______________________________________________________________________________

This document is available to the public from the National Technical Information Service, Springfield, VA 22161

U.S. Department

of Transportation

National Highway

Traffic Safety

Administration

DOT HS 809 403 January 2002

(Revised October, 2002)*

Technical Report

Transitioning to Multiple Imputation – A New

Method to Impute Missing Blood Alcohol

Concentration (BAC) values in FARS 

Published By:

National Center for Statistics and Analysis

Research and Development

* This report was revised [June, 2002] from its original version [January, 2002] to reflect corrected 

crash-level alcohol estimates from Multiple Imputation for 1998-2000 and again revised [October, 

2002] to reflect updated programs to analyze the imputed data.
This publication is distributed by the U.S. Department of Transportation, National Highway Traffic 

Safety Administration, in the interest of information exchange. The opinions, findings and

conclusions expressed in this publication are those of the author(s) and not necessarily those of the 

Department of Transportation or the National Highway Traffic Safety Administration. The United 

States Government assumes no liability for its contents or use thereof. If trade or manufacturers’ 

names are mentioned, it is only because they are considered essential to the object of the publication 

and should not be construed as an endorsement. The United States Government does not endorse 

products or manufacturers.
Technical Report Documentation Page

1. Report No.

DOT HS 809 403

2. Government Accession No. 3. Recipients's Catalog No.

5. Report Date

January, 2002

4. Title and Subtitle

Transitioning to Multiple Imputation – A New 

Method to Estimate Missing Blood Alcohol 

Concentration (BAC) values in FARS

6. Performing Organization Code

NRD-31

7. Author(s)

Rajesh Subramanian

8. Performing Organization Report No.

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)n code

Mathematical Analysis Division, National Center for Statistics and Analysis

National Highway Traffic Safety Administration

U.S. Department of Transportation

NRD-31, 400 Seventh Street, S.W.

Washington, DC 20590

11. Contract of Grant No.

13. Type of Report and Period Covered

NHTSA Technical Report

12. Sponsoring Agency Name and Address

Mathematical Analysis Division, National Center for Statistics and Analysis

National Highway Traffic Safety Administration

U.S. Department of Transportation

NRD-31, 400 Seventh Street, S.W.

Washington, DC 20590

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract

The National Center for Statistics and Analysis (NCSA) of the National Highway Traffic Safety

Administration (NHTSA) has undertaken several approaches to remedy the problem of missing blood alcohol 

test results in the Fatality Analysis Reporting System (FARS). The current approach employs a linear 

discriminant model that estimates the probability that a driver or nonoccupant has a BAC in grams per 

deciliter (g/dl) of 0, .01 to .09 or .10 and greater. Estimates are generated only for drivers and nonoccupants 

(pedestrians, pedalcyclists) for whom alcohol test results were not reported.

Beginning with the 2001 data, NHTSA will transition to Multiple Imputation, a new method to estimate 

missing BAC in FARS. The publications for the 2001 data will reflect the estimates of alcohol involvement 

generated using Multiple Imputation. The new methodology improves on the current model by imputing 

specific values of BAC across the full range of possible values rather than estimating probabilities. Imputing 

ten values of BAC for each missing value will permit the estimation of valid statistics such as variances, 

measures of central tendency, confidence intervals and standard deviations. 

17. Key Words 

Alcohol, BAC, Multiple Imputation, Fatal Crashes

18. Distribution Statement

Document is available to the public through the National 

Technical Information Service, 

Springfield, VA 22161

19. Security Classif. (of this report)

 Unclassified

20. Security Classif. (of this page)

 Unclassified

21. No of Pages

36

22. Price

Form DOT F1700.7 (8-72) Reproduction of completed page authorized

i
Table of Contents

1. Introduction . . . . . 1

2. Reasons for changing the Imputation methodology . . . . . 1

3. Advantages of the new method . . . . . 2

4. Analyzing the Multiply-imputed Datasets . . . . . 3

5. Comparison of estimates from the two methods . . . . . 4

6. Conclusions . . . . . 21

7. Transitioning Schedule . . . . . 21

8. References . . . . . 22

9. Appendix . . . . . 23
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_ National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 1

1. Introduction

The National Highway Traffic Safety Administration (NHTSA) through the National Center for 

Statistics and Analysis (NCSA) has undertaken several approaches to remedy the problem of 

missing blood alcohol test results in the Fatality Analysis Reporting System (FARS). The 

current approach employs a linear discriminant model that estimates the probability that a driver 

or nonoccupant has a BAC in grams per deciliter (g/dl) of 0, .01 to .09 or .10 and greater. 

