The Prevalence and Excess Mortality Risk of Driving with Children

Abstract

Introduction:

The presence of passengers can affect the driving behavior of motor-vehicle operators. Child passengers present unique motivations to drive more safely, as well as opportunities to distract drivers. Because motor-vehicle crashes are an important cause of premature childhood mortality, this study assesses whether adult drivers with child passengers are more or less likely to cause a fatal crash.

Method:

Data include fatal crashes involving one or two vehicles from 2007 to 2017 in the U.S. Fatality Analysis Reporting System. We apply methods developed by Levitt and Porter (2001) and Dunn and Tefft (2020) -the LPDT approach-to estimate the risk that adult drivers (21 years or older) with at least one child passenger (15 year or younger) cause a fatal crash relative to adults without child passengers.

Results:

Childhood crash exposure when traveling with an adult driver is low: 0.78% of vehicle miles traveled by adults included a child passenger. Nevertheless, adult drivers with child passengers were significantly more likely to cause a fatal crash than adult drivers without child passengers. The estimated risk of causing a single-vehicle crash was 6.2 times higher among the full sample of adults, 7.2 times higher among female drivers, and 5.0 times higher among drivers 25–44 years old.

Conclusions:

Despite their relatively low crash exposure, child passengers are associated with much greater risk of causing a fatal crash.

Practical Applications:

This study not only informs about the need to develop interventions to remind parents and adult drivers of the risks associated with driving children, but also reminds researchers about the enormous potential of the LPDT approach when applied to traffic safety issues.

Introduction

The presence of passengers can affect the driving behavior of motor-vehicle operators and the subsequent risk of involvement in a fatal crash. For example, passengers may encourage safer driving practices (slower speeds, longer following distances, usage of seatbelts, and signaling devices) or share in driving responsibilities (navigating, changing radio stations, checking for obstacles; Baxter et al., 1990; Stutts, et al., 2003; Geyer & Ragland, 2005). On the other hand, passengers can also be an additional source of distraction or create social pressure to engage in high-risk behavior. Existing research suggests that the relative importance of these countervailing forces depends on the attributes of both the operator and other vehicle occupants. For instance, the presence of an adult passenger tends to reduce the incidence of risky driving behaviors and crash risk relative to driving alone, a result that is remarkably robust over time and across study locations, including the United States (Braitman et al., 2014; Hing et al., 2003; Geyer & Ragland, 2005; Lee & Abdel-Aty, 2008); the United Kingdom (Baxter, et al. 1990); Spain (Rueda-Domingo et al., 2004); Sweden (Engström et al., 2008); and Canada (Evans & Wasielewski, 1983). On the other hand, the risk of crash involvement is higher for teenage drivers when traveling with peer passengers, particularly at night (Chen et al., 2000; Curry et al., 2016; Oimet et al., 2015; Pradhan et al., 2015).

In this article, we examine how the presence of a child passenger (an occupant 15 years of age or younger) is related to the fatal crash risk of adult motor-vehicle operators (a driver 21 years of age or older), recognizing that child passengers present both unique motivations to drive more safely, as well as opportunities to distract drivers (Stutts et al., 2003). Previous research has indicated that the presence of a child tends to cause motor-vehicles operators to drive with additional caution, which should reduce total crash risk. Specifically, Rueda-Domingo et al. (2004) showed that drivers in Spain with at least one passenger between 4 and 15 years of age were approximately 25% less likely to cause a collision as drivers without passengers.

Nevertheless, this behavioral response is neither universal nor absolute. For instance, rates of cellphone usage among drivers with child passengers in the United States typically range from 75% to 90% (Roney et al., 2013; Macy et al., 2014; Massey et al., 2016). In a study of parents in the United States, while the probability of using a handheld mobile phone while driving decreased when a child was present (OR=0.66), nearly 80% of study participants reported a cell-phone related distraction, including twenty-five percent who reported using a cell phone on nearly every trip (Macy et al., 2014). Similarly, although most adults do not drive with child passengers after consuming alcohol, a random sample of drivers in Washington state revealed that 0.2% of vehicles with a child were operated by an adult under the impairment of alcohol (DUI; Romano et al., 2019). This form of child endangerment (CE) has been labeled DUI-CE and remains a source of concern for researchers, practitioners, and policy-makers (Kelley-Baker & Romano, 2014a; Quinlan et al., 2014; Romano et al., 2015; Romano et al., 2019).

While the presence of child passengers reduces risk-taking behavior among a potentially large share of vehicle operators, children have also been identified as a source of driver distraction that increases crash risk (Koppel et al., 2011; Maasalo et al., 2019; Kuo et al., 2016). A study of Australian drivers that videorecorded in-vehicle activity revealed that the majority (72%) of distractive interactions between adult drivers and children occur when the vehicle is moving (Koppel et al., 2011), while data from fatal crashes in the United States revealed that drivers with child passengers were significantly more likely to be distracted (3.6 times for male drivers and 3.5 times for female drivers) compared to those without passengers (Maasalo et al., 2019). Kuo and colleagues (2016) reported that the presence of children increases driver distraction and crash risk when there is more than one child in the car.

