The Interface Between Statistical Research and Teenage ...hidden Markov model for risky teenage driving behavior. In Press at Annals of Applied Statistics. 3 Kim, S., Chen, Z., Zhang,

The Interface Between Statistical Research andTeenage Driving: What Statistics Can Teach Us

About How Our Kids Drive and Visa-Versa

Paul S. Albert

Biostatistics and Bioinformatics BranchDivision of Intramural Population Health Research

Eunice Kennedy Shriver National Institute of Child Health and Human DevelopmentNational Institutes of Health, DHHS

Fourth International Naturalistic Driving Research Symposium

Scientific Questions

How does risky driving behavior measured by g-force eventsvary by condition and over time?

Do composite g-force events change over time?Do trip-specific covariates (e.g. adult passengers, nightdriving, etc.) effect g-force events?What are the sources of variation in g-force events?What is the serial dependence in g-force events?

How do g-force events relate to teenage accidents?

Can we predict actual or near crashes from g-force events?

Paul S. Albert Statistics and Teenage Driving

Outline

Exploring features of the data

Random process and marginal modeling of LONGitudinalcounts:

A hierarchical Poisson regression modeling approach (Kim,Chen, Zhang, Simons-Morton, Albert, 2013 JASA )Marginal analysis of longitudinal counts data in longsequences (Zhang, Albert, Simons-Morton, 2012 AOAS)

Joint models of kinematic measurements and crashes forprediction

Ordinal latent variable models and their application in thestudy of newly licensed teenage drivers (Jackson, Albert,Zhang, Simons-Morton, 2013 JRSS-C)A two-state mixed hidden Markov model for risky teenagedriving behavior (Jackson, Albert, Zhang, In press atAOAS).

Discussioninteresting problems?


Exploring the Data

0 5 10 15

01

23

45

Time since licensure (month)

Comp

osite

kinem

atic m

easur

e per

mile

Individually Smoothed Curves


Exploring the Data (Continued)

0 5 10 15

1.60

1.65

1.70

1.75

1.80

Time since licensure (month)

Comp

osite

kinem

atic m

easur

e per

mile

Mean Trajectory


Exploring the Data (Continued)

0 5 10 15

6.06.5

7.07.5

8.0

Temporal separation (month)

Varia

nce

Lowess smoothed empirical variograms for the composite kinematic events based on10 random pairings with each observation in the dataset randomly paired with another

on the same individual.


A Hierarchical Model

We assume the hierarchical Poisson regression models asfollow:

yij ∼ Poisson{

mij exp(

g(tij) + x ′ijβ + τi + γij + εij

)}

where

g(tij) is a polynomial regression spline of order p with k knots.

τi ∼ N(0, σ∗2τ ): a random effect for subject

γij ∼ N(0, σ∗2γ ): a random effect for overdispersion

εij ∼ N(0, σ∗2

η

(1 − ρ2dij

))with ρ = exp(−θ) and dij = |tij − ti,j−1|: a

random effect with serial correlation among trips


Posterior Estimates Under the Full Model


Estimated Log-longitudinal Trajectory


Serial Correlation (Model Based)


The Association of G-force Events with Crashes

Kinematic measures and their correlation with C/NCs


Risk Prediction

GEE With Logistic Regression Prediction of C/NC by Period

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Composite Event Rate

Prob

abilit

y of C

/NC

First 6-months

Second 6-months

Third 6-months

Simons-Morton et al., American Journal of Epidemiology, 2012


Joint Model for C/NC and Kinematics: A Hidden Markov Modeling Approach

Latent Markov chain: δ

Kinematic composite events: Poisson with

mean h(δ)

C/NC: Poisson with mean g(δ)


Hidden Markov Model:Prediction


Hidden Markov Model:Prediction


Summary

Exciting opportunities for collaborative work with researchstatistical scientists

Understanding variation in kinematic measurements

Developing dynamic predictors of crashes

Future research

Identify subgroups of teenagers that are at extreme risk:Tree-based approaches

Understanding effect of a C/NC on subsequent kinematicdynamics: Recurrent events

Cost-effective and efficient designs for large scale studies


References

1 Jackson, J.C., Albert, P.S., Zhang Z., and Simons-Morton,B. Ordinal latent variable models and their application inthe study of newly licensed teenage drivers. Journal of theRoyal Statistical Socieity- Series C 62, 435-450, 2013.

2 Jackson, J.C., Albert, P.S., and Zhang Z. A two-state mixedhidden Markov model for risky teenage driving behavior. InPress at Annals of Applied Statistics.

3 Kim, S., Chen, Z., Zhang, Z., Simons-Morton, B., andAlbert, P.S. Bayesian hierarchical Poisson regressionmodels: an application to a driving study with kinematicsevents. The Journal of the American Statistical Association108, 494-503,2013.

4 Zhang, Z., Albert, P.S., and Simons-Morton, B. Marginalanalysis of longitudinal count data in long sequences:methods and applications to a driving study. Annals ofApplied Statistics 6, 27-54, 2012


Documents

The Interface Between Statistical Research and Teenage ...hidden Markov model for risky teenage driving behavior. In Press at Annals of Applied Statistics. 3 Kim, S., Chen, Z., Zhang,