Estimates are generated only for drivers and nonoccupants (pedestrians, pedalcyclists) for whom 

alcohol test results were not reported.

Beginning with the 2001 data, NCSA will transition to Multiple Imputation, a new method to 

estimate missing BAC in FARS. The Multiple Imputation procedure in FARS has been

implemented and validated as outlined in an earlier NHTSA Technical Report (Rubin et al., [8]). 

The new methodology improves on the current model by imputing specific values of BAC across 

the full range of possible values rather than estimating probabilities. Imputing ten values of 

BAC for each missing value will permit the estimation of valid statistics such as variances, 

measures of central tendency, confidence intervals and standard deviations. As a result,

researchers will be able to draw inferences and test hypotheses about BAC as a factor in fatal 

traffic crashes. The estimation of discrete values also facilitates analysis by nonstandard

boundaries of alcohol involvement (e.g., .08+). 

This report outlines the Multiple Imputation methodology and explains the reasons for and the 

advantages of shifting from the old methodology of estimating missing BAC. It also documents 

the results from both methodologies for certain categories from the 1982 to the 2000 data years. 

The estimates are based on the Final FARS data for 1982 through 1999 and the Annual Report 

File (ARF) for 2000. State-by-state estimates of alcohol involvement from the two methods are 

also presented in this report for the 1999 data year. 

2. Reasons for changing the Imputation methodology

Multiple Imputation is a state of the art methodology - Imputation of missing data points is a 

constantly evolving field of statistics. When the discriminant analysis methodology was adopted 

in 1986, NHTSA recognized the need to constantly evaluate alternative methods of imputation to 

improve the quality and usefulness of our data. The current method permits the calculation of 

probabilities that a missing va lue falls within one of the three ranges. The inability to impute 

discrete values with this method greatly limits analysis of the effects of alcohol involvement on 

traffic crashes and fatalities. The quest for a technique that will provide the most statistically 

robust estimates of discrete values has led to Multiple Imputation. Multiple Imputation is the 

state-of-the-art imputation methodology that will permit computation of standard errors of

estimates and confidence intervals, thus enabling researchers to test hypotheses.

NHTSA assembled a panel of leading experts in different forms of imputation who evaluated the 

available methodologies and their applicability to FARS data. The panel recommended Multiple 
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_ National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 2

Imputation unanimously. The work of this panel was summarized in a NHTSA document (de 

Wolf, [1]) that focuses on the major recommendations of the panelists. The panel members 

outlined their recommendations in papers submitted to NHTSA (Huberty, C.J. et. al. [2], Kalton, 

G. et. al. [3], Little, R. [5], Rubin, D.B. [7]). Multiple Imputation has already been implemented 

to solve nonresponse problems in various Government and Private data systems. It is a

procedure that has been peer-reviewed and published in leading professional journals.

Changing legislative needs – At the federal level, a BAC of .08 has been established as the legal 

definition of intoxication. Through the use of fiscal incentives, the states are being encouraged 

to adopt this threshold as a standard. Using the current Discriminant Analysis methodology, 

NCSA has no way to estimate alcohol involvement at .08 and above without significantly

altering the method. Even with modification, the method of estimation might not be consistent 

with the process used in the earlier years, which will affect the reporting of trends in alcohol 

involvement. 

Multiple Imputation permits statistics along any BAC standard as it imputes BAC along the 

entire scale of plausible BAC values. A historic revision of estimates up to the 1982 data also 

ensures the consistency of estimates of trends.

3. Advantages of the new method

Multiple Imputation provides significant advantages to NCSA in its efforts to address changing 

research and reporting needs. The imputed values are actual values of BAC along the entire 

plausible range, and can therefore be combined to provide estimates for any defined category of 

alcohol involvement. Analysts can use the imputed values to include BAC in models and to 

prepare estimates of error attributable to the imputation process. These procedures were not 

possible with the Discriminant Analysis method.

The multiple imputation procedure replaces each missing BAC with ten simulated values. The 

ten imputations, together with the non-missing BAC values, produce ten apparently complete 

versions of BAC, each of which may be analyzed by standard complete-data techniques. Results 

from analyzing the ten versions will vary somewhat. This variation is used to estimate the extra 

uncertainty in statistical summaries that is attributable to missing data. The ten sets of answers 

are combined with simple computational macros implementing rules given by Rubin [6]. 

