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NHTSA- single device calculations

December 23, 2009

Lives Saved Calculations for Seat Belts and Frontal Air Bags
DOT HS 811 206
PDF: 68 pages
http://www-nrd.nhtsa.dot.gov/Pubs/811206.PDF

SINGLE DEVICE ONLY

Page 10-11:

4.1 For a Sole Safety Device
We first explain the relatively simple case of the effectiveness of a solitary safety device. Section 4.2 presents the more complex scenario of multiple devices designed to protect occupants in a common setting, such as belts and bags protecting people in crashes.

4.1.1 Devices and Settings
In general, to estimate lives saved, one must specify a potentially life-threatening situation, called the setting, and one or more factors, called devices, that affect survival. In this report, the setting is the crash of a passenger vehicle and the devices are seat belts and air bags.

In the “single-device scenario” (or “sole-device scenario”) there is only one device. We use this simplified situation to introduce the basic concepts of benefits calculations, including effectiveness ratings, potential fatalities, lives saved, and potential lives saved (or savable lives). We then expand these concepts to the more complex two-device scenario used in our calculation for seat belts and air bags.

4.1.2 Potential Fatalities
In general, when a single device A protects people in a certain setting, then Device A is rated on the hypothetical population of all people in potential instances of that setting who would die without A. This population is said to consist of the potential fatalities. For instance, in the single device scenario of motorcycle helmets protecting people in the setting of motorcycle crashes, the potential fatalities would be the motorcyclists in crashes severe enough that they would die without a helmet.

Note that the notion of potential fatality applies to the person experiencing the setting, not the particular instance of the setting that the person experiences. An instance of the setting can be potentially fatal to one person and survivable to another. For example, a particular frail elderly person might die in a crash in which a healthy young adult (in the same seating position) would have survived. However, the instance of the setting is sometimes called potentially fatal (e.g., potentially fatal crashes), with the understanding that this depends on the person experiencing the setting.

Note that the device is not rated on the entire population of people and instances of the setting, but only those in danger of dying. It would be disingenuous to rate helmets for motorcyclists in very minor crashes. Note also that the population on which the device is rated may include people who would die for reasons that have nothing to do with the setting or the device. For instance, the population against which motorcycle helmets are rated includes motorcyclists who died of impacts to the chest that occurred during the crashes.

Here, potential fatalities are a hypothetical population. However we also speak of a person who actually experiences the setting, with or without the single Device A, who would die without Device A as a potential fatality. Potential fatalities who live are generally not identifiable in particular instances of the setting. For example, we cannot say whether a helmeted motorcyclist who survives a particular crash would have died if the motorcyclist had not worn the helmet.

Every fatality that does not use Device A is a potential fatality. For example, for the device of motorcycle helmets in the setting of motorcycle crashes, all unhelmeted potential fatalities become fatalities when they experience their crashes.

4.1.3 Effectiveness Ratings
The effectiveness of the Device A is the proportion of the potential fatalities who would live if Device A had been used. For instance, the effectiveness of helmets is the percentage of motorcyclists who would survive crashes helmeted among those in crashes severe enough to kill them unhelmeted. Letting e denote the effectiveness of Device A, means that e100 percent of the potential fatalities who use A live, while the others who use A die, and all who do not use A die. We assume in this report that devices increase the chance of survival, and so 0<e1. We note however that NHTSA does compute some negative effectiveness ratings, e.g., for children and air bags in Kahane (2004).

4.1.4 Estimated Effectiveness
Effectiveness is estimated from data. See Kahane (2000) for details on how this is done. For brevity, the estimated effectiveness of a device is frequently also called its effectiveness.

Because it is calculated from data, the estimated effectiveness represents the ability of A to protect the types of people and settings that occurred in the data set used. For example, the belt effectiveness ratings in Kahane (2000) represent the efficacy of belts in the types of crashes and people in crashes that occurred in the period 1986 – 1999, whose crash data was used to estimate this effectiveness. In particular, ratings may increase or decrease over time. If the nature of a crash were to suddenly change so that it was generally unsurvivable, the estimated belt effectiveness for that crash would become very small.

A device might be assessed different effectiveness ratings on different subpopulations. For instance, belts will be assessed for various vehicle types and seating positions, while NHTSA only rates air bag effectiveness for people over age 12.
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Page 27:

6. Lives Saved
In this section, we define what we mean when we say that a person was “saved” by a device, and derive how the number saved is estimated. This is complex for two devices if one wants to say which device saved a person, and not just that s/he was saved by at least one of the two. We first discuss the simpler one-device scenario, then the two-device scenario, and finally the application of the two-device scenario to seat belts and frontal air bags.

6.1 For a Sole Device
For a sole Device A, we say that a person in the setting was saved by A if s/he used A, survived, and would have died had s/he not used A. That is, the people saved by A are the potential fatalities who survive. Using the notation of Section 5.2, the number of lives saved is eP, or eF/(1-e). Equivalently, one can think of the number of saved lives as the number of potential fatalities F/(1-e) minus the number of actual fatalities F.

Throughout the estimation of the number of lives saved, it is important to remember that not everyone who lives using the devices are saved by them, only those who were in danger of dying. We cannot identify which survivors owe their lives to the devices.

Note that since the function eF/(1-e) is an increasing function of e on the domain 0<e<1, underestimated effective ratings result in underestimated lives saved.

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Page 35:

7.1 For a Sole Device
Suppose that more people use Device A. For example, say that a proportion of xactual people actually used A, and we hypothesize xhypoth to use A, where xhypoth > xactual. Suppose that the corresponding use rates among potential fatalities are uhypoth and uactual, respectively. Then an additional proportion of uhypoth – uactual potential fatalities would have used A. If there are P potential fatalities, then
(e)(uhypoth – ucurrent)(P)
of the new users would have lived. That is, a total of (e)(uhypoth)(P) people would have lived if the use rate had been xhypoth, and the corresponding use rate among potential fatalities had been uhypoth

NOTE:
Calculating Lives Saved by Motorcycle Helmets
PDF 3 pages:
http://www-nrd.nhtsa.dot.gov/Pubs/809861.PDF

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