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gwern comments on Wear a Helmet While Driving a Car - Less Wrong

47 Post author: James_Miller 30 July 2015 04:36PM

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Comment author: gwern 17 January 2016 02:44:22AM 4 points [-]

OK, so 42k injuries/9k deaths is sobering, but does it justify wearing a driving helmet? I've been curious about this topic and also walking helmets for a while and now that I have my own car again (ironically, given the datasets here, an old 2000 car), the topic of reducing car risks is also of some personal relevance. I'm going to give a stab at a quick and dirty decision analysis here to get an idea of how the case for driving helmets look.

First, we want to convert the absolute numbers to a probability of injury/death per mile driven:

So if you drive 5000 miles (roughly what I currently drive per year), then you have a risk of death or injury of 5000 * 1.977408384e-08 = 9.88704192e-05.

For mortality, we could say the expected loss this year for our 5k driver who is 30 years old is ~50 years at the usual \$50k/QALY, without discounting, would be 5000 * 3.431544214e-09 * (50 * 50000) = \$42. That's just the first year, while 30yo, and each year the loss shrinks since you get closer to death; a quick hack to sum the series to get a total expected loss with discounting at the usual 3%:

R> sum(sapply(seq((80-30), 0), function(t) { 5000 * 3.431544214e-09 * t * 0.97^t * 1.0 * 50000 }))
# [1] 420.5466717

Injuries is more difficult. Browsing through a few papers on TBI and QALYs, I find QALY/life-expectancy losses from TBI in juveniles: "Measuring the Cost-Effectiveness of Technologic Change in the Treatment of Pediatric Traumatic Brain Injury", Tilford 2007 The estimates are kind of shocking - TBI is a very serious problem. (Not too surprising after looking at "Quality of Life After Traumatic Brain Injury: A Review of Research Approaches and Findings" and some of the citations in "Is aggressive treatment of traumatic brain injury cost-effective?" Whitmore et al 2012, or when I remember that a lot of military veteran dysfunctionality is probably due to TBI.)

Preference-weighted health outcomes in children who survived a TBI hospitalization were reported from a cohort of children admitted to 10 pediatric intensive care units (PICUs) that were located nationally. Subject inclusion criteria followed the inclusion criteria for estimating survival probabilities and required that the child be less than 18 years of age and admitted to the PICU with a Centers for Disease Control and Prevention-defined TBI^13^ that required either endotracheal intubation or mechanical ventilation. An initial description of these outcomes and construct validity has been reported elsewhere.^9^ Scores ranged from 0.09 to 1.00 at 3 and 6 months after discharge from the ICU, but mean scores increased from 0.51 to 0.58 between the two periods...Recent work on life expectancies after TBI suggests that life expectancy will differ significantly depending on the functional outcome of the patient after hospital discharge.^20,21^ Patients with moderate disabilities were found to have a 4-year reduction in life expectancy, whereas patients rated as extremely severe were found to have a life expectancy only 50% of the population average.^22^ A study of children and adolescents after TBI also found substantial reductions in life expectancy when severe functional limitations were present.^23^ For a child aged 15 years, life expectancy was an additional 14.9 years if the child was not mobile, 34.2 years if the child had poor mobility, and 54.8 years if mobility was fair or good...Hospital charges for pediatric TBI patients increased to a maximum of \$19,000 and then fell to approximately \$13,000...On average, children who required an ICP monitor used approximately \$18,600 worth of services in the immediate period after discharge. Service costs decreased by approximately 50% between the 3-month follow-up interview and the 6-month follow-up interview. Assuming that service use declines linearly over time, the average cost per patient is approximately \$35,750 in the first year after discharge from the PICU.

Whitmore et al 2012 reports similar QALY estimates for adults; for example, QALY drops from 1 at #5 (healthy) to 0.63 at #4 on the Glasgow Coma Scale (concussion-like: "Opens eyes spontaneously / Confused, disoriented / Flexion/withdrawal to painful stimuli"), and 0.26 at #3. Details on estimates:

Life expectancy for Glasgow Outcome Scale (GOS) score categories 4 and 5 were obtained from 2001 US vital statistics.^2^ We assumed a GOS status of 4 had no adverse effect on life expectancy. Diminished longevities associated with GOS scores of 3 or 2 were calculated according to formulas derived from survival studies of these patients' mortality rates.^4,10,11,13^ Appendix Table 1 shows the expected years of life for each of the 4 age categories studied. Aoki and associates1 elicited utilities of different GOS states from 140 medical professionals, using the routine gamble approach. Their results are shown in Appendix Table 2. Quality-adjusted life years (QALYs)—and costs—are discounted at 3% per year of life. It is assumed that future rewards and costs are valued less than immediate ones, and routine practice is to discount them at 3% or 5% per year.^8^ As an example, a 20-year-old can expect to live, on average, 58^12^ years. If he or she remains in perfect health (utility = 1), that translates to 28.21 QALYs, with discounting. Appendix Table 3 illustrates the number of expected QALYs associated with a given age and GOS score.