Combining the ten answers according to these special rules produces statistical inferences that 

are valid (i.e., estimation of parameters that are consistent, nominal 95% confidence intervals are 

in fact 95% confidence intervals etc.) under quite general conditions. This offers an advantage 

over single imputation which, even if done properly to allow consistent estimation of parameters, 

uniformly underestimates variability because one imputed value cannot possibly represent

uncertainty.
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_ National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 3

The Discriminant Analysis method estimates the probabilities that the actual value falls within 

each of the three broad BAC classes. Although limiting in ways as discussed in Section 2, this 

method is preferable to single imputation. Nevertheless, the estimated probabilities cannot be 

used for many complete-data analyses, especially those pertaining to other categorizations of 

BAC, such as the .08+ category. Moreover, they do not reflect any uncertainty about the 

estimated parameters in the discriminant models used to compute the probabilities.

4. Analyzing the Multiply-imputed Datasets

When assessing the extent of alcohol involvement in traffic crashes, the quantity of interest is 

usually the proportion of a population that shows the involvement of alcohol (e.g., percent of 

drivers killed that were intoxicated, percent of fatally injured nonoccupants, etc). This

proportion is the percentage of the standard population of the stratum of interest that has alcohol 

involvement. Alcohol involvement is determined jointly from the known set of alcohol test 

results as well as the imputed values for unknown BAC. Under multiple imputation, each 

missing BAC value is replaced by ten imputed values. In order to estimate population

proportions, the results (proportions) from each of the ten sets of values have to be combined by 

standard computational macros.

Rubin’s method of scalar estimands (Rubin, [6]) is used to estimate quantities of interest. Let Q

be a one-dimensional quantity of interest – a proportion of crashes or persons that showed a 

positive alcohol test result in a universe of crashes or people or a coefficient from a linear or 

logistic regression model. The goal is to find a confidence interval or test a hypothesis about Q. 

Let Y denote the data from FARS that are necessary to estimate Q. Y is partitioned into observed 

and missing parts,

( , ) Y = Yobs Ymis

where Yobs is known and Ymis is unknown and has been multiply-imputed. Let Qˆ be the 

complete-data point estimate for Q , the estimate to be used if no data were missing. Let U be 

the variance estimate associated with Qˆ , so that U is the complete-data standard error. As U 

and Qˆ are both functions of ( , ) Y = Yobs Ymis , they may be rewritten as ( , )

ˆQ Yobs Ymis and U(Yobs, 

Ymis), respectively. Multiple Imputation inference assumes that the complete data problem is 

sufficiently regular and sample size sufficiently large for the asymptotic normal approximation

) ~ (0,1)

ˆ

(

1/ 2 U Q −Q N−

to work well. With m imputations, m different versions of Qˆ and U can be calculated.

Let

( , )

ˆ ˆ

( ) (t)

obs mis

t Q = Q Y Y

and
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 4

( , )

( ) (t)

obs mis

t U =U Y Y

be the point and variance estimates using the t-th set of imputed data, t=1,2,...,10. The multiple 

imputation point-estimate for Q is simply the average of the complete-data point estimates.

∑=

=

10

1

( ) ˆ

10

1

i

t Q Q

Q is the final quantity of interest, for example, the proportion of drivers involved in fatal 

crashes whose BAC was .01 or above.

The variance estimate associated with Q has two components. The within-imputation variance 

is the average of the complete-data variance estimates,

∑=

=

10

1

( )

10

1

t

t U U

and the between-imputation variance is the variance of the complete-data point estimates,

∑=

= −

10

1

( ) 2

)

ˆ

(

9

1

t

t B Q Q

The total-variance is defined as

T U (1 m )B

−1

= + +

5. Comparison of estimates from the two methods

Under Multiple Imputation, the estimated rates of alcohol involvement were generally higher 

than those under Discriminant Analysis. Positive differences of up to about 2 percent in the rate 

of alcohol involvement appeared consistently across most of the broader categories of vehicle 

classes and demographic subgroups, and across classifications of crashes by time of day and day 

of week. Differences in rates across subgroups, and trends in rates across time, were quite similar 

under the two methods.

The discrepancy between the new and old imputation methods can be traced to the fact that the 

new model is a General Linear Location Model (GLOM) which is a two-stage model1 while the 

 

1 The two-stage model consists of a first stage conventional loglinear model to determine BAC as a binary 

indicator, i.e., if BAC=0 or BAC>0. The second stage of the GLOM is a conventional linear regression 

model used to predict the actual level of BAC given that BAC>0 (Rubin et al., 1998). 
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 5

old model was a discriminant model. To the uninformed observer, it may seem disturbing that 

changing the form of the missing data model would have so much impact on the final estimates. 

