Evaluating the Impact of Bicycle-Friendly Infrastructure on Cyclist Crash Rate in Denver, CO

Abstract

This study investigates the spatial relationship between bicycle-friendly infrastructure density and cyclist crash rates across Denver, Colorado, with the goal of informing targeted infrastructure investments that reduce crash risk. Using five years of collision data (2019–2024), annual cyclist crash rates were standardized per 1,000 daily cyclists by combining collision records with cyclist volume estimates at the census tract level. Infrastructure density was measured as miles of protected bike lanes and trails per square mile of each tract. Preliminary choropleth mapping revealed considerable spatial heterogeneity in both crash rates and infrastructure density, with South and Northwest Denver exhibiting high crash rates and low infrastructure density, while Central Denver showed the inverse pattern.

To assess the relationship between these variables, a Global Moran's I test revealed significant positive spatial autocorrelation in crash rates, prompting the use of a Geographically Weighted Regression (GWR) and a Spatial Error Model (SEM) rather than a standard OLS regression. GWR results revealed a spatially non-stationary relationship: South and Northwest Denver showed a meaningful negative association between infrastructure density and crash rate, while Central-East Denver exhibited a negligible or even positive association. This result suggests that other local factors, such as traffic volumes, intersection design, and land use, also shape crash risk. The SEM produced a global slope coefficient of -1.58, indicating a modest negative association, though the result was statistically insignificant (p = 0.282). The findings underscore the need for localized, context-sensitive planning strategies rather than uniform citywide infrastructure investments.

I. Introduction

Cycling is an important mode of urban transportation due to its affordability and environmental benefits relative to cars. Several studies have also shown that cycling can lower risks of obesity, cardiovascular disease, and other chronic health conditions, while promoting active and sustainable mobility (Oja, et. al., 2011). Although cyclist-friendly infrastructure in the United States, including bike lanes, trail networks, and traffic calming features, still lags behind European nations, cities across the U.S. have recently undertaken projects to encourage cycling and improve safety for riders.  

Despite these recent advances, bicycle safety remains a central concern for transportation planners in North America, particularly in urban areas where cyclists and vehicles are often interacting in the same street space. To reduce bicycle injuries, it is imperative to first understand the causes of risk for cyclists. Bicycle safety research consistently shows that crash risk is primarily shaped by street network design that effectively separates cyclists from vehicles. For example, a 2011 study conducted in Montreal found that cyclist-only trails and protected bike lanes reduced injury risk by approximately 28% compared to shared streets between cyclists and vehicles (Lusk, et. al., 2011). Another study, conducted in 2012 in Vancouver and Toronto, assessed injury risk across 14 different route types to quantify the impact of several variables on cyclist risk (Teschke, et. al. 2012). The researchers found that infrastructure physically separating cyclists from vehicles, such as concrete barriers between bike lanes and car traffic, was the greatest determinant in reduced risk, more so than other variables such as the number of lanes on a street, downhill grades, and the presence of parked cars. 

Although existing literature on the benefits of cyclist-friendly infrastructure is well documented, less is known about how the relationship between infrastructure and crash risk varies across space within a single city. To fill this gap in research, this study utilizes five years of cyclist crash rate data, as well as bicycle-friendly infrastructure records, to investigate the spatial relationship between infrastructure and risk in Denver, Colorado. Because protected bike lanes and trails tend to attract more cyclists, thus increasing exposure to risk, crash data is standardized by cyclist volume estimates to enable a direct comparison between crash rate and infrastructure density. Additionally, a Geographically Weighted Regression and Standard Error Model are employed to account for spatial autocorrelation in crash rate and produce statistics that summarize both local and global relationships. Ultimately, the maps and statistics presented in this report aim to answer the following research question: Does the density of bicycle-friendly infrastructure explain the spatial distribution of cyclist crash rate in Denver, Colorado?

II. Methods

a. Cyclist crash rate standardization

Cyclist-vehicle collision and daily cyclist count data for the City of Denver were compiled from the five most recent years of available data (2019 – 2024) provided by the Denver Regional Council of Governments (DRCOG, 2025). Crash data points were then spatially joined to census tract boundaries and divided by five years to calculate the annual average number of crashes within each census tract. Census tracts were used instead of block groups to ensure that each geographic unit contained enough crash observations to support reliable statistical analysis. Because daily cyclist count data were collected at discrete point locations throughout the city of Denver, Empirical Bayesian Kriging (EBK) was employed to create a continuous surface of estimated cyclist activity (Figure 1). Since there are approximately 500 cyclist counting stations in the DRCOG dataset, which are mostly located along major bike corridors, EBK was selected for the interpolation method as it handles small, clustered point samples better than Classical Kriging. This is because EBK models uncertainty in the semivariogram of cyclist counts by simulating multiple semivariograms for subsets of data and combining them into a final prediction, thus producing more robust estimates when points are sparse compared to Classical Kriging. After running the EBK model, the output raster cell values were averaged within each census tract to estimate cyclist volume at a shared spatial scale with annual cyclist crashes. Lastly, annual cyclist crash rate per 1,000 daily cyclists was calculated for each census tract according to the following formula:

Crash Rate = Annual Crashes / (Estimated Daily Cyclist volume * 1000)

Following the computation of the crash rate field, a choropleth map was produced to illustrate how crash rate varies across Denver. Although this map does not rely on any advanced statistical tests (e.g., Getis-Ord GI*), it highlights areas where crash rates are particularly high or low, such that a comparison can be drawn to bicycle-friendly infrastructure density.

b. Bicycle-friendly infrastructure standardization

Bicycle infrastructure data were compiled from the City of Denver’s Geospatial Portal (CCD, 2025). The dataset included all completed and planned protected/buffered bike lanes, bike- and pedestrian-only streets/trails, and neighborhood bikeways (streets intended to be shared between both cyclists and motorized vehicles). For this study, only existing protected or buffered bike lanes, bike- and pedestrian-only streets, and trails were included to capture infrastructure that physically separates cyclists from vehicular traffic. The “Summarized Within” tool was then used to compute total mileage of selected bicycle infrastructure within each census tract, enabling the standardization of bicycle infrastructure by the area of each census tract using the following formula:

Infrastructure Density = Mi. of Selected Bicycle Infrastructure / Sq. Mi. of Census Tract

To enable a direct comparison between crash rate and bicycle-friendly infrastructure density, a second choropleth map was produced by symbolizing census tracts by the infrastructure density field.

c. Correlational Analysis

Global Moran’s I statistics were computed for crash rate to test for spatial autocorrelation across census tracts, using the Queen’s Case conceptualization of contiguity to best capture spatial autocorrelation when dealing with polygon data (e.g., census tracts) (Table 1). Because significant positive spatial autocorrelation was detected, a Geographically Weighted Regression (GWR) model was used to assess spatially varying relationships between bike infrastructure (independent variable) and crash rate (dependent variable). The GWR model was run with the “Golden Search” neighborhood selection method, such that the model would automatically find the optimal number of neighbors that results in the best Akaike Information Coefficient (AIC) for the model. After running the model, GWR outputs, including local slope coefficients, local R2, and standardized residuals, were mapped to evaluate the relationship of cyclist crash rate and bike infrastructure density, model fit, and spatial heterogeneity.

To compare the local model with a global alternative that accounts for spatial dependence, a Spatial Error Model (SEM) was estimated. Coefficients, standard errors, and p-values from the SEM were examined to assess the overall, spatially adjusted relationship between cyclist crash rate and bike infrastructure density.

III. Results

a. Choropleth Maps of Crash Rate and Infrastructure Density

The choropleth map of crash rate, represented by annual cyclist crashes per 1,000 daily cyclists at the tract level, reveals that crash risk is heterogeneous across space in the City of Denver (Figure 2). Cyclist crash risk is the greatest in South Denver, as several tracts report a crash rate of over 250 annual crashes per 1,000 daily cyclists between 2019 and 2024. Risk during this same time span is generally the lowest in Northeast and Central Denver, with most tracts reporting a crash rate of less than 10 annual crashes per 1,000 daily cyclists. 

Comparing these results to the choropleth map of bicycle-friendly infrastructure density, represented by miles of bike infrastructure by square miles of tract area, shows that infrastructure density likely influences crash rates in certain areas of Denver (Figure 2). For example, tracts in South and Northwest Denver have comparatively low infrastructure density and high crash rates, while central Denver has high infrastructure density and lower crash rates. However, other parts of the city, such as Central-East Denver, do not reflect the same relationship. Both crash rate and infrastructure density are relatively low in Central East-Denver, indicating that other factors besides infrastructure density, such as low traffic volumes, may reduce crash risk. The following maps and tables in this report show the results of more advanced statistical methods to quantitatively assess the relationship between infrastructure density and crash rate.

b. Geographically Weighted Regression (GWR) Output

Figure 4 depicts the standardized residuals produced by the GWR, enabling an evaluation of whether the model successfully accounted for the spatial autocorrelation found in the crash rate metric. Based on the residual map, the model does not have any clear spatial trends, as there are no well-defined areas where the model consistently over- or under-estimates crash rates. This is a good indication that there is minimal spatial autocorrelation in the errors of the GWR output. 

Local R2 values assess where the infrastructure density metric most accurately predicts the crash rate metric, as shown by a higher R2 (Figure 5). The GWR model does the best job predicting crash rate in Southwest, Northwest, and Central Denver, with most tracts reporting a local R2 value greater than 0.4. The model does the worst job predicting crash rate in Central-East Denver, with several tracts reporting negative R2 values and others reporting R2 values less than 0.1. 

Figure 6 displays the slope coefficients, which represent the magnitude of the linear relationships between infrastructure density and crash rate in different parts of the city. South and Northwest Denver show a negative relationship between the two variables, suggesting that higher infrastructure density is associated with lower crash rates in those tracts, and lower infrastructure density is associated with higher crash rates. However, the model output shows a positive relationship in much of Central-East Denver, meaning that greater infrastructure density is associated with increased crash rates. These results generally align with preliminary observations made from the comparison of two choropleth maps, discussed above.  