Because it is unclear which of these countervailing forces—behavioral modification versus distraction—is more influential at the population level, it is still an open question whether the presence of child passengers increases the fatal crash risk of adult drivers. Indeed, although the previously discussed study by Ruedo et al. (2014) found drivers with passengers 4–15 years old were less likely to cause a collision than those without passengers, the magnitude of the protective effect varied widely depending on the age and gender of the driver, and was often lower than the protective effect of carrying older passengers. For example, the adjusted odds-ratio of causing a collision for female drivers 35–44 years old with at least one passenger 4–15 years old ranged from .94 to 1.09 relative to those without any passengers. Among the same group of drivers, however, the adjusted odds-ratio of causing a collision with at least one passenger 35–44 years old ranged from .73 to .77.

Therefore, this study will contribute to the literature by estimating how the presence of at least one child passenger (aged 15 or younger) is associated with the risk that an adult driver (aged 21 or older) makes an error that causes a fatal crash. To do so, we adopt a statistical approach previously applied to other driver characteristics (alcohol impairment status, age, gender, driving history), but which has not been used to study the risk of driving with child passengers (Levitt & Porter, 2003; Dunn & Tefft, 2020, 2021; Fujiwara & Takechi, 2021). It will also assess whether the estimated relative risk of driving with a child passengers differs by driver characteristics such as age, gender, and alcohol-usage. These subgroup analyses are particularly important because they provide additional support that the presence of children in the vehicle is the source of risk differentials, rather than underlying differences in the characteristics of drivers that transport children relative to drivers that do not.

Methods

To estimate how the presence of children in a vehicle influences crash risk, we adopted the methods developed by Levitt and Porter (2001) and extended by Dunn and Tefft (2020) (hereafter denoted as the LPDT model), which have previously been used to characterize the prevalence and risk of drinking-and-driving in the United States. Under conditions described below (and the accompanying Technical Appendix), this approach identifies three parameters: (1) the share of vehicles that include at least one child passenger; (2) the probability that drivers of such vehicles will cause a fatal crash involving two-vehicles relative to drivers without child passengers; and (3) the analogous probability of causing a fatal crash involving only their vehicle. These lattermost probabilities are collectively referred to as the relative fatal crash risk—although these are two distinct parameters, their estimated values in previous applications have always been quantitatively similar (Levitt & Porter 2001; Dunn & Tefft 2020, 2021). As we describe below, the existence of two risk parameter estimates is critically important for implementation of model selection.

Motor Vehicle Crash Fatalities:

To implement the LPDT model, we used the 2008–2017 Fatality Analysis Reporting System (FARS). The FARS is a census of motor-vehicle traffic crashes in the United States that resulted in a fatality within 30 days of the crash. Each crash record includes variables that characterize the attributes of the crash, as well as the vehicles and individuals involved. Some attributes commonly associated crash risk are well-measured in FARS (e.g., the age and sex of drivers, which are readily available on driver’s licenses). Dunn and Tefft (2020) report that age was missing for 3.9% of drivers, while sex was missing for 3.3% when considering fatal crashes involving one or two vehicles. A measure of the alcohol impairment status was slightly more likely to be unavailable in FARS. Dunn and Tefft (2020) report that only 15% of crashes lacked both a BAC test result and the judgment of the responding officer.

Other potential risk factors, however, are either unmeasured or there are continuing concerns about the quality of the data collected through the FARS. Of particular interest, driver distraction is not universally available on crash reports and law enforcement judgment about the causal factors for particular crashes are potentially subject to significant mismeasurement. As a result, no attempt is made to estimate the risk associated with distraction caused by the presence of child passengers specifically. Rather, the estimated risk parameters presented subsequently capture the total risk from all factors associated with vehicles that have child occupants.

The ability to draw conclusions about the underlying causes of differences in crash risk therefore depends critically on constructing estimation samples where the treatment group (drivers with child passengers) are as similar as possible to the control group (drivers without child passengers). Thus, we considered seven groups of drivers: all drivers aged 21 years old or older; drivers aged 21 or older in crashes with no evidence of alcohol involvement; female drivers aged 21 or older; female drivers aged 21 or older in crashes with no evidence of alcohol involvement; all drivers 25 to 64 years of age; all drivers 25 to 54 years of age; and all drivers 25 to 44 years of age. Within each group, we identified those driving at least one child 15 years old or younger (treatment), and compared them with the remaining vehicles in the group without a child passenger (control). Defining alternative driver samples will allow us to ascertain whether subsequent results are simply reflecting confounding variation in underlying driver risk profiles. Of special interest are our analyses involving female drivers and those aged 25–44 years old, as females tend to be the primary caregivers of children (McGuckin & Murakami, 1999; Root & Schintler, 1999; Rosenbloom, 2004; Pew Research, 2017; Zamarro & Prados, 2021) and the 2020 Current Population Survey revealed that 74% of individuals 25–44 years old are members of a household that include at least one biological, step, or adopted child under age 18 (Census Bureau, 2020). Therefore, it is of great interest to assess the relative fatal crash risk of individuals most likely to have children or be the caregiver of child passengers.

Similarly, adults who drive with child passengers are less likely to consume alcohol before operating their vehicle (Kelley-Baker & Romano, 2014b; Romano & Kelley-Baker, 2015), thus a separate analysis that omits drinking drivers allows us to mitigate the potential confounding role of alcohol. Following Dunn and Tefft (2020), we categorize a driver as drinking if the responding officer judges the driver to be alcohol-involved and not drinking when the officer judges not alcohol-involved. If this judgment is missing or unknown, a driver is categorized as drinking if the result of a BAC test is positive and non-drinking if the result is zero.

