2.4 Computation of the preliminary effectiveness estimates

The "preliminary" effectiveness estimate is the average reduction in the age-adjusted log odds of a rear impact for an MY 1986 or later car relative to a pre-1986 car, as calculated from the tabulated data by the procedure described in this section. Later, in Section 2.6, the preliminary estimates will transformed to "final" estimates by converting the log odds ratios back to odds ratios and correcting for: pre-1986 cars retrofitted with CHMSL, miscoded vehicle types, miscoded model years. A "preliminary" estimate is calculated separately for each calendar year in each State, based on statistics derived from the crash experience of MY 1982-89 passenger cars in that calendar year - i.e., cars of the last four MY before CHMSL vs. cars of the first four MY with CHMSL. Florida data from CY 1992 will be used throughout this section to illustrate the computational process.

The starting point for this process is the tabulation, by impact location and model year, of actual crash records of MY 1982-89 cars. The log odds of a rear impact is calculated in each model year. The tabulation for 1992 Florida data is an excerpt from Table 2-1:

 REAR IMPACT? MODEL YEAR Frequency Row Pct NO YES Total LOGODDS 82 8629 80.22 2128 19.78 10757 -1.400 83 10181 79.84 2571 20.16 12752 -1.376 84 14318 78.38 3949 21.62 18267 -1.288 85 14981 77.14 4439 22.86 19420 -1.216 86 16423 77.50 4768 22.50 21191 -1.237 87 16944 76.98 5068 23.02 22012 -1.207 88 17452 76.38 5396 23.62 22848 -1.174 89 16018 75.76 5125 24.24 21143 -1.140

The percent of rear impacts escalates steadily from MY 82 to 89, and the log odds of a rear impact becomes steadily less negative, except for a brief interruption in MY 1986, the year cars got CHMSL. Figure 2-6 graphs these unadjusted log odds, indicated by "U," and it clearly shows how the vehicle age effect, over the years, is much stronger than the effect of CHMSL. (The vertical line between MY 85 and 86 indicates the effective date of CHMSL, and the U's jog slightly down from their otherwise upward trend.)

The next step is to adjust each of the log odds for the vehicle age effect. The regression equation of the preceding section estimated an "age effect" that is in fact the year-to-year change in the log odds as a function of vehicle age. In Florida, for a j-year-old car, the estimated age effect is:

D_LOGODDS = - .00734 + .01693 j - .001232 j 2

The cumulative vehicle age effect for a j-year-old car is the integral, from 0 to j, of that function:

adjusted logodds = actual logodds - .00734 j + ½ (.01693 j 2) - (.001232 j 3)

In other words, the cumulative adjustment factor tells us what the log odds of a rear impact would have been if the cars were brand new (0 years old) instead of j years old. The actual and adjusted log odds in the 92 Florida data are:

 Model Year Vehicle Age Actual Log Odds Cumulative Age Adjustment Adjusted Log Odds 82 10 -1.3999 .3624 -1.0375 83 9 -1.3762 .3200 -1.0560 84 8 -1.2881 .2728 -1.0153 85 7 -1.2164 .2226 -0.9938 86 6 -1.2368 .1720 -1.0648 87 5 -1.2070 .1236 -1.0834 88 4 -1.1738 .0798 -1.0940 89 3 -1.1396 .0431 -1.0965

Figure 2-6 graphs the adjusted log odds, indicated by "A." The adjustment more or less flattens out the effect of vehicle age and highlights the effect of CHMSL. All four of the MY 86-89 values are more negative than any of the MY 82-85 values. Give or take some residual noise, the adjusted log odds with CHMSL (MY 86-89) are all close to -1.08, while without CHMSL (MY 82-85) they are close to -1.02, suggesting a reduction of rear impacts by something close to 6 percent with CHMSL.

The last step in this portion of the analysis is to define a composite statistic CHMSLAVG derived from the eight adjusted log-odds numbers that will serve as the preliminary estimate of CHMSL effectiveness. Let:

AVG(- 1) = ADJODDS(85) = -0.9938

FIGURE 2-6

LOG ODDS OF A REAR IMPACT - BEFORE AND AFTER ADJUSTMENT FOR VEHICLE AGE

1992 FLORIDA CRASHES, MODEL YEAR 1982-89 PASSENGER CARS

CHMSL1 = AVG(- 1) - AVG(+1) = .07095

CHMSL2 = AVG(- 2) - AVG(+2) = .06953

CHMSL3 = AVG(- 3) - AVG(+3) = .05902

CHMSL4 = AVG(- 4) - AVG(+4) = .05901

CHMSLAVG = ¼ [CHMSL1 + CHMSL2 + CHMSL3 + CHMSL4] = .06463

In other words, the effect of CHMSL in 1992 Florida data is about 6.5 percent. CHMSL1 is a simple comparison of the MY 86 and 85 adjusted log odds: first year with CHMSL vs. last year without CHMSL. CHMSL2 compares the arithmetic average of the adjusted log odds for the first two MY with CHMSL to the corresponding average for the last two MY without CHMSL, etc. CHMSLAVG is an unweighted arithmetic average of CHMSL1, CHMSL2, CHMSL3 and CHMSL4, but it does not give equal weight to each of the model years. Since MY 85 and 86 data are used to compute all of CHMSL1, but also contribute part to CHMSL2, CHMSL3 and CHMSL4, they have a higher net contribution to CHMSLAVG than MY 82 and 89 data, which only are used in computing CHMSL4. The relative weights of the model years are:

MY 85 and 86: 25 parts

MY 84 and 87: 13

MY 83 and 88: 7

MY 82 and 89: 3

Although CHMSLAVG is the estimate of CHMSL effectiveness in this report, it is, of course, just one of the many statistics that could have been chosen for that purpose. It would have been possible to consider a wider range of model years (as in NHTSA's 1989 evaluation [19], p. 15), or a narrower one, or even limit the analysis to a comparison of MY 86 vs. 85, as Farmer did [9]; the various model years could have been given different weights than the above, or even given equal weights. Many statistics will produce unbiased estimates, but some may be more reliable than others. CHMSLAVG was selected because it offers an intuitively good balance between concentrating on MY 85 and 86, where the effect of CHMSL is least diluted by other factors that might have become involved over time, and extending the comparison to adjacent model years to increase the sample of data included in the analysis.

Another issue is whether or not to include all make-models. Farmer included only those make-models that did not undergo a redesign at the time they received CHMSL [9]. In a way, that is ideal, but it does cut down on available data, especially in State files where the make-model is often unknown (Farmer did not analyze State files, but insurance data, where make-models are

known). It can be reasoned, however, that the inclusion of all make-models will neutralize biases that may occur in individual make-models that were redesigned. For example, if a certain model became much more sporty in 1986, it might attract more aggressive drivers and it will have proportionately fewer rear impacts. However, the less aggressive drivers who chose this model before 1986 will eventually buy some other car; thus, while aggressiveness may vary from year to year on individual models, it probably changes little from one model year to the next in the entire passenger car fleet.

CHMSLAVG was computed separately for every State, in every calendar year, always relying on the MY 82-89 crash statistics. The formulas need to be modified, however, in the CY 86, 87 and 88 analyses, since data are not available for the later model years (e.g., MY 87-89 in CY 86). In those years, the CHMSL-equipped average log-odds are based only on the model years that are available. In CY 86,

AVG(+1) = AVG(+2) = AVG(+3) = AVG(+4) = ADJODDS(86)

In CY 87, AVG(+1) = ADJODDS(86) and