:
- Important in terms of the size of the estimated effect
- Highly significant in the model (P<0.0001)

## Predictions from the Linear Model

- Model describes rollover risk as a function of the explanatory variables and can be used to:
- Estimate rollover risk as a function of the SSF for any mix of road-use conditions
- Adjust the observed rollover rate for each summary data point to account for differences in vehicle use
- Next graph shows results for average conditions observed in the study data as a whole
- Rollover risk is estimated as 0.20 in both the adjusted and the unadjusted data

## Fit of Linear Model

- <footer>

## Interpreting the Linear Model

- Estimated rollover risk given a single-vehicle crash is halved when the SSF increases by 0.21
- For example, a vehicle with an SSF of 1.00 has twice the estimated rollover risk of a vehicle with an SSF of 1.21

## Specifying Logistic Model Forms

- Variables used
- Individual explanatory variables or
- Scenario risk variable
- Approach used with states
- Model each state, and average the results or
- Model pooled data with dummy variables to capture state-to-state reporting differences

## Concept of Scenario Risk

- Data divided into cells defined by explanatory variables
- For each cell, scenario risk is rollovers per single-vehicle crash
- For each crash, scenario risk is adjusted to reflect rollovers per single-vehicle crash for all other crashes in the cell
- Idea is to use scenario risk in the logistic model in place of all the explanatory variables

## Fitting the Logistic Models

- Models from individual states were based on the explanatory variables available in that state
- Models from pooled data were limited to the explanatory variables available in all six states

## Results of the Logistic Models

- The models from the six individual states and the two models based on pooled data all fit the data well
- These models were consistent in showing a large and significant effect for SSF

## Predictions from the Logistic Models

- Logistic models describe the change in the log(odds) of rollover as a function of the change in the SSF
- Results can be used to predict the absolute rollover risk as a function of the SSF for a given set of conditions
- Here, estimates of average SSF and odds of rollover are based on the data as a whole
- The four summary models produce similar results

## Comparison of Linearand Logistic Models

- Linear and logistic models both suggest SSF has a large effect on rollover risk
- Next graph compares results of linear model with results of logistic model from pooled data with individual explanatory variables

## Predictions from the Models

- <footer>

## Conclusions

- Advantages of linear model of summary data
- All summary data can be shown
- Simpler to explain
- Advantages of logistic analysis
- Includes full range of values and interactions because not restricted to averages for each vehicle group
- Better for measuring effects of explanatory variables because most were significant in the models
- In this analysis, logistic analysis appeared to confirm the general pattern of the linear results