It would be desirous to also exclude drivers based on drug impairment, particularly given recent changes in the legal use of recreational cannabis and the ongoing opioid crisis. Nevertheless, concerns about these data, including widespread missingness from crash reports, the accuracy of law enforcement judgments, and the difficulty of translating test results to contemporaneous impairment suggest that doing so may introduce measurement error that is worse than the potential confounding variation.

Analytical Approach

The LPDT model uses the observed distribution of characteristics among drivers involved in fatal crashes to estimate three parameters: the prevalence (share of vehicle miles traveled) of drivers with that characteristic (π); the risk that a driver with that characteristic commits an error that causes a two-vehicle fatal crash relative to drivers without that characteristic (θ); and the risk that a driver with that characteristic commits an error that causes a fatal crash involving only their vehicle relative to drivers without that characteristic (λ). For the interested reader, the Technical Appendix provides a formal derivation of the LPDT estimator. In this section, we limit discussion to two issues specific to the current application: the LPDT identification assumption and the parameter selection criterion.

The equal-and-independent mixing (EIM) assumption

The standard implementation of the LPDT approach assumes that drivers obey equal-and-independent mixing (EIM) within observational units defined at the state-year-hour-day level (Levitt & Porter, 2001; Dunn & Tefft, 2020, 2021). Independent mixing is a fairly weak assumption, requiring that the distribution of drivers involved in one crash does not depend on the distribution of drivers in another crash. Levitt and Porter (2001) convincingly argued that unless observational units are narrowly defined (e.g., one road segment for 30 to 60 minutes), this property is likely to hold sufficiently well so that plausibly sized departures will not meaningfully affect parameter estimates.

The implications of assuming equal mixing—that drivers do not clump either spatially or temporally within observational units—is subject to greater concern. For example, the assumption that all drivers have equal opportunity to interact is unlikely to hold exactly in the application to drinking-and-driving: “Although heterogeneity in the distribution of driver types across time and space can be accommodated by defining sufficiently small observational units, it is unlikely that the number of interactions a driver has with other vehicles and the composition of the drivers encountered are completely independent of driver type” (Dunn & Tefft, 2021). For example, because of different transportation options, the share of drinking drivers in the rural areas of a state may be different than the share of drinking drivers in urban areas of the same state at the same time.

Despite this theoretical objection, in practice the LPDT model has shown to be robust to moderate departures of the EIM assumption. Levitt and Porter examined departures from the EIM assumption and concluded that “if two drinking drivers were 10 percent more likely to interact than would be predicted by EIM, results are qualitatively similar” to a case in which the EIM assumption would fully hold (Levitt & Porter, 2001). In a thorough sensitivity analysis, Dunn and Tefft (2021) similarly find that while the existence of unequal mixing may lead to bias in parameter estimates, even large departures from equal mixing may not meaningfully affect parameter estimates.

When considering driving with children, the existing definition of observational unit over which equal mixing is assumed seems inappropriate. Specifically, equal mixing is assumed at the state-year-hour-day level, where day is a dichotomous variable (weekend nights, weekday nights) (Levitt & Porter, 2001; Dunn & Tefft, 2020, 2021). For this effort, because the share of drivers with children may vary depending on whether school is in-session, we introduced an additional level of disaggregation, assuming equal mixing at the state-year-hour-day-season level, where day is dichotomous [weekend (Friday 8 p.m. to Monday 4 a.m.) versus weekday (Monday 4 a.m. to Friday 8 p.m.)] and season is dichotomous [school-year (September to May) versus summer (June to August)].

Selecting a solution

The maximum likelihood function of the LPDT estimator is quadratic in θ, the relative two-vehicle fatal crash risk. Thus, depending on the initial values, the maximization algorithm can converge to a solution, denoted $\widehat{\theta }$, of either θ or 1/θ. Selecting between these options is fundamental to the LPDT method. The solution we propose is both new to the literature and potentially useful in other applications. Thus, despite some of its technical aspects, we present it here, rather than in an appendix.

In previous applications, risk order across driver types was assumed on (strong) a priori grounds: drinking drivers tend to be riskier than sober drivers; drivers with poor driving records tend to be riskier than those with good driving records; males tend to be riskier than females; and young drivers tend to be risker than older drivers (Dunn & Tefft, 2021). In these instances, because of extensive previous knowledge on drivers’ drinking and driving behaviors, the determination of whether the solution to the maximization algorithm should be interpreted as θ or 1/θ was straightforward. In other words, if estimating the relative risk of drinking-drivers, a result of $\widehat{\theta }=10$ would naturally be interpreted as drinking-drivers being 10 times as risky as non-drinking drivers, while a result of $\widehat{\theta }=0.1$ would be interpreted as non-drinking drivers being 10 times less risky as drinking drivers.

In the current application, however, it is not clear whether driving with children is more or less risky than driving without children. Therefore, because of the lack of a priori knowledge, we provided a range of initial values for the maximum likelihood estimator, allowed convergence to both possible solutions, and calculated two sets of estimates for {θ,λ,π }, denoted $\{\widehat{\theta },\widehat{\lambda },\widehat{\pi }\}$. We then evaluated the soundness of either set of solutions using the criterion that the relative risk of causing a fatal two-vehicle crash should be similar to the relative risk of causing a fatal one-vehicle crash.