Lastly, Figure 7 includes a chart of the Ordinary Least Squares (OLS) regression plot of the relationship between infrastructure density and crash rate. Datapoints on the plot are color-coded using the same symbology as the local slope coefficients shown in Figure 6, such that a comparison can be made between the local GWR modeled relationship and global OLS modeled relationship. Based on the global OLS model, which does not account for the spatial autocorrelation of crash rate, bicycle infrastructure density and bicycle crash rate do not exhibit a strong linear correlation, as indicated by the low R2 value of 0.02. This result further justifies the use of a GWR to explore how relationships vary locally and aligns with the metrics produced from the Global Moran’s I analysis testing for spatial autocorrelation in crash rate.

c. Standard Error Model (SEM) Output

To compare GWR results to a global model that does account for spatial autocorrelation, output from an SEM testing the relationship between infrastructure density and crash rate is shown in the tables below. Table 2 highlights the improvements in both model lag and error achieved by the SEM model in relation to the OLS model. The Lagrange Multiplier (LM) error and lag decreased from 127.02 to 0.27 and 129.52 to 2.78 respectively, indicating that a spatial autoregression model (e.g., SEM) will produce more reliable results regarding the global relationship between variables relative to an OLS model. 

Table 3 highlights the key metrics produced from the SEM model, including the global coefficients, standard errors, and p-values for the intercept and the slope of the model. The intercept coefficient of 48.64 means that the model predicts a crash rate of 48.64 annual crashes per 1,000 daily cyclists in a census tract with no bicycle infrastructure. More importantly, to the implications of this study is the slope coefficient produced by the model, which is shown to be -1.58. This indicates that for every increase of 1 mi./sq. mi. of infrastructure density, the model predicts crash rate will decrease by 1.58. Although the model found a global negative association, the p-value of the slope coefficient, shown to be 0.282, is much higher than the 0.05 alpha threshold used for this analysis. Therefore, the global association between infrastructure density and crash rate was determined to be insignificant.

IV. Limitations

Several limitations should be considered when interpreting the results of these analyses. First, the study is subject to both the ecological fallacy and Modifiable Areal Unit Problem (MAUP), as variables were aggregated to the census-tract level. These geographic units may not accurately reflect the true spatial relationship between cyclist crashes and bike infrastructure density. Therefore, the results of this study are only applicable to the level of aggregation used in this study, and future research should investigate this relationship at different levels of aggregation (e.g., block groups) such that results can be compared.

Second, uncertainty in the crash rate metric limits the reliability of results. Individual cyclist crash data relies on crashes being reported to the City and County of Denver (e.g., via police reports), so unreported cyclist crashes are not represented in this study. Additionally, average daily cyclist volumes were estimated in this study and may not reflect the true number of cyclists traveling through each census tract daily. For example, census tracts with no cyclist counting infrastructure were entirely reliant on EBK interpolation to produce estimates. Future studies may employ more cyclist counting infrastructure to achieve greater reliability in estimated cyclist volumes. 

Third, model assumptions contribute further to limited results. GWR assumes linear relationships exist between crash rate and infrastructure density within spatial neighborhoods. The model relies on having enough neighboring observations within each kernel to estimate a stable local linear relationship. However, census tracts along the boundary of Denver typically have fewer neighbors, and therefore, trends shown in the output of the model for these areas may be less reliable. Additionally, SEM assumes a global spatial structure for the autocorrelation of crash rate, which does not capture local differences. 

Finally, the global slope coefficient between crash rate and infrastructure produced by the SEM was weak, as indicated by a high p-value (0.282). This reduces the explanatory power of the models, suggesting that additional variables may be influencing cyclist crashes in Denver. Future studies should incorporate multiple variables into their analysis of cyclist crashes, in addition to bike-friendly infrastructure, to achieve more comprehensive results. 

V. Discussion

The results of this study highlight the spatial complexity of bicycle crash risk in Denver, Colorado. A Global Moran’s I analysis confirmed that crash rates are spatially autocorrelated, indicating that geographic factors influence spatial patterns in crash rate. Geographically Weighted Regression further revealed that the relationship between crash rate and bicycle-friendly infrastructure density is non-stationary, as maps of local slope coefficients and R2 values output show that in some areas of Denver (e.g., South Denver), there is a strong negative association between variables, while in other areas (e.g., Central Denver) there is a negligible or even positive association (e.g., Central-East Denver). The weak global relationship and low significance in the Spatial Error Model suggest that infrastructure is not the sole determinant of crash risk. Other factors such as traffic volumes, intersection design, and land use, likely influence spatial patterns in cyclist crashes as well. Despite low significance, the use of spatial methods such as GWR and SEM provide valuable insight into where infrastructure may be particularly impactful in reducing crash risk, as well as areas where additional research is needed. This finding highlights the need for localized planning strategies that consider neighborhood-specific contexts, such as differences in traffic volumes, intersection design, and land use (e.g., residential vs. commercial areas), rather than assuming uniform effects of implementing additional bike-friendly infrastructure citywide.

Ryan Goodale is a master's student in the Department of Geography and Environmental Sciences (MA Applied Geography and Geospatial Science).