However, given the high rates of missing information (>50%) about BAC, the results should be 

sensitive to model specification. This underscores the need to provide meaningful estimates of 

uncertainty (e.g. standard errors) for statistics related to BAC. The new method addresses this 

issue and can now provide standard errors of estimates of alcohol involvement.

Also, the old imputation method is based on a linear discriminant model that distinguishes 

among the three classes of BAC. The new model, however, models BAC in two stages: a logit 

model for distinguishing BAC=0 and BAC>0, and a regression model for predicting BAC given 

that BAC>0. In many situations, discriminant and logit models tend to produce similar estimates 

for the classification probabilities. On occasion, however, the probabilities can be different 

because of a critical assumption that the discriminant model makes. The assumption is that the 

normal distributions for the three classifications share a common covariance matrix. If the group 

means are far apart, then the classification probabilities from the linear discriminant model can 

be substantially less efficient than those of the logit model.

Tables 1 through 4 present a comparison of the BAC estimates from the multiple imputation 

method to those of the discriminant analysis (Klein, [4]) model under various categories

traditionally reported and released by NHTSA in its annual fact sheets. The estimates from 

multiple imputation are printed in each cell accompanied by the corresponding estimates from 

the discriminant method in parenthesis. The values in each cell are the percentage of all crashes 

or drivers in that category for two levels of BAC, namely, .01 and greater (.01+)2 and .10 and 

greater (.10+). For example, an entry of 36.2 for a given year for drivers killed in the .01+ 

category means that for that particular year, 36.2 percent of all the drivers killed in fatal crashes 

had a BAC of .01 or greater.

Table 1 presents the overall rates of alcohol involvement and intoxication in fatal crashes 

as estimated by the two methods. Alcohol is said to be involved in a fatal traffic crash if either 

the driver of any vehicle or a nonoccupant (pedestrian or pedalcyclist) involved in the crash has a 

BAC of .01 or greater. A driver or nonoccupant is deemed “intoxicated” if the BAC is .10 or 

greater. However, according to new legislation, the legal threshold for intoxication is .08. In the 

tables, figures in parentheses represent the values obtained using Discriminant Analysis.

 

2A BAC level of 0.01 implies that the alcohol content is 0.01 grams/deciliter. Because BAC is reported to 

two decimal places, the 0.01+ category includes all positive values of BAC.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 6

Table 1 : Alcohol Involvement (Percentage) in Fatal Crashes and Fatalities by Crash BAC 

and Imputation Methodology, FARS 1982-2000*

Fatal Crashes Fatalities

Year BAC=.01+ BAC=.10+ BAC=.01+ BAC=.10+

1982 59 (57) 49 (46) 60 (57) 49 (46)

1983 57 (55) 48 (45) 58 (56) 48 (45)

1984 56 (53) 45 (43) 56 (54) 46 (43)

1985 53 (52) 42 (41) 53 (52) 43 (41)

1986 54 (52) 43 (41) 54 (52) 43 (41)

1987 52 (51) 41 (40) 52 (51) 41 (40)

1988 50 (50) 41 (40) 51 (50) 41 (40)

1989 49 (49) 40 (39) 49 (49) 40 (39)

1990 50 (49) 41 (40) 51 (50) 41 (40)

1991 48 (48) 40 (38) 49 (48) 40 (38)

1992 47 (46) 38 (36) 47 (45) 38 (36)

1993 45 (43) 36 (35) 45 (44) 36 (35)

1994 43 (41) 35 (32) 43 (41) 34 (32)

1995 42 (41) 34 (33) 42 (41) 34 (32)

1996 42 (41) 34 (32) 42 (41) 34 (32)

1997 40 (38) 32 (30) 40 (39) 32 (30)

1998 40 (39) 32 (30) 40 (39) 32 (30)

1999 40 (38) 32 (30) 40 (38) 32 (30)

2000 41 (40) 33 (31) 41 (40) 33 (31)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(Values in parentheses represent estimates from the old imputation methodology)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 7

Figure 1 illustrates the differences in the trend of alcohol involvement in fatal crashes from 1982 

to 2000. The trend of alcohol involvement follows the same pattern for the estimates from both 

the methods. The discrepancy may be higher in the earlier years due to the high degree of 

missing information in the earlier years. Using the estimates based on Multiple Imputation, trend 

lines can be generated for any level of alcohol along the range of plausible values (0 to .94).

