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:

• in 2001, Americans drove 2,569,980,000,000 in "millions of vehicle-miles" or 2.57 trillion vehicle-miles (trillion is correct here, compare https://research.stlouisfed.org/fred2/series/M12MTVUSM227NFWA or https://fredblog.stlouisfed.org/2014/06/how-much-do-americans-drive/ )

• in 2001, the American population was 284,970,000 (note that injuries/deaths also happen to people who are not the driver, and most people spend a fair amount of time in a car, one way or another), so that's an average annual mileage of 9,018 which sounds pretty reasonable So:

• deaths: 8819 / 2569980000000 = mortality risk of 3.431544214e-09 per mile driven

• injuries: 42000 / 2569980000000 = injury risk of 1.634253963e-08 per mile -total risk of either mortality or injury of 3.431544214e-09 + 1.634253963e-08 = 1.977408384e-08 (we just sum, since the CDC numbers seem to be mutually exclusive)

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.