# Relationship Between Traffic Volume and Accident Frequency at Intersections

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Processing Workflow

#### 2.3. Accident Data

#### 2.4. Processing Accident Data

#### 2.5. Intersection Traffic Volume Data

#### 2.6. Processing Intersection Traffic Volume Data

#### 2.7. Joining Accident and Traffic Volume Datasets

#### 2.8. Rainfall Data

#### 2.9. Accounting for Variability in Intersection Capacity

#### 2.10. Analysing the Relationship Between Traffic Volume and Accident Frequency

**Linear:**- accident frequency ~ traffic volume
**Quadratic:**- accident frequency ~ traffic volume + (traffic volume)
^{2} **Natural****Spline:**- accident frequency ~ natural spline (traffic volume, 4 d.f.)

#### 2.11. Accident Severity Analysis

#### 2.12. Rainfall Risk Analysis

## 3. Results

#### 3.1. Relationship Between Traffic Volume and Accident Frequency

#### 3.2. Accident Severity

#### 3.3. Rainfall Risk

## 4. Discussion

#### 4.1. Relationship Between Traffic Volume and Accident Frequency

#### 4.2. Accident Severity

#### 4.3. Rainfall Risk

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Determining the Ideal Number of Traffic Volume Bins

**Table A1.**The ideal number of bins for accidents in low, middle- and high-volume intersections calculated using the Freedman–Diaconis rule.

Intersection Rank | Ideal Bin Width | Ideal number of Bins |
---|---|---|

Low-volume | 281.995 | 9.71 |

Middle-volume | 299.131 | 16.69 |

High-volume | 426.830 | 17.62 |

All | 320.916 | 23.46 |

**Figure A1.**Comparison of traffic volumes grouped into 10, 15, 20 and 25 bins. Accident frequencies are plotted against the median traffic volume of each bin, and separate loess curves are fit for accidents at low, middle- and high-volume intersections.

## Appendix B. Calculating the Median Traffic Volumes of Congestion Levels

**Figure A2.**Traffic volume density distributions of the top, middle and bottom two intersection sites, ordered by median traffic volume. The lines represent where the 15 bins sit in the distribution.

## Appendix C. Effect of Traffic Volume on Accident Frequency

**Figure A5.**Loess curves showing the response of accident frequency to changing congestion in different sized intersections. Error bands are at a 95% confidence level.

## Appendix D. Normalised Not-Raining and Raining Accident Frequencies

**Figure A6.**(

**A**) Change in normalised not-raining and raining accident counts with increasing congestion; (

**B**) Change in the ratio of raining accidents to not-raining accidents with increasing congestion. The fitted lines are loess regressions. Error bands are at a 95% confidence level.

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**Figure 1.**Location of the study area and intersection sites where high temporal resolution traffic volume data exists.

**Figure 2.**Workflow for processing and joining the intersection traffic volumes and traffic accident datasets.

**Figure 3.**Relationship between traffic volume (median of each congestion level) and accident frequency. The dashed lines are linear regressions. For low-volume intersections, the linear regression is only fit for the median traffic volumes of the first 12 congestion levels. For middle- and high-volume intersections, the linear regression is fit for median volumes of the first 13 congestion levels. 95% confidence intervals relate to loess regressions fit to the same data.

**Figure 4.**Effect of congestion on property damage only (PDO) and minor injury (MI) accidents: (

**A**) Response of PDO and MI accident frequencies to congestion index. The y-axis shows normalised accident counts. The curves are loess regressions; (

**B**) Change in the ratio of MI and PDO accidents with increasing congestion index level. Confidence band is 95%.

**Figure 5.**(

**A**) Not-raining and raining accident risks; (

**B**): Relative risk between not-raining and raining accident risks. Confidence band is 95%.

Raw | Processed | |
---|---|---|

Spatial Extent | South Australia | ACC |

Temporal Extent | 2010–2017 | 2010–2014 |

n | 146,718 | 2336 |

Raw | Processed | |
---|---|---|

Spatial extent | ACC intersections | |

Temporal extent | 2010–2014 | |

Temporal resolution | 60 minutes | |

Measurement resolution | 1 vehicle | |

Number of intersections | 122 | 120 |

n | 5,369,323 | 5,213,580 |

Accident volumes | |
---|---|

Spatial extent | ACC intersections |

Temporal extent | 2010–2014 |

n | 1629 |

**Table 4.**Dispersion statistics for poisson models fitted to data for low, middle- and high-volume intersections. Dispersion ratios above one indicate possible overdispersion of data. A p-value of less than 0.05 indicates that the data is overdispersed.

Intersection Rank | Dispersion Ratio | Pearson’s Chi^{2} | p-Value | Overdispersed |
---|---|---|---|---|

Low-volume | 1.37 | 17.82 | 0.164 | No |

Middle-volume | 3.77 | 48.99 | <0.001 | Yes |

High-volume | 3.25 | 42.25 | <0.001 | Yes |

**Table 5.**Model selection statistics for models fit to accident data for low, middle- and high-volume intersections.

Model | d.f. | Log Lik. | AICc | Delta AICc | Weight | Evidence Ratio |
---|---|---|---|---|---|---|

Low-volume intersections | ||||||

Quadratic | 3 | −30.57 | 69.3 | - | 0.938 | 17.7 |

Natural spline | 5 | −29.21 | 75.1 | 5.8 | 0.053 | - |

Linear | 2 | −36.82 | 78.6 | 9.3 | 0.009 | - |

Middle-volume intersections | ||||||

Quadratic | 4 | −48.05 | 108.1 | - | 0.912 | 11.5 |

Natural spline | 6 | −45.25 | 113.0 | 4.9 | 0.079 | - |

Linear | 3 | −54.57 | 117.3 | 9.2 | 0.009 | - |

High-volume intersections | ||||||

Quadratic | 4 | −53.55 | 119.1 | - | 0.634 | 1.80 |

Natural spline | 6 | −48.89 | 120.3 | 1.2 | 0.352 | - |

Linear | 3 | −59.34 | 126.9 | 7.8 | 0.013 | - |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Retallack, A.E.; Ostendorf, B. Relationship Between Traffic Volume and Accident Frequency at Intersections. *Int. J. Environ. Res. Public Health* **2020**, *17*, 1393.
https://doi.org/10.3390/ijerph17041393

**AMA Style**

Retallack AE, Ostendorf B. Relationship Between Traffic Volume and Accident Frequency at Intersections. *International Journal of Environmental Research and Public Health*. 2020; 17(4):1393.
https://doi.org/10.3390/ijerph17041393

**Chicago/Turabian Style**

Retallack, Angus Eugene, and Bertram Ostendorf. 2020. "Relationship Between Traffic Volume and Accident Frequency at Intersections" *International Journal of Environmental Research and Public Health* 17, no. 4: 1393.
https://doi.org/10.3390/ijerph17041393