Our measure of similarity is the arc-difference of θ and λ, δ(θ,λ), defined as:

$$\delta (\theta ,\lambda )=\frac{|\theta -\lambda |}{(\theta +\lambda )/2}$$

The arc-difference is a base-independent version of the percent difference that uses the arithmetic mean of the two values being compared in the denominator. It therefore avoids the problem that the percent difference of θ from λ is not equal to the percent difference of λ from θ. This is a justifiable metric as previous research has found that the relative-risk of a drinking-driver causing a fatal two-vehicle crash is similar to the relative risk of a drinking-driver causing a fatal one-vehicle crash. For example, the arc-difference between estimates of these values ranges from .019 to .157 (Dunn & Tefft, 2021).

The arc-difference is particularly useful for comparison in this application because it is invariant to reciprocals [δ(θ,λ) = δ(1/θ,1/λ)] and scale [δ(θ,λ) = δ(aθ,aλ)]. The former attribute is critical because while the solutions to θ are reciprocals, the estimates of λ are not. Therefore, for each $\{\widehat{\theta },\widehat{\lambda }\}$-solution to the maximum likelihood function, we calculated $\delta (\widehat{\theta },\widehat{\lambda })$. If one set of estimates generated an arc-difference substantially smaller than the other, then we took that as strong ex post evidence that the risk order implied by the former was correct. The second attribute is equally critical because departures from equal-mixing introduce equiproportional bias across estimated risk parameters. In other words, if a violation of the equal mixing assumption causes $\widehat{\theta }$ to be twice as large as θ, then $\widehat{\lambda }$ will also be twice as large as λ. Although the estimated values of both θ and λ would be biased, the value of their arc-difference would be unbiased. As a result, selecting the parameter pair with the smallest arc-difference would still yield the correct risk order (i.e., whether driving with children increased or decreased fatal crash risk), even if the magnitude of relative risk were biased.

Estimation was undertaken with the Generic Likelihood Model of the statsmodels package for Python using Spyder and standard errors were calculated using bootstrapping with 100 iterates.

Results

Descriptive Statistics

Table 1 reports summary statistics of fatal crashes for the full sample, those crashes with no drinking involved, those crashes with no male drivers, and crashes with neither drinking involved nor any male drivers. Between 2008 and 2017 there were 315,623 crashes with 473,449 vehicles reported in FARS that did not contain missing information about month, day, hour, or state. After only including crashes that involved one or two vehicles with drivers, our full analytic sample consisted of 294,050 crashes and 401,887 vehicles. Alcohol was absent in about 68% (N=127, 423) of single-vehicle crashes and 77% (N=83,808) of two-vehicle crashes. A drinking driver was present in 32% of all single-vehicle crashes and 12% of all two-vehicle crashes. Female-only drivers were present in 22% (N=41,633) of single-vehicle crashes and 7% (N=7,772) of two-vehicle crashes. About 5% of all vehicles involved in single-vehicle crashes and 7% of all vehicles involved in two-vehicle crashes had a child passenger (i.e., aged 15 y/o or younger) at the time of the crash. The proportion of vehicles with children increase among female-only crashes: 11% and 14% of all vehicles involved in single-vehicle and two-vehicle crashes, respectively.

Table 1.

Summary statistics for analytic samples

	Full sample				No Alcohol				Female drivers only				No Alcohol, Female drivers only
	One vehicle		Two vehicles		One vehicle		Two vehicles		One vehicle		Two vehicles		One vehicle		Two vehicles
	mean	SD	mean	SD	mean	SD	Mean	SD	mean	SD	mean	SD	mean	SD	mean	SD
Crashes
N	186,213		107,837		127,423		83,808		41,633		7,772		32,438		6,679
Crash persons involved	1.59	1.24	3.02	1.54	1.61	1.33	3.01	1.57	1.75	1.28	3.32	1.68	1.78	1.33	3.32	1.68
Crash during school day	48 %	50	49 %	50	50 %	50	51 %	50	50 %	50	52 %	50	51 %	50	53 %	50
Crash during weekend	30 %	46	22 %	42	24 %	43	18 %	38	26 %	44	18 %	39	22 %	41	16 %	36
Crash during nighttime	45 %	50	26 %	44	35 %	48	18 %	38	38 %	49	18 %	38	30 %	46	12 %	33
Any driving with children	5 %	21	13 %	34	6 %	23	13 %	34	11 %	31	26 %	44	12 %	33	26 %	44
Any driver drinking	32 %	46	22 %	42	0 %	0	0 %	0	22 %	41	14 %	35	0 %	0	0 %	0
Vehicles
N	186,213		215,674		127,423		167,616		41,633		15,544		32,438		13,358
Vehicle occupants	1.54	1.28	1.52	1.23	1.54	1.40	1.51	1.25	1.69	1.34	1.67	1.41	1.71	1.41	1.67	1.42
Driver age (years)	40.4	17.8	43.7	18.7	42.7	19.1	45.0	19.3	40.3	18.5	45.2	20.3	42.0	19.4	46.2	20.7
Driving with children	5 %	21	7 %	25	6 %	23	7 %	26	11 %	31	14 %	35	12 %	33	14 %	35
Driver drinking	32 %	46	12 %	33	0 %	0	0 %	0	22 %	41	8 %	26	0 %	0	0 %	0
Driver female	22 %	42	27 %	44	25 %	44	28 %	45	100 %	0	100 %	0	100 %	0	100 %	0

Notes: N denotes total number of cases. “ percent” denotes percent of “N”. SD stands for Standard Deviation. “Crash persons involved” indicate the mean number of individuals involved in the crash. “Vehicle occupants” indicate the mean number of occupants per vehicle.

