Fatality risks in eccentric time localities: Not that elevated

Dear Editors,

Recently, Gentry et al. (2022) analyzed the impact of the east–west gradient within a US time zone on the vehicle fatalities from the year 2006 to the year 2017. They distinguished control localities—those inside the physical time zone corresponding to their winter local time, referred as solar, as an example Houston, Texas—and the tested localities—those outside, west of, their physical time zone, referred as Eccentric Time Locality (ETL), as an example Amarillo, Texas. Their results were summarized on their Table 3, where population sizes P, accumulated fatalities F, and the fatality rates R = F/P are listed for the solar and the ETL groups. Gentry et al. (2022) reported worse scores (larger fatalities) in the Eastern, Central, and Mountain ETL: 23.8%, 17.7%, 26.5%, respectively, comparing pairwise a solar location to their corresponding ETL.

All else equal, east–west gradient may impact societal issues like traffic accident rates. However, the impact reported by Gentry et al. (2022) is staggering large. I offer an alternative explanation for their findings.

In their analysis, the authors implicitly assume that F scales with P through different geographical localities. However, when dealing with heterogenous social magnitudes like F, one should consider F ∝ P α e , where α _e is an empirical exponent, which may or may not be equal to one. I provide an analogy based on mortality. I got weekly numbers of deaths in Spain since the year 2000 disaggregated by NUTS3 regions ¹ (N = 52). I tested the logarithm of the accumulated values against the logarithm of the average population in every region. I found α _e = 0.921 with 95% confidence interval (CI) [0.864, 0.978] and Person’s r² = 0.95. In this case, α _e ≠ 1 is related to the myriad of societal issues that impact mortality, of which differences in the age distribution along the Spanish NUTS3 regions are probably the most significant: with rural regions less populated and aged, the distribution flattens and the effective exponent is smaller than one.

In the case of the vehicle fatalities, Gentry et al. (2022) list a series of factor that also lead to road accidents in Section Limitations. That is, in addition to the east–west gradient, F must depend on other environmental conditions such as, but not limited to, population density, population age, miles traveled, road conditions, emergency responses, and weather conditions. Eventually, all these factors challenge a simple F ∝ P coupling.

I show in Figure 1 a double logarithmic plot of the fatalities versus population sizes. Visually speaking, ETL observations are not outliers in this chart.OPEN IN VIEWER

I performed several F = a × P α e tests, where a is an effective rate of fatalities. The tests involved (1) the set of seven observations; (2) the set of four solar observations; and (3) the set of three ETL observations. Results are summarized in Table 1. In Figure 1, I show the fitting results for the seven observations (orange line) and the four solar observations (blue line). I find point estimates α _e < 1, with the 95% CI including α _e = 1. In reverse, this usually means that the null hypothesis “F/P does not depend on P” sustains at the standard level of confidence in every analysis. This is due to the scarcity of observations and their strong variability. In addition, the 95% CI for the rates a are extremely wide.

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Table 1.

Results from the fit F = a × P α e for set of data. Figure 1 shows the fittings for the solar and total observations. The effective exponent drives the slope in the double-logarithm plot; the effective rate a drives the intercept value at P = 1.

Set	N	α e	95% CI	log10(a)	95% CI	p−value
All observations	7	0.898	[0.778, 1.018]	−2.074	[−2.961, −1.188]	< 0.001
Solar observations	4	0.938	[0.363, 1.512]	−2.399	[−6.820, 2.022]	0.02
ETL observations	3	0.935	[0.311, 1.559]	−2.306	[−6.670, 2.0571]	0.03

Finally Table 2 mimics the results presented by Gentry et al. (2022) in their Table 3. I include two more data columns aiming to simulate the effect of the scaling relation: F / P α e solar and F / P α e , where from Table 1, α e solar is the point estimate exponent for the solar analysis, and α _e is the point estimate exponent for the complete analysis.

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Table 2.

Main results from Table 3 in Gentry et al. (2022) augmented with the F / P α e solar and F / P α e columns. From left to right, the changes in the percentage worse of the ETL observations on α _e can be appreciated. Point estimate values of the effective exponents were α e solar = 0.938 and α _e = 0.898. See Table 1 for their 95% CI.

Time zone	Class	Fatalities F	Population P	F/P1 × 1000	Pct worse	F / P α e solar × 1000	Pct worse	F / P α e × 1000	Pct worse
Eastern	Solar	132,722	110,133,372	1.205		3.833		7.992
	ETL	58,478	39,199,427	1.492	23.8	4.448	16.1	8.903	11.4
Central	Solar	124,890	78,783,002	1.585		4.938		10.159
	ETL	23,789	12,746,474	1.866	17.7	5.188	5.1	9.930	−2.3
Mountain	Solar	19,180	12,834,599	1.494		4.156		7.957
	ETL	2959	1,564,684	1.891	26.5	4.611	11.0	8.121	2.1
Pacific	Solar	55,381	52,317,788	1.059		3.214		6.506
Total	Solar	332,173	254,068,761	1.307		4.381		9.444
	ETL	85,226	53,510,585	1.593	21.8	4.842	10.5	9.812	3.9
Total	Total	417,399	307,579,346	1.357		4.602		9.995

I also computed the percent worsening deduced from the ratio of ETL rates to solar rates. I do not claim that those percents were a good measure of the impact of west–east gradient on fatalities. The numbers only replicate Gentry et al. (2022) argument and help to visualize the strong dependence of this metric on α _e .

More observations would be needed to assess a precise value for α _e in the United States. Disaggregated numbers by county may provide some insight on this relation. Very likely the impact of the eccentric time zones is not an increase of 20% in vehicles fatalities as Gentry et al. (2022) claimed.