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Claims about excess road deaths on “4/20” don’t add up

Sam Harper writes:

Since you’ve written about similar papers (that recent NRA study in NEJM, the birthday analysis) before and we linked to a few of your posts, I thought you might be interested in this recent blog post we wrote about a similar kind of study claiming that fatal motor vehicle crashes increase by 12% after 4:20pm on April 20th (an annual cannabis celebration…google it).

The post is by Harper and Adam Palayew, and it’s excellent. Here’s what they say:

A few weeks ago a short paper was published in a leading medical journal, JAMA Internal Medicine, suggesting that, over the 25 years from 1992-2016, excess cannabis consumption after 4:20pm on 4/20 increased fatal traffic crashes by 12% relative to fatal crashes that occurred one week before and one week after. Here is the key result from the paper:

In total, 1369 drivers were involved in fatal crashes after 4:20 PM on April 20 whereas 2453 drivers were in fatal crashes on control days during the same time intervals (corresponding to 7.1 and 6.4 drivers in fatal crashes per hour, respectively). The risk of a fatal crash was significantly higher on April 20 (relative risk, 1.12; 95% CI, 1.05-1.19; P = .001).
— Staples JA, Redelmeier DA. The April 20 Cannabis Celebration and Fatal Traffic Crashes in the United States JAMA Int Med, Feb 18, 2018, p.E2

Naturally, this sparked (heh) considerable media interest, not only because p<.05 and the finding is “surprising”, but also because cannabis is a hot topic these days (and, of course, April 20th happens every year).

But how seriously should we take these findings? Harper and Palayew crunch the numbers:

If we try and back out some estimates of what might have to happen on 4/20 to generate a 12% increase in the national rate of fatal car crashes, it seems less and less plausible that the 4/20 effect is reliable or valid. Let’s give it a shot. . . .

Over the 25 year period [the authors of the linked paper] tally 1369 deaths on 4/20 and 2453 deaths on control days, which works out to average deaths on those days each year of 1369/25 ~ 55 on 4/20 and 2453/25/2 ~ 49 on control days, an average excess of about 6 deaths each year. If we use our estimates of post-1620h VMT above, that works out to around 55/2.5 = 22 fatal crashes per billion VMT on 4/20 vs. 49/2.5 = 19.6 on control days. . . .

If we don’t assume the relative risk changes on 4/20, just more people smoking, what proportion of the population would need to be driving while high to generate a rate of 22 per billion VMT? A little algebra tells us that to get to 22 we’d need to see something like . . . 15%! That’s nearly one-sixth of the population driving while high on 4/20 from 4:20pm to midnight, which doesn’t, absent any other evidence, seem very likely. . . . Alternatively, one could also raise the relative risk among cannabis drivers to 6x the base rate and get something close. Or some combination of the two. This means either the nationwide prevalence of driving while using cannabis increases massively on 4/20, or the RR of a fatal crash with the kind of cannabis use happening on 4/20 is absurdly high. Neither of these scenarios seem particularly likely based on what we currently know about cannabis use and driving risks.

They also look at the big picture:

Nothing so exciting is happening on 20 Apr, which makes sense given that total accident rates are affected by so many things, with cannabis consumption being a very small part. It’s similar to that NRA study (see link at beginning of this post) in that the numbers just don’t add up.

Harper sent me this email last year. I wrote the above post and scheduled it for 4/20. In the meantime, he had more to report:

We published a replication paper with some additional analysis. The original paper in question (in JAMA Internal Med no less) used a design (comparing an index ‘window’ on a given day to the same ‘window’ +/- 1 week) similar to some others that you have blogged about (the NRA study, for example), and I think it merits similar skepticism (a sizeable fraction of the population would need to be driving while drugged/intoxicated on this day to raise the national rate by such a margin).

As I said, my co-author Adam Palayew and I replicated that paper’s findings but also showed that their results seem much more consistent with daily variations in traffic crashes throughout the year (lots of noise) and we used a few other well known “risky” days (July 4th is quite reliable for excess deaths from traffic crashes) as a comparison. We also used Stan to fit some partial pooling models to look at how these “effects” may vary over longer time windows.

I wrote an updated blog post about it here.

And the gated version of the paper is now posted on Injury Prevention’s website, but we have made a preprint and all of the raw data and code to reproduce our work available at my Open Science page.



  1. Alex says:

    Why is 6x relative risk absurdly high? It doesn’t seem so in an absolute sense — isn’t it like 20x with alcohol for young people at a typical BAC limit? And compared to the 2x estimate from meta-analysis linked in the first blog post ( — 6x would be on the high end of estimates from single studies, but it’s easy to imagine that a deviation from typical smoking habits or populations makes up the difference. I’d guess there would be more inexperienced smokers, as well as more people smoking and drinking. There’s certainly more variation than that in alcohol-related fatal crash relative risk between different populations or BAC levels.

    (It still looks like Harper is right to be skeptical that we can conclude something is happening with road deaths on 20 Apr.)

  2. Rmadillo says:

    There is some R code to download and tidy Harper & Palayew’s data for more exploration for non Stata users at

  3. Kaiser says:

    Kudos to Harper/Palayew for bringing this to our attention, and to provide underlying data for others to contribute.

    Here is my contribution.

    1. A data graphic that tells the story of the each-day analysis:

    2. Via a forking paths argument, I offer up 20 paper topics for aspiring professors looking to publish in journals like JAMA. See the blog post for more.

  4. JFA says:

    This is also another skeptical take on the original paper:

  5. Adam says:

    Are the p values used in the original paper actually correct? Would it be more appropriate to use empirical test statistics with adjusted p values?

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