To the Editor

We thank Harper & Palayew for replicating our analysis of traffic risks on April 20.1 2 We agree that the absolute risks on April 20 must be modest because the majority of Americans do not celebrate the ‘high holiday’ and because comparison days are not devoid of impaired driving. Similarly, secular trends in relative risks for April 20 reflect evolving driving norms, fluctuating traffic enforcement, changing baseline rates of cannabis use, variable celebration behaviours and rapid growth of the cannabis industry. We also agree that crashes are already recognised to be more frequent on traditional holidays such as Independence Day and Thanksgiving.3 Beyond this shared understanding, however, we disagree with Harper & Palayew on a key assumption in their analysis.

Distant or unmatched control days can be biased comparators because prevailing weather, road conditions, daylight hours, driver fatigue and travel patterns vary substantially across time. More crashes, for example, occur on weekends relative to weekdays, in summer than winter and during 2016 than 2010.4 This was our rationale for performing a matched analysis by comparing April 20 to control days precisely 1 week earlier and 1 week later, thereby exactly controlling for weekday, month and year. In addition to reducing bias, a study that assembles data in a matched design can be evaluated in a matched analysis with more powerful statistical tests (akin to applying McNemar’s test rather than a X² test for matched binomial data).5

Harper & Palayew introduce negative binomial regression as an alternative statistical approach to account for overdispersed data, yet their analysis fails to adjust for rudimentary temporal variation in crash risks and thus yields biased estimates and underestimates precision (online supplementary appendix). Indeed, a negative binomial regression model that simply adjusts for annual, weekly and seasonal variations indicates that crash risks are significantly elevated on April 20 relative to April 13 and April 27 (OR 1.12, 95% CI 1.02 to 1.22, p=0.01). The increased risk on April 20 is particularly apparent for younger drivers who may be prone to riskier substance use and especially likely to crash if impaired (OR 1.36, 95% CI 1.13 to 1.62, p<0.001; figure 1).6 ,7

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Figure 1

Forest plot showing relative increase in risk of a traffic crash on April 20 compared with control days using negative binomial regression to account for overdispersion of crash counts and adjustment to account for year-to-year, seasonal and weekly variation in traffic crash risk. Vertical columns show total counts between 4:20 PM and 11:59 PM on April 20 and control days. Solid squares indicate point estimate; relative dimensions, sample size and horizontal lines, 95% CI. Blue squares and horizontal lines correspond to estimates derived from comparison to two control days (April 13 and April 27) after adjustment for year as a nominal categorical variable; red corresponds to estimates derived from comparison to four control days (April 6, April 13, April 27 and May 4) after adjustment for year and month. Main findings show a significant increase in relative risk on April 20 for all ages when compared to two matched controls (OR 1.12, 95% CI 1.02 to 1.23, p=0.01); a marginal result for all ages when compared to four matched controls (OR 1.09, 95% CI 1.00 to 1.19, p=0.05) and a statistically significant and clinically meaningful increase in relative risk of fatal crash involvement for drivers <21 years with either two or four matched controls (OR for two controls 1.36, 95% CI 1.13 to 1.62, p<0.001; OR for four controls 1.26, 95% CI 1.07 to 1.48, p=0.006). Results were robust to changes in the number of controls (including 8, 16, 30 and 51 control days matched for day-of-week and year).

We concur with Harper & Palayew that no single statistical design is ideal and that no serious study suggests that cannabis consumption lowers traffic risks. Most of the debate, therefore, is around the capacity to detect a population-wide effect from increased cannabis consumption. A new study by Vandoros & Kawachi replicated our analysis and found an 18% increase in crash risk on April 20 in the United Kingdom (OR 1.18, 95% CI 1.08 to 1.28, p<0.001).8 Other countries have jointly decriminalised cannabis and maintained traffic safety by applying countermeasures such as roadway engineering, public education, speed control, designated driver programmes and action against impaired driving. The high burden of traffic injury in the United States suggest these measures merit more attention throughout the year.