So Whitmore et al 2012 finds that a healthy 20 year old's expected (discounted) QALYs of 28.21 drops to 17.77 if he is hit hard enough to trigger a #4, which at \$50k again is a huge lifetime loss of \$522,000. For the 40yo, the same calculation is \$436,500. Splitting the difference gives me a \$479,250. The losses get worse with more severe Glasgow Coma Scales, where #1 effectively equals death. Since I'm not sure how TBIs break down by Glasgow rating, I can't do an overall expected value but whatever it is, it must be >\$479,250 since that was the least damaging scenario Whitmore considered. So the expected loss from a TBI injury but not death is \$479k (ignoring the immediate medical costs since those will generally be paid by other people like insurers or the government); now we again need to compute the probability of a TBI injury each year and sum the series:

R> sum(sapply(seq((80-30), 0), function(t) { 5000 * 3.431544214e-09 * t * 0.97^t * 0.63 * 50000 }))
# [1] 264.9444032

So a quick estimate of the net present expected loss caused by TBI death or injury while in a car over a lifetime for a 30yo is -\$685. Or to put it the other way, we should be willing to pay up to \$685 to reduce our car TBI risk to zero.

Comment author: gwern 17 January 2016 02:44:37AM *  4 points [-]

How much do these helmets reduce risk and how much do they cost to buy & use? That's tricky to answer, but maybe some bounds will be helpful.

\$685 in present value is roughly equivalent to \$27 spent each year over the next 50 years, discounting at 3% (sum(sapply(1:50, function(t) { 27 * 0.97^t }))). So even something which reduced your car TBI risk to zero would not be worth paying more than \$27 each year for the rest of your life. The mentioned helmets all sound like they only reduce acceleration or energy somewhat, and Crasche is quoted by Dorikka as estimating a 25% reduction in impact (which translates to an unknown reduction in TBI risk); another quote claims seatbelts reduce death/injury by ~50%. Let's be extremely optimistic and go with the latter, that our TBI risk falls by 50% using a Crasche helmet. Then the gain from a Crasche helmet is 685 * 0.5 = \$342.

The cost of the Crasche helmet is ~\$30, leaving \$312. Let's assume there's never any replacements and we just need to consider the annual hassle of wearing it. Working backwards again, that leaves room for an annual cost of no more than ~\$12.3, which is small. I drive maybe thrice a week, so the per-trip cost of use needs to be <12.3 / (52*3) or <\$0.07. Alternatively, if we don't think the Crasche helmet is remotely sufficient, a much better helmet might cost more like \$100 up front, leaving \$242, leaving \$9.5 for annual expenses, or <\$0.06.

Personally, while I don't mind driving with a helmet as much as \$1 an hour (and so extremely high annually) like some people claim, I think I would mind a nickel's worth each trip, which defeats Crasche even with extremely optimistic assumptions on efficacy. If we wanted to make Crasche cost-effective, we could argue that \$100k/year is a better value, which will double estimates of benefit; or we could try to expand our sources of harm to include TBIs from other sources like falls (although that would also increase the cost of usage: it's one thing to only need to wear it in your car where no one will see, another thing to walk around routinely wearing it); or we could deny discounting, which increases the loss considerably and helps overcome the fixed present cost of buying the helmet. But to be fair, we'd also want to reduce the efficacy of Crasche to much less than 50%, take into account that we're wearing seat belts while a large fraction of TBI cases likely were not, consider the advent of self-driving cars in the next 15 years reducing human error rates, and overall, I'm not seeing much that looks like it could make a driving helmet the sort of slamdunk case that one can make for, say, vitamin D. As far as car safety goes, a helmet feels like it's going to be inferior to stuff like getting a dashcam, upgrading to an electric car with its bigger crumple zones & higher mechanical reliability (I understand the Tesla cars may be the safest ones on the market right now), saving up for self-driving cars, making a habit of reinflating tires more regularly, taking a defensive driving class, etc - to say nothing of much larger risks like falling getting out of the shower. (I installed some anti-slip treads after I did just that; feels like money well-spent every time I step out.)

The same also applies to walking helmets: falls are highly concentrated in the elderly and very young (while car TBIs are more evenly distributed) and you would need to wear a helmet almost 24/7 once you've guarded against ice and shower falls (increasing costs much more over car TBIs). So race-car drivers, football players*, people at much higher than usual risks? Probably, maybe. Regular people? Not really.

* although I would say after reading through all the football studies and these TBI studies, I would not, hypothetically, let my children ever play contact football and especially not highschool football. If they want to play sports, there must be safer ones they could try. Like BASE jumping.

Comment author: gwern 24 August 2016 12:47:20AM 1 point [-]

"Long-Term Outcomes Associated with Traumatic Brain Injury in Childhood and Adolescence: A Nationwide Swedish Cohort Study of a Wide Range of Medical and Social Outcomes", Sariaslan et al 2016, is a population registry study which reports within-family correlations adjust for education about various negative outcomes with 1 or more diagnosed TBIs representing 9.1% of the population (their twin sample was too small); within-family studies control for tons of the usual confounders (and indeed the correlations are smaller than if you had used the general population) and are probably close to the causal effect (possibly underestimating it since so many TBIs go unreported).

