Article Text

## Abstract

**Background** Vehicle speed changes impact the probability of injuring a pedestrian in ways that differ from the way that it impacts the probability of a collision or of death. Therefore, return on investment in speed reduction programmes has complex and unpredictable manifests. The objective of this study is to analyse the impact of motor vehicle speed reduction on the collision-related morbidity and mortality rates of urban pedestrians.

**Methods and Findings** We created a simple way to estimate the public health impacts of traffic speed changes using a Markov model. Our outcome measures include the cost of injury, quality-adjusted life years (QALYs) gained and probability of death and injury due to a road traffic collision. Our two-way sensitivity analysis of speed, both before the implementation of a speed reduction programme and after, shows that, due to key differences in the probability of injury compared with the probability of death, speed reduction programmes may decrease the probability of death while leaving the probability of injury unchanged. The net result of this difference may lead to an increase in injury costs due to the implementation of a speed reduction programme. We find that even small investments in speed reductions have the potential to produce gains in QALYs.

**Conclusions** Our reported costs, effects and incremental cost-effectiveness ratios may assist urban governments and stakeholders to rethink the value of local traffic calming programmes and to implement speed limits that would shift the trade-off to become between minor injuries and no injuries, rather than severe injuries and fatalities.

- Speed Reduction
- Economic Analysis
- Urban Development
- Public Health
- Burden of Disease

## Statistics from Altmetric.com

## Objective

In 2010, road traffic collisions were the eighth leading cause of death worldwide with the number of causalities estimated to be 1.5 million deaths.1 An additional 20–50 million people are severely injured every year due to road traffic collisions, producing inestimable losses in human health and economic productivity.2 In the USA, nearly 5000 pedestrians died due to a motor vehicle collision, with an additional 150 000 injured,3 which accounted for near 15% of all motor vehicle casualties in 2013.4 Slowing traffic will reduce deaths and also has the potential to increase the time people spend travelling in cars over the short term, thereby increasing pollution, obesity and congestion, and potentially interrupting commercial activities.5 6 Policymakers must balance the trade-offs between the costs of slowing traffic and the benefits. One central piece of understanding this trade-off is to understand the impact of speed changes on the complex interaction among the probability of a collision, a severe injury and a death.

The WHO emphasises that the setting and enforcement of speed limits is an effective strategy for changing driver behaviour towards safer outcomes.7 8 Decreases in speed are associated with lower fatalities and injuries in consistent and predictable non-linear mathematical functions.9–19 Many communities have implemented programmes with the aim of making roads and traffic areas safer on a design level for pedestrians, and the most common and significant component of these programmes has been to lower speed limits within population centres.8

We use mathematical relationships between motor vehicle speed and the probability of pedestrian/motor vehicle collision, pedestrian injury and pedestrian death to analyse and to further quantify the economic impact of motor vehicle speed change on collision-related health system costs versus gains in the health and longevity of city dwellers.

Specifically, we estimate the additional societal costs associated with an injury (including lost productivity and medical costs) relative to the loss of life. We do not include the cost of the speed reduction programme because these costs vary widely. Rather, the purpose is to illustrate how a change in speed influences the trade-off between societal costs of suffering (measured in medical costs and health-related quality of life (HRQL) lost) and the loss of life.

## Methods

### Probabilities

In order to make our model generalisable to diverse urban settings, we used the broad range of speed differentials from traffic calming programmes designed to reduce pedestrian injury—5 to 40 miles per hour (mph = 1.61 km/h) before and after traffic calming programme implementation.20 21 Previous empirical research shows that the speed of a motor vehicle determines the probability of a collision with a pedestrian.20 When a collision occurs, speed also influences the probability of injury and death due to a collision.21–23 We combine and reproduce the graphical representation of the relationship between these probabilities and motor vehicle speed change in figure 1.

There are two important observations apparent in figure 1. The first thing we noticed was that the magnitude of the impact of speed changes on the probability of a collision is much smaller than the magnitude of impact of speed changes on the probability of injury or death.