Figure 1 : Alcohol Involvement in Fatal Crashes by Crash BAC and Imputation 

Methodology, FARS 1982-2000

20

30

40

50

60

1982198319841985198619871988198919901991199219931994199519961997199819992000

Year

Percent

BAC=0.01+

BAC=0.10+

95% Confidence Intervals and Standard Errors

The ten sets of imputations are combined with simple computational macros implementing rules 

given by Rubin [6]. Combining the ten answers according to these special rules produces 

statistical inferences that are valid (i.e., estimation of parameters that are consistent, nominal 

95% confidence intervals are in fact 95% confidence intervals etc.) under quite general

conditions. The total variance T estimated above is used in evaluating the 95% confidence 

intervals. The inferences are based on the assumption that
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 8

Q Q tT n( ) ~

1/ 2

−

−

where the degrees of freedom < are given by

]

(1 1)

[1

2

( 1)

m B

U

m

+ −

n = − +

Thus a 100(1-")% confidence-interval estimate for the estimate is given by 

Q T tn ,1−a / 2±

Figure 2 depicts the 95% Confidence Interval band of the estimated percentage of alcohol

involvement (.01+) in fatal crashes. The upper and lower bounds are estimated according to the 

SAS procedures listed in Appendix B.

Figure 2 : 95% Confidence Interval of the estimated percentage of Alcohol Involvement in 

Fatal Crashes by Crash BAC, FARS 1982-2000

20

30

40

50

60

1982198319841985198619871988198919901991199219931994199519961997199819992000

Year

Percent

Alcohol Related (0.01+) Crashes Lower Boundary Upper Boundary
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 9

The standard error of the estimate is the square-root of the total variance T, as estimated by

S tan dard Error U (1 m )B

−1

= + +

 Table 3 shows the Standard Error of the estimated alcohol involvement in fatal crashes by Crash 

BAC.

Table 3 : Standard Error of the Estimate of Alcohol Involvement (Percentage) in Fatal 

Crashes by Crash BAC, FARS 1982-2000*

Year Estimate Standard Error

1982 59 0.39435745

1983 57 0.38229963

1984 56 0.41550553

1985 53 0.30986141

1986 54 0.26917724

1987 52 0.36467598

1988 50 0.29723237

1989 49 0.36094569

1990 50 0.29752044

1991 48 0.31703266

1992 47 0.30584581

1993 45 0.29541456

1994 43 0.30842406

1995 42 0.31074702

1996 42 0.29497051

1997 40 0.31334548

1998 40 0.32099755

1999 40 0.27862571

2000 41 0.32049002

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 10

Table 2 shows the trend of fatally injured persons in crashes where at least one driver or 

nonoccupant (pedestrian or pedalcyclist) was intoxicated. On average, about 70 percent of 

people killed in such crashes were themselves intoxicated. The remaining 30 percent were 

passengers, nonintoxicated drivers, or nonintoxicated nonoccupants.

Table 2: Types of Fatalities in Fatal Crashes Involving at Least One Intoxicated Driver or 

Nonoccupant Expressed as a Percent of Such fatalities, FARS 1982-2000*

Year Intoxicated 

Drivers

Nonintoxicated 

Drivers

Passengers Intoxicated 

Nonoccupants

Nonintoxicated 

Nonoccupants

1982 52 (53) 7 (7) 22 (21) 13 (13) 5 (6)

1983 52 (53) 7 (7) 23 (22) 12 (12) 5 (5)

1984 53 (54) 8 (7) 21 (21) 12 (13) 5 (6)

1985 54 (54) 8 (7) 22 (21) 12 (13) 5 (5)

1986 54 (54) 8 (7) 22 (22) 12 (12) 5 (5)

1987 54 (55) 8 (7) 22 (21) 12 (12) 5 (5)

1988 54 (55) 8 (7) 22 (21) 12 (12) 4 (5)

1989 55 (55) 7 (7) 22 (21) 12 (12) 4 (5)

1990 53 (55) 7 (6) 22 (21) 12 (12) 5 (5)

1991 54 (55) 7 (7) 22 (22) 12 (13) 4 (4)

1992 54 (54) 7 (7) 22 (21) 13 (13) 4 (4)

1993 54 (54) 7 (7) 21 (21) 14 (14) 4 (4)