TBI is common enough that the effects are large on a population-wide basis:

We found that the crude population contributions of TBI explained approximately...2%–6% of the population differences in the outcomes. The strongest population attributable risks were found for the severe outcomes, including psychiatric inpatient hospitalisation (PAF = 5.5%; 4.9%–6.1%), premature mortality (PAF = 4.7%; 2.9%–6.5%), and disability pension (PAF = 4.6%; 3.8%–5.3%).

Interestingly, the effects of TBI get worse with age: the youngest age bracket (despite having lots of falls) has the smallest RRs while they increase especially for adolescents. (This was the opposite of what I expected.)

They find RRs of:

  1. disability pension: 1.49

    • Population rate: 3.9%
    • Lifetime cost: Sariaslan gives a quick opportunity cost estimate of "US$1.3 million per person" from the inability to work & earn a normal income over the next 30 years
  2. Psychiatric visit: 1.31

    • Population: 14.2%
    • Lifetime cost: ?
  3. Psychiatric hospitalization: 1.57

    • Population: 5.7%
    • Lifetime cost: ?
  4. Premature mortality (death age <41): 1.40

    • Population: 0.8%
    • Lifetime cost: tricky since it's not quite a RR on all-cause mortality: the age 41 is when they stopped following individuals in their sample. If we assume that the mortality RR remained indefinitely, then using my Gompertz curve functions, a RR of 1.40 for a 30yo would represent a loss of 3.09 years over the next ~50 years, for a 10yo a loss of 3.147 years over the next ~70 years etc. So ignoring discounting, ~\$150k from the mortality alone.
  5. Highschool dropout: 1.28

    • Population: 8.9%
    • Lifetime cost: somewhere upwards of $250k in the USA, estimates as high as $1m.
  6. On means-tested welfare benefits: 1.19

    • Population: 11.5%
    • Lifetime cost: Sweden is famous for spending a lot on welfare, but the welfare & public spending are quite diverse, this doesn't specify how long each individual is on welfare or whether it's household or individuals. http://ec.europa.eu/social/BlobServlet?docId=9044&langId=en suggests that a prevalence of 11.5% must refer to household welfare, and estimates that in 2008 the average number of months (from 1990 to 2008) was 6.1 months at 43987 SEK per month or \$5.2k or \$31.72k total on average.

So the undiscounted cost of 1 nonfatal TBI for a 10yo (why 10yo? so they have time to drop out of highschool) in Swedish America would be something like:

(0.039*1.49 -0.039)*1300000 + ? + ? (0.008*1.40 - 0.008)*3.147*50000 + (0.089*1.28 - 0.089)*250000 + (0.115*1.19 - 0.115)*31720 = >\$32,269

For the 30yo

(0.039*1.49 -0.039)*1300000 + ? + ? (0.008*1.40 - 0.008)*3.09*50000 + (0.115*1.19 - 0.115)*31720 = >\$26,030.482

Unfortunately, hard to see how to do much about this. The top category of TBI is normals falls, cars, then assaults, then miscellaneous: https://www.cdc.gov/traumaticbraininjury/pdf/blue_book.docx

An estimated average of 595,095 are fall-related TBIs, 292,202 motor vehicle traffic TBIs, 279,882 struck by or against events, and 169,625 assault-related TBIs occurred annually....Struck by or struck against events are those in which a person was struck unintentionally by another person or an object, such as falling debris or a ball in sports, or that someone struck against an object, such as a wall or another person. For this report, only unintentional and undetermined struck by or struck against events were included. Struck by or struck against events related to assaults (for example, being struck by a fist) are in the assault category. Struck by or struck against events were only reported for all ages because small sample sizes precluded reporting them for all three data sources (NHAMCS, NHDS and NVSS)

For 30yos, cars are 40% of TBIs, falls are 2.7% of TBIs, assault is 19% of TBIs, struck by by or against is 0.7%, and the ominous 'other' is 37%. So while we can probably ignore the 'assault' due simply to demographics (I suspect most readers here have low risk of crime), and car travel represents a fairly focused area of intervention, the 'other' can't be fixed except by always wearing a helmet, which would be difficult if only for social reasons.

Comment author: pepe_prime 25 August 2016 07:21:22PM *  0 points [-]

For injuries

R> sum(sapply(seq((80-30), 0), function(t) { 5000 * 3.431544214e-09 * t * 0.97^t * 0.63 * 50000 }))
# [1] 264.9444032

Rate should be 1.634253963e-08, yielding about $1261.78 lifetime loss.

Comment author: adamzerner 30 June 2016 12:20:49AM *  0 points [-]

The analysis uses $50k for a QALY. The analysis also assumes a normal lifespan of 80 years.

My impression is that LW readers are likely to place much higher values on their life, and to have longer expected lifespans. I could see LW readers having QALY's of 2-5 times the $50k figure. And I could see LW readers (ex. signed up for cryonics) having much longer expected lifespans.

So I could see that for many readers here, the downside should be multiplied by, perhaps an order of magnitude.

Comment author: adamzerner 29 June 2016 11:46:47PM 0 points [-]

Thank you so much for this analysis!