Estimation Results

Table 2 reports the estimated risk of causing a two-vehicle crash, a one-vehicle crash, and share of vehicles with a child by driver subsample from maximum likelihood estimation of equation, relative to crashes and vehicles in which no vehicle was present. As explained above, the estimate of θ reported in Panel A for any subsample is the reciprocal of the analogous estimate in Panel B. Remaining completely agnostic about which set of results is correct, drivers aged 21 or older (column 1) with a child in their vehicle are approximately five times more likely (5.23, 95% CI = (3.98, 6.48), P<.001; Panel A) or five times less likely (0.19 (0.17, 0.21), P<.001; Panel B) to cause a fatal two-vehicle crash than those without children in the vehicle. Although both sets of estimates are mathematically valid, only one set is plausible: the estimates of λ overwhelmingly support the conclusion that the results from Panel A should be accepted. First, the arc-differences between the estimated risks of causing one- and two-vehicle fatal crashes in Panel B are all above 1.34, which is far outside the range of arc-differences in studies of drinking-and-driving. In contrast, the arc-difference for drivers aged 21 or older are all less than 0.41. Second, the estimate of λ for all driver subgroups in Panel B would suggest that while drivers with child passengers are four-to-five times less likely to cause a fatal two-vehicle crash, they are between 18% and 51% more likely to cause a single-vehicle fatal crash. That reversal of relative risk is exceedingly improbable. Thus, based on the totality of the results, we conclude there is exceptionally strong evidence that overall, driving with a child in a vehicle increases the probability of causing a fatal crash by a statistically significant amount.

Table 2.

Relative risk of causing a two-vehicle, and a one-vehicle crash, and share of vehicles by driver subsample

	Full sample	No alcohol	Female	Female, no alcohol	Ages 25–64	Ages 25–54	Ages 25–44
Panel A
Risk of two-vehicle fatal crash	5.23 (0.64)	4.24 (0.54)	4.95 (1.74)	4.89 (1.7)	4.83 (0.86)	4.43 (0.74)	4.12 (1.15)
Risk of one-vehicle fatal crash	6.20 (0.62)	6.40 (0.66)	7.07 (1.95)	7.21 (1.97)	6.04 (0.83)	5.64 (0.72)	5.00 (0.97)
Share of vehicles with children	0.0078 (0.0007)	0.0095 (0.0010)	0.0167 (0.0037)	0.0189 (0.0048)	0.0107 (0.0014)	0.0132 (0.0016)	0.0175 (0.0034)
Risk arc-difference	0.17	0.41	0.35	0.38	0.22	0.24	0.19
Panel B
Risk of two-vehicle fatal crash	0.19 (0.02)	0.24 (0.03)	0.20 (0.09)	0.20 (0.08)	0.21 (0.03)	0.23 (0.04)	0.24 (0.08)
Risk of one-vehicle fatal crash	1.18 (0.04)	1.51 (0.07)	1.43 (0.18)	1.47 (0.2)	1.25 (0.05)	1.27 (0.07)	1.22 (0.13)
Share of vehicles with children	0.0396 (0.0011)	0.0388 (0.0016)	0.0773 (0.0079)	0.0861 (0.0094)	0.0498 (0.0020)	0.0559 (0.0030)	0.0683 (0.0061)
Risk arc-difference	1.45	1.45	1.51	1.52	1.42	1.39	1.34
Residual degrees of freedom	6187	5158	2631	2194	4984	4478	3447

Panel A and B denote two sets of solutions that are technically valid. Estimates of the risk arc-difference indicate that estimates in panel A are optimal and those in panel B should be discarded. Risks are estimated relative to events in which no child was present

From the estimates in Panel A (those accepted as correct), 0.78% (0.65%−0.92%) of vehicle-miles-traveled by drivers at least 21 years of age include at least one child passenger aged 15 or younger. Non-drinking drivers, females, and younger adults would be expected to be more likely to have child passengers, and that is indeed the pattern that emerges: 0.98%, 1.67%, and 1.75%, respectively.

Table 2 also shows that regardless of the sample of drivers considered, the presence of a child passenger is associated with an elevated fatal crash risk. The estimate on the relative risk of causing a fatal two-vehicle crash ranges narrowly from 4.12 (1.86–6.37, P=.01) among drivers 25–44 years old to 5.23 (3.98–6.48, P<.001) when using the entire sample of drivers above age 21. The analogous estimate for causing a fatal one-vehicle crash ranges slightly more widely, from 5.00 (3.10–6.90, P<.001) among drivers 25–44 years old to 7.21 (3.35–11.07, P=.003) among non-drinking female drivers above age 21.

Sensitivity analysis

As stated earlier, there is reason to be skeptical that equal mixing holds exactly at the state-year-hour-day-season level used to define observational units. Figure 1 plots the estimated value of the relative risk of causing a fatal two-vehicle crash as function of the excess mixing probability of vehicles transporting minor passengers. These are undertaken assuming that the relative risk of causing a two-vehicle fatal crash equals the relative risk of causing a one-vehicle fatal crash, i.e., θ = λ As is evident, as excess mixing increases, the estimated relative fatal crash risk is increasingly downward biased. Thus, the results presented earlier, even in the case when equal-mixing failed to hold exactly, would provide lower bounds on the additional fatal risk that drivers with child passengers impose.

Figure 1: Estimated value of relative risk of causing a two-vehicle fatal crash from LPDT when equal mixing assumption fails.

