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 + (.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

AVG(+1) = ADJODDS(86) = -1.0648

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

(U = UNADJUSTED, A = ADJUSTED FOR VEHICLE AGE)

AVG(- 2) = [ADJODDS(84) + ADJODDS(85)] = -1.0045

AVG(+2) = [ADJODDS(86) + ADJODDS(87)] = -1.0741

AVG(- 3) = [ADJODDS(83) + ADJODDS(84) + ADJODDS(85)] = -1.0217

AVG(+3) = [ADJODDS(86) + ADJODDS(87) + ADJODDS(88)] = -1.0807

AVG(- 4) = [ADJODDS(82) + ADJODDS(83) + ADJODDS(84) + ADJODDS(85)] = -1.0257

AVG(+4) = [ADJODDS(86) + ADJODDS(87) + ADJODDS(88) + ADJODDS(89)] = -1.0847

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 = [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

AVG(+2) = AVG(+3) = AVG(+4) = [ADJODDS(86) + ADJODDS(87)]

In CY 88, AVG(+1) = ADJODDS(86), AVG(+2) = [ADJODDS(86) + ADJODDS(87)], and

AVG(+3) = AVG(+4) = [ADJODDS(86) + ADJODDS(87) + ADJODDS(88)]

Table 2-4 shows the preliminary effectiveness estimates for each State and calendar year. As explained above, no estimate could be made for 1986 Virginia data. Whereas a detailed statistical analysis of the findings, including computation of averages and significance tests, will only be performed on the "final" effectiveness estimates in Section 2.6, two phenomena are immediately apparent from Table 2-4. The estimates are almost all positive: of 79 individual numbers, only 2 are negative, and even those are barely below zero. The effect in CY 1987 is consistent across States (6 to 10 percent) and it is almost always higher than the effects in subsequent years.