We also noticed that the relative lag of the probability of injury curve in relation to the probability of death curve is such that the former peaks at higher speeds compared with the latter. Therefore, at the higher speeds, small speed reductions will result in small drops in the probability of injury (as shown in points a, b and c in figure 1) but large drops in probability of death (as shown in points a′, b′ and c′ in figure 1). In figure 1, an equal increase in speed will result into a small increase in the probability of injury (a–c), but it will cause a large increase in the probability of death (a′–c′).

The difference in the rate of probability change between pedestrian injury and pedestrian death is important since the cost of pedestrian injury, which is nearly eight times larger than the cost of death, is the main driver of monetary costs associated with pedestrian/motor vehicle collisions. Changes in the probability of a collision due to changes in speed are small relative to injury or death (bottom curve in figure 1) and therefore play a smaller role in explaining direct cost and effect differences.

### Costs

The average cost of injury from a pedestrian/motor vehicle collision is $56 775,24 25 which includes medical and lost productivity costs based on data from Healthcare Cost and Utilization Project—Nationwide Inpatient Sample.25 The probability of injury depicted in figure 1 represents an injury severe enough to lead to hospitalisation. We conservatively assumed that an injury would incur the average hospital cost irrespective of severity. Trade association estimates of mortality-related funeral costs are $7181 on average.26 We included the cost of death (burial costs) in the model, even though the entire cohort will eventually expire over time because a death today costs more than the cost of a death in the future (in constant current dollars).

We measured all costs in 2015 US dollars. Our analysis followed the recommendations of the Panel on Cost-Effectiveness in Health and Medicine, and employs a 3% rate of discount for both costs and effects.27 28

### Quality-adjusted life years

Our measure of morbidity and mortality is the quality-adjusted life year (QALY), which is a year of life lived in perfect health. This metric is the product of the duration of life lost and the HRQL score. The HRQL score is scaled from 0 to 1, with 0 equals death and 1 equals a state of perfect health. We assumed that a person may either lose QALYs as a result of (1) death from natural causes, (2) death by a pedestrian versus vehicle collision or (3) through being injured in a pedestrian versus vehicle collision measured using HRQL via the five-level version of the Euro quality of life five-dimensional (EQ-5D-5L) survey, a QALY-compatible measure.29 The EQ-5D-5L scale is a standardised instrument for use as a measure of health outcomes and it measures mobility limitations, capability of self-care, ability to participate in usual activities of work and leisure, level of pain and anxiety/depression.29 30 It is the morbidity component of a QALY, such that 10 years lived at an EQ-5D score of 0.45 is equal to 10×0.45=4.5 QALYs.

### Markov model

We employed TreeAge decision analysis software31 to build a simple Markov model with a control leg and an intervention leg. In the control leg, which simulated outcomes without the implementation of a traffic calming programme, costs and QALYs were estimated by exposing each hypothetical participant to his or her age-specific probability of death during each year-cycle as derived from an unabridged US life table.32 Participants who ‘die’ exit the model and participants who ‘survive’ remain in the model. This approach has been validated using established methods.33 Next we assumed that, if the person survives, they will be sequentially exposed to the probability of being in a collision, with the result being no injury, severe injury or death. The probability of each of these events is dependent on the speed of the motor vehicle during the time of the collision (figure 1).

In every annual cycle of the model, the majority of people would survive and enter the next cycle (year of life) intact, after living a full year of life and therefore gaining a full QALY. Some people may die in a vehicle collision or of a natural cause with a resulting 0 QALY for that cycle and then exit the model. Finally, those who are severely injured lose 0.45 QALY for each of the remaining years of their life.34 We also accounted for the rare event of multiple collisions and injuries for a single individual by tracking injured subjects as they continue to cycle through the model. Table 1 summarises all model input parameters.

The control leg was compared with a parallel leg that simulated outcomes for the same population with the implementation of a traffic calming programme, in which we assume that the speed of the motor vehicle during the time of the collision is considerably less. Lower speeds reduce the probability of being in a collision, being killed in the collision and being severely injured as the result of the collision (figure 1). All other aspects of this parallel model were identical to the first. This speed calming leg of the model is shown in figure 2. We then employed this model to conduct a series of a two-way sensitivity analysis. The two parameters that we varied were the traffic speed before traffic calming and the traffic speed after traffic calming. Each of these parameters was varied over a range of 5–40 mph.