Note: Assumes the relative risk of causing a two-vehicle fatal crash equals the relative risk of causing a one-vehicle fatal crash, i.e., θ = λ. Python script available as in GitHub repository.

Discussion

This study makes a number of important contributions to the traffic safety literature. First, it applies the LPDT method to a new issue in traffic safety research: estimating the relative risk of adult drivers with child passengers. This question differs from previous applications of the LPDT method where the risk order of driver characteristics could be assumed a priori. In contrast, child passengers can induce drivers to exercise additional caution or increase crash risk through distractive behaviors. This study successfully implemented a new model selection criterion that yielded estimates of prevalence and relative fatal crash risk without imposing a priori parameter restrictions.

Second, this study provides a new national estimate of children’s exposure to crashes when riding with adults: 0.78% of all vehicle-miles driven by adults aged 21+ years include at least one child 15 years old or younger. Existing federal surveys do not specifically elicit this information from drivers. Rather, the closest information on this issue come from the National Household Travel Survey (NHTS), which reports vehicle miles traveled by trip purpose. For example, in 2017, 2.9% of all miles traveled in private vehicles were associated with school, daycare, or religious activity. But, this figure includes drivers under age 21 driving themselves to school and childless adults traveling to religious services (NHTSA, 2018). Thus, the estimated prevalence is both plausible and novel. Further, despite their relative low exposure to crashes, motor-vehicle crashes are the leading cause of death among U.S. children (Centers for Disease Control and Prevention, 2021).

Third, this study clearly demonstrates that at the population level, adult drivers with child passengers are significantly more likely to cause a fatal motor-vehicle crash than drivers without child passengers. The risk of committing an error that causes a fatal crash involving either one or two vehicles is 4.1 to 7.1 times higher among the former compared to the latter, depending on the definition of the study sample. Of particular note, this result holds when restricting attention to population subgroups that are more likely to transport children or to live in households with children: non-drinking drivers, younger adults, and females.

Although this result indicates that adults who drive with children are more likely to cause a fatal crash, the underlying mechanisms responsible remain unclear. Among the several (neither exhaustive nor mutually exclusive) explanations considered subsequently, each is accompanied by distinct implications for public health and traffic safety policy.

First, children may engage in distractive behaviors that increases the crash risk of adult drivers. Because drivers have limited control over the behavior of other vehicle occupants—indeed, attempts to control the behavior of children may be its own source of increased crash risk— the implied policy recommendation would be to encourage drivers to transport children only when necessary and to select driving environments that limit the negative consequences of child-initiated distractive events.

Second, children in the vehicle may cause drivers to behave in more dangerous ways without being the proximate cause. For example, drivers may feel the impulse to check the interior of the vehicle or be tempted to interact with their child passengers rather than focus on the roadway. These are instances of drivers altering their behavior because children are present, though the child passengers have not initiated that change. Because these actions are under the control of drivers, interventions that encouraged adults who transport children to recognize such tendencies and limit their occurrence may reduce the higher crash risk associated with transporting children.

A third possibility is motor vehicle trips that include child passengers may already be more taxing on adult drivers. For example, picking up a child from daycare or after-school activities may be the first in several errands that need to be completed between the end of the workday and preparing dinner. Attention may be partially directed toward these tasks, reducing the focus on driving and increasing the perceived need to use handheld devices for telephone calls, texting, or GPS directions. Suggesting that parents should simply “be less busy” without providing the financial and time resources they require to make that prescription feasible is inappropriate, thus policy interventions to address this potential mechanism should be respectful of the challenges that many parents face and may require structural changes that increase parental support.

Finally, our results may capture unobserved differences in the driving risk profiles of adults who transport children and those that do not. Even when restricting attention to population subgroups with the largest share of drivers that live with children (e.g., females or adults 25–44), it may be the case that the subset who are most risk-averse (i.e., the individuals who drive most safely in all situations) already choose to limit their travel with child passengers to the absolute minimum. On the one hand, it may be the case that the most risky drivers are also the least able to avoid driving with children. Potential interventions must be cognizant of resource constraints faced by such drivers. Nevertheless, improving adherence to safe driving practices while transporting children may need to receive greater emphasis in public health and traffic safety outreach, precisely because children are being transported by relatively higher risk drivers.

The preceding discussion informs some of the important limitations of this study. Although the LPDT method can provide an estimate of the relative fatal crash risk of adult drivers with child passengers, it cannot parse the relative importance of the underlying mechanisms that are responsible for that increased risk. Given the importance of fatal motor-vehicle crashes to premature childhood and adolescent mortality, documenting which of the aforementioned channels are most influential in associating child passengers with higher crash risk is crucial for developing appropriate policy responses. Because of the data quality issues discussed previously, the ability to do so using products like FARS may be limited. Rather, future research that drew upon alternative data sources and experimental designs will likely be critically important in resolving this question.

A related limitation is that, while we can define the estimate sample in a manner that maximizes the share of drivers that come from households with children, we are not able to explicitly restrict the sample to drivers that live in households with children. To the extent that (1) some of the drivers in vehicles without children involved in fatal crashes do not have children in their household and (2) becoming a parent tends to reduce risk-taking behavior, our estimates of the additional risk of driving with a child are lower bounds on the additional risk that driving with a child creates.

