Analysis of Real-World Data

1
Analysis of Real-World Data

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

2
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

3
Need to Specify

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

4
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

5
Vehicles Selected

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

6
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

7
Calendar Years Selected

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

8
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

9
States Selected

• Florida
• Maryland
• Missouri
• North Carolina
• Pennsylvania
• Utah

10
Other SDS VIN States

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

11
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)

12
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

13
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

14
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

15
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

16
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

17
Statistical Models

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

18
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

19
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

20
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

21
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 (Plt0.0001)

22
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

23
Fit of Linear Model
24
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

25
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

26
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

27
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

28
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

29
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

30
Comparison of Linearand 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

31
Predictions from the Models
32
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