We calculated ICER for the change in speed before and after the traffic calming programme. The costs included in the numerator of this ratio are injury and productivity losses associated with a collision, but not the programme cost. (For example, if traffic speeds are reduced with speed cameras, infrastructure costs will be higher than simply posting speed limit changes.) The ICERs, in turn, were calculated by arithmetically dividing the incremental change in cost values by the incremental life expectancy change (ICER=Change in Cost/Change in Effect).

## Results

We present the results as changes in costs (figure 3), changes in effects and changes in ICERs (table 2). The results of the two-way sensitivity analysis of the changes in direct costs ($) from speed-related death and injury according to traffic speed before and after a speed change programme is depicted in figure 3. Eight colour-coded curves in this figure represent eight different pretraffic calming speeds. Each curve in turn is defined by eight points, which each represents the cost of injuries and death at the relevant speed increment after the implementation of the traffic calming programme.

As shown in figure 3, the range of the changes in the direct costs of injury and death varies between −$1138 for reducing the speed from 30 to 5 mph and $1138 for increasing the speed from 5 to 30 mph. In figure 3, a positive amount that rises above the horizontal zero line reveals an increase in the costs of injury and death, while a negative figure that drops below the horizontal zero line shows a decrease in the costs of injury and death as measured by dollars ($). Figure 3 depicts that the per capita cost changes from a speed change programme are dependent on the speed before the start of the programme as well as speed after the implementation of the programme. For example, if the speed before the start of the programme is 30 mph, both reducing and increasing the speed by 5 mph will result in per capita cost savings. Ironically, if the speed before the start of the programme is 35 mph, reducing the speed by 5 mph will increase the cost of injury and death by $380 per capita while an increase in speed of 5 mph will reduce the cost of injury and death by $443 per capita. We believe that these non-linear changes are due to the probability discrepancies discussed in figure 1. Due to the important policy implications of these non-linear changes, we expand on this in the Discussion section.

The results of the two-way sensitivity analysis of incremental effect change (life expectancy as measured by QALY), due to change in speed before and after the traffic calming programme, across the range from 5 to 40 mph, covered a range of the changes between −1.14 QALYs and 1.14 QALYs. At the extremes of this range, the 1.14 QALY gain was for reducing the speed from 40 to 10 mph or 5 mph, as well as −1.14 QALY loss for increasing the speed from 5 or 10 mph to 40 mph. Unlike the costs of injury and death, which followed a more non-linear pattern, the effects follow a more linear pattern of increasing as the speed goes down, as well as decreasing as the speed goes up.

Table 2 details the results of the ICERs according to traffic speed before and after a speed change programme. When, as a result of the speed change, the costs of death and injury increases but the life expectancy decreases, the speed change programme is creating no value and is therefore dominated. When, as a result of the speed change, the costs of death and injury decrease and the life expectancy increases, the speed change programme is surely creating value and is therefore dominant. When, as a result of the speed change, the costs of death and injury and the life expectancy are both increasing, or are both decreasing, we report a numerical pay-off. For example, when the speed before the speed change programme is 35 mph, and it drops to 25 mph after the speed change programme, the per capita costs of injury and death increase by $264, and the per capita life expectancy increases by 0.59 QALY. Therefore, the ICER of this speed drop intervention is $264/0.59 QALY = $449/QALY. This means that, in order to increase the per capita life expectancy by 1 QALY, the local healthcare system will need to accept $449 per capita in additional costs, which are mostly due to injury rather than death.

## Discussion

Communities that consider traffic calming programmes are weighing the cost and benefits (both human and fiscal) of investing in preventing pedestrian injuries versus paying for them afterwards. Our two-way sensitivity analysis of speed before and after traffic calming showed that lower speeds do not necessarily lead to lower direct costs from injury and lost productivity for each QALY gained. Small incremental changes, specifically from high speeds, may reduce the probability of death but impact the probability of injury to a relatively smaller magnitude (figure 1), thereby increasing suffering while also increasing costs (but also reducing death). Taken as a whole, one conclusion that can be drawn from our study is that, politics and local considerations aside, policies should be directed at keeping urban speeds under 25 mph (or, ideally, under 20 mph). This is consistent with the ‘Vision Zero’ philosophy that no traffic fatality is acceptable.35

When smaller speed reductions occur in the context of higher road speeds than 25 mph, there are more pedestrians alive, but with a high probability of severe injury, leading to higher lifelong suffering. Urban planners and administrators need to be aware of this conundrum, and they design their speed reduction programmes in a way that they are impacting both the probability of death and the probability of injury in rational ways.