Finally, the equal-mixing assumption imposed by the LPDT approach is not likely to hold exactly. Nevertheless, violations of equal mixing would tend to bias the estimated relative fatal crash risk of driving with child passengers downward. Thus, the values reported here would act as lower bounds and are sufficient to confidently say that those who drive with children in the vehicle are relatively more likely than those who do not, even when restricting attention to relatively narrow age categories.

Regardless of these limitations, this study provides a valuable new estimate that adult drivers with child passengers are 4–7 times more likely to cause a fatal motor-vehicle crash than adult drivers without children in the vehicle. This result not only informs about the need to develop interventions to remind parents and adult drivers of the risks associated with driving children, but also demonstrates the enormous potential of the LPDT approach when directed toward traffic safety issues beyond its previously narrow application to drinking-and-driving.

Biographies

Richard A. Dunn, Ph.D., is an Associate Professor in the Department of Agricultural and Resource Economics at the University of Connecticut with a Ph.D. in Economics from the University of Wisconsin-Madison. He is an applied microeconomist with an emphasis on identification and causal inference in econometric models using observational data. His research interests have focused on the determinants and consequences of health-related risky behavior, including suicide, obesity, and drinking-and-driving.

Nathan W. Tefft, Ph.D., is an Associate Professor in the Department of Economics at Bates College with a Ph.D. in Economics from the University of Wisconsin-Madison. His background is in economics with applications in health and health-related behaviors, and he has published articles on the effects of taxation, tobacco control, and other policies on health-related behaviors and outcomes including obesity, soft drinks, and alcohol-related fatal car crashes. He has expertise working with large datasets and advanced econometric models, including instrumental variable, demand system estimation, and panel data analysis.

Eduardo Romano, Ph.D., is a Senior Research Scientist at the Pacific Institute for Research and Evaluation. An economist by training, his research interests have focused on risk-related behaviors as well as on the analyses of risk-reducing and risk-managing policies. His recent interests include risk perceptions and impaired driving, particularly among children, adolescents, women, and minorities. He is conducting research on the effectiveness of alcohol interlock devices, and on the developmental trajectories towards impaired driving outcomes. Among others organizations, he is a member of the Research Society on Alcoholism, the Research Society on Marijuana, ICADTS, National Hispanic Science Network, and the TRB Committee on Impaired Driving

Technical Appendix: Derivation of LPDT Maximum Likelihood Function

Classify an adult driver as transporting a minor passenger (denoted C) if they are at least 21 years of age and have at least one vehicle occupant 15 years old or younger. Classify an adult driver without minor passengers (denoted 0) if they are at least 21 years of age and do not have at least one vehicle occupant 15 years old or younger. Thus, the set of adult driver types is {C,0}. Let N_C and N₀ denote the number of C- and 0-type drivers operating a vehicle within a given geographic area and time period, respectively. The share of type i drivers operating a vehicle is N_i/(N_C+N₀).

Assume that the number of interactions a driver has with other vehicles and the composition of the drivers encountered is independent of driver type, i.e., equal-and-independent-mixing (EIM). Then, the probability that an interaction involves a driver of type i and a driver of type j is Pr(i,j|I=1)=N_iN_j/(N_C+N₀)².

Further assume that a fatal crash occurs when a driver makes a fatal error, the likelihood of which, θ_i, depends upon driver type (allowing for heterogeneity within driver type, θ_i is the mean fatal error probability for drivers of type i). Then, the probability that a fatal crash occurs when a driver of type i interacts with a driver of type j is Pr(A=1|I=1, i, j)=θ_i+θ_j−θ_iθ_j. Ignoring the final term, which is the product of very small fractions, the probability of a fatal crash between drivers of type i and j is:

$$\mathrm{Pr}(A,i,j\mid I=1)=\mathrm{Pr}(A\mid I=1,i,j)\mathrm{Pr}(i,j\mid I=1)=\frac{N_i{N}_j\left({\theta }_i+{\theta }_j\right)}{{\left(N_C+N_0\right)}^2}$$ [1]

These probabilities are conditional on an interaction occurring, but FARS is a dataset of crashes, not interactions. Applying Bayes’ Rule, yields:

$${\text{P}}_{\text{ij}}=\mathrm{Pr}(i,j\mid A=1)=\frac{N_i{N}_j\left({\theta }_i+{\theta }_j\right)}{2\left[{\theta }_C{\left(N_C\right)}^2+\left({\theta }_C+{\theta }_0\right)N_C{N}_0+{\theta }_0{\left(N_0\right)}^2\right]}$$ [2]

The collection of these probability expressions offers two linearly independent equations in four unknowns: N_C, N₀, θ_C, and θ₀. Let N=N_C/N₀ denote the ratio of adults drivers transporting minors to adult drivers without minor passengers and θ=θ_C/θ₀ denote the relative risk of an adult driver with a minor passenger causing a fatal crash. Then, the probabilities of observing the three different combinations of driver types in a fatal two-vehicle crash are:

$${\text{P}}_{\text{CC}}=\frac{\theta N^2}{\theta N^2+(\theta +1)N+1},{\text{P}}_{\text{C}0}=\frac{(\theta +1)N}{\theta N^2+(\theta +1)N+1},{\text{P}}_{00}=\frac{1}{\theta N^2+(\theta +1)N+1}$$ [3]

Assuming that the composition of drivers is independent across crashes, the joint distribution of two-vehicle crashes characterized by driver type is multinomial:

$$\mathrm{Pr}\left({\text{A}}^{CC},{\text{A}}^{C0},{\text{A}}^{00}\right)=\frac{\left({\text{A}}^{CC}+{\text{A}}^{C0}+{\text{A}}^{00}\right)!}{A^{CC}!A^{C0}!A^{00}!}{\left({\text{P}}_{CC}\right)}^{{\text{A}}^{CC}}{\left({\text{P}}_{C0}\right)}^{{\text{A}}^{C0}}{\left({\text{P}}_{00}\right)}^{{\text{A}}^{00}}$$ [4]

where A^ij denotes the number of two-vehicle crashes involving one type i and one type j driver. Maximum likelihood estimation of [4] substituting [3] is then undertaken. Because of the quadratic nature of the binomial distribution, two real solutions exist.