Our methods generally follow the recommendations of the Second Panel on Cost-Effectiveness Analysis,27 but they do not include important costs, such as pollution or exercise induced by any given policy. As they are agnostic to the type of intervention, they should be taken as an adjunct to policymaking only.27 28

Our study was subject to a number of important limitations. We managed this uncertainty by conducting broad sensitivity analyses on model inputs. Our study should only be used as an adjunct to policymaking. Speed can be reduced via a large array of interventions, each of which can impact air pollution, exercise or other factors that were not included in our analysis.

For example, productivity losses due to higher congestion and the potential for reduced commercial activity (due to slower speed for deliveries and customers) also need to be considered. Furthermore, the heavier congestion may lead higher levels of air pollution,6 36 which may lead to additional morbidity and costs from respiratory health effects. Conversely, busy road traffic may induce switching the mode of transportation from cars and, therefore, lead to higher rates of walking and bicycle use, which could have positive effects on health but are hard to quantify5. Our study takes the perspective of the health system. A complete societal perspective analysis, necessary for the calculation of a complete cost-effectiveness analysis, would include our results and environmental costs and effects associated with congestion and pollution, as well as costs to the judiciary and legal system, namely, the cost of law enforcement.27 Studies which contribute to further understanding the dynamic relations between these factors are already emerging from the literature.37 38 We recommended the expansion of system dynamic studies, with the objective of creating an analytic tool which allows for interactive use in order to explore the outcomes of varied parameter inputs of traffic speed. Such studies could help inform better road policy instruments, such as drivers insurance and the liability justice system.

Finally, the numbers we present should be contextualised within societal standards for the value of a QALY. In the US, such thresholds exceed $100 000/QALY gained,39 40 so the additional cost of going from 40 to 30 mph (about $1000/QALY gained) would amount to little more than a rounding error.

As health systems move to invest more in non-medical policies in the name of health prevention, policymakers and payers are too often left wondering where their investments might produce good value. Traffic speed reduction programmes may be one investment that has the potential to fit the bill, especially in large cities where the probability of interactions between pedestrians and motor vehicles is high. Given the complex and dynamic impacts that speed reduction programmes may have, they must be used intelligently so that they create more value by both reducing healthcare costs and increasing vitality.

### What is already known on the subject

Higher vehicle speeds are associated with higher probabilities of pedestrian collision, injury and death.

Speed reducing programmes reduce collision, injury and death.

The dynamic interplay between collision speed and the probability of injury and death can produce counter-intuitive outcomes.

### What this study adds

This study quantifies non-linear impacts between speed and health system costs and disability from injury.

The non-linear change in costs can impact the incremental cost-effectiveness ratios of speed change programmes in unpredictable ways.

## Acknowledgments

The authors thank Ms Jinjing Wu from Peking University for the intellectual input she provided in the development of this manuscript.

## References

## Footnotes

Contributors BM did the literature search, developed the main underlying probability relations, developed the Markov model, ran the Markov model and generated results, wrote the original paper and managed the revisions. ZR provided key intellectual insights in generating the Markov model and edited the first draft and later revisions. PAM developed the idea and the initiative for the research, provided guiding insights towards model development and provided major edits towards the final manuscript.

Funding This research was supported by Grant 1 R49 CE002096 from the National Center for Injury Prevention and Control of the CDC to the Center for Injury Epidemiology and Prevention at Columbia University Medical Center. The contents of the manuscript are the sole responsibility of the authors and do not necessarily reflect the official views of the funding agency.

Competing interests None declared.

Provenance and peer review Not commissioned; externally peer reviewed.