Single-vehicle crashes

Define λ_i as the (mean) probability that a driver of type i commits an error causing a fatal one-vehicle crash. If A is an indicator for a one-vehicle crash occurring, then the probabilities of each driver type’s involvement in a crash (defined as P_i) are:

$$P_C=\mathrm{Pr}(i=C\mid A=1)=\frac{{\lambda }_C{N}_C}{{\lambda }_C{N}_C+{\lambda }_S{N}_{S^{\prime }}};P_0=\mathrm{Pr}(i=0\mid A=1)=\frac{{\lambda }_S{N}_S}{{\lambda }_C{N}_C+{\lambda }_S{N}_S}$$ [5]

If the relative risk an adult driver transporting minors causing a fatal crash is $\lambda =\raisebox{1ex}{${\lambda }_C$}\!\left/ \!\raisebox{-1ex}{${\lambda }_0$}\right.$, then P_C/P₀ = λN=A^C/A⁰, the ratio of single-vehicle fatal crashes. Notice that the distribution of one-vehicle crash driver types cannot separately identify prevalence or relative risk. Rather, identification of θ and N from two-vehicle crashes allows identification of λ. Nonetheless, a separate estimate of single-vehicle fatal crash risk can be useful for policy-makers. In practice, it also improves estimation of N and can serve as a specification check as similar estimates of θ and λ suggest that differing crash-avoidance abilities are not driving results.

Following Dunn and Tefft (2020), we use the relationship for single-vehicle fatal crashes to define the share of adult drivers transporting minor passengers in observational unit k: $N_k=A_k^C/\lambda A_k^0$, where $A_k^i$ is the number of one-vehicle crashes involving drivers of type i in observational unit k. We then substitute for N_k in the probabilities from [3] to define the likelihood of observing {A^C,A⁰,A^CC,A^C0,A⁰⁰} within a state-year-hour-day-season observational unit:

$$\begin{array}{l}\mathrm{Pr}\left({\mathrm{A}}^C,{\mathrm{A}}^0,{\mathrm{A}}^{CC},{\mathrm{A}}^{C0},{\mathrm{A}}^{00}\mid \theta ,\lambda \right)\\ =\frac{\left({\text{A}}^{CC}+{\text{A}}^{C0}+{\text{A}}^{00}\right)!}{{\mathrm{A}}^{CC}!{\mathrm{A}}^{C0}!{\mathrm{A}}^{00}!}{\left(\frac{\theta {\left(\frac{{\text{A}}^C}{\lambda {\text{A}}^0}\right)}^2}{\theta {\left(\frac{{\text{A}}^C}{\lambda {\text{A}}^0}\right)}^2+(\theta +1)\left(\frac{{\text{A}}^C}{\lambda {\text{A}}^0}\right)+1}\right)}^{{\mathrm{A}}^{CC}}{\left(\frac{(\theta +1)\frac{{\mathrm{A}}^C}{\lambda {\mathrm{A}}^0}}{\theta {\left(\frac{{\mathrm{A}}^C}{\lambda {\mathrm{A}}^0}\right)}^2+(\theta +1)\left(\frac{{\mathrm{A}}^C}{\lambda {\mathrm{A}}^0}\right)+1}\right)}^{{\mathrm{A}}^{C0}}\\ {\left(\frac{1}{\theta {\left(\frac{{\text{A}}^C}{\lambda {\text{A}}^0}\right)}^2+(\theta +1)\left(\frac{{\text{A}}^C}{\lambda {\text{A}}^0}\right)+1}\right)}^{{\text{A}}^{00}}\end{array}$$

The likelihood function is then defined as the product over state-year-hour-day-season observational units:

$$\mathcal{L}\left({\text{A}}^C,{\text{A}}^0,{\text{A}}^{CC},{\text{A}}^{C0},{\text{A}}^{00}\mid \theta ,\lambda \right)=\prod _k\mathrm{Pr}\left(A_k^C,A_k^0,A_k^{CC},A_k^{C0},A_k^{00}\mid \theta ,\lambda \right)$$

Once estimates of θ and λ are recovered, $\{\widehat{\theta },\widehat{\lambda }\}$, a national estimate of N is then constructed as $\widehat{N}=A_{Total}^C/\widehat{\lambda }{C}_{Total}^0$, where $C_{Total}^i$ is the number of one-vehicle crashes involving drivers of type i nationally. Finally, recall N is the ratio of adult drivers with and without minor passengers. We therefore calculate prevalence of driving with minor passangers among adults as $\widehat{\pi }=\widehat{N}/(1+\widehat{N})$.

• Childhood crash exposure when travelling with an adult driver is low.

• Although children tend to induce adults to drive with caution, they can also be a source of distraction and crash risk.

• Despite their relatively low crash exposure, child passengers are associated with much greater risk of causing a fatal crash.