1994 53 (56) 8 (7) 22 (20) 13 (13) 5 (4)

1995 55 (56) 7 (6) 20 (20) 13 (14) 4 (4)

1996 54 (55) 7 (6) 22 (21) 13 (14) 4 (4)

1997 55 (55) 7 (6) 21 (21) 13 (13) 4 (4)

1998 56 (56) 6 (6) 21 (20) 14 (14) 4 (4)

1999 56 (57) 7 (6) 21 (20) 13 (14) 3 (4)

2000 55 (57) 7 (6) 22 (21) 12 (12) 3 (4)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(values in parentheses represent estimates from the old imputation methodology)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 11

Table 3 compares the results obtained by the two methods for drivers only. The table shows 

BAC levels, by year, for drivers who were either involved in a fatal crash or killed in a fatal 

crash. As in the previous table, the figures in parentheses represent the values obtained by the 

current method of imputation. Alcohol involvement for drivers involved in fatal crashes, who 

themselves may be fatally injured or have survived, ranged from a high of about 41 percent in 

1982 to a low of about 24 percent in 1999. This trend was also reflected when looking at just 

male or female drivers involved in fatal crashes.

Table 3 : Alcohol Involvement for Drivers Involved in Fatal Crashes by Sex, 

FARS 1982-2000*

Male Female Total

Year .01+ .10+ .01+ .10+ .01+ .10+

1982 44 (42) 35 (32) 27 (26) 20 (19) 41 (39) 32 (30)

1983 43 (40) 35 (31) 25 (25) 20 (18) 39 (38) 32 (29)

1984 41 (39) 32 (30) 25 (24) 18 (17) 38 (36) 29 (27)

1985 38 (37) 30 (28) 22 (22) 16 (15) 35 (34) 27 (26)

1986 40 (38) 30 (29) 22 (21) 16 (15) 36 (34) 27 (26)

1987 37 (36) 29 (28) 21 (21) 16 (15) 34 (33) 26 (25)

1988 37 (36) 29 (28) 20 (20) 15 (15) 33 (33) 26 (25)

1989 35 (35) 28 (27) 19 (20) 15 (14) 31 (32) 25 (24)

1990 37 (36) 29 (28) 20 (19) 15 (14) 33 (32) 26 (25)

1991 35 (35) 28 (27) 19 (19) 14 (14) 31 (31) 25 (24)

1992 33 (32) 26 (25) 18 (18) 13 (13) 30 (29) 23 (22)

1993 32 (31) 25 (24) 17 (17) 13 (12) 28 (27) 22 (21)

1994 30 (29) 24 (22) 17 (15) 13 (11) 27 (25) 21 (19)

1995 30 (28) 23 (22) 16 (16) 12 (11) 26 (25) 20 (19)

1996 29 (28) 23 (21) 16 (16) 12 (11) 26 (25) 20 (19)

1997 28 (27) 22 (20) 15 (14) 11 (10) 24 (24) 19 (18)

1998 28 (27) 22 (20) 15 (14) 11 (10) 24 (23) 19 (18)

1999 28 (26) 21 (20) 14 (14) 11 (10) 24 (23) 19 (18)

2000 29 (27) 22 (20) 16 (16) 12 (11) 26 (24) 20 (18)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(values in parentheses represent estimates from the old imputation methodology)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 12

Table 4 shows the alcohol involvement of drivers involved in fatal crashes by the type of vehicle 

they were driving. Overall, the highest proportion of drivers involved who had any alcohol were 

motorcycle operators. The lowest such proportion is observed with drivers of large trucks.

Table 4 : Alcohol Involvement for Drivers Involved in Fatal Crashes by Vehicle Type and 

Driver’s BAC, FARS 1982-2000*

Passenger Cars Light Trucks and 

Vans

Large Trucks Motorcycles

Year

.01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+

1982 42 (40) 33 (31) 44 (43) 36 (35) 10 (8) 5 (4) 55 (53) 43 (41)

1983 40 (39) 33 (30) 43 (42) 36 (33) 10 (8) 6 (5) 57 (54) 43 (41)

1984 39 (36) 30 (28) 41 (39) 32 (31) 9 (8) 6 (4) 55 (54) 42 (40)

1985 36 (35) 28 (26) 37 (36) 30 (29) 7 (6) 4 (4) 53 (53) 39 (39)

1986 36 (35) 28 (26) 38 (37) 30 (29) 7 (5) 4 (3) 56 (54) 42 (41)

1987 35 (34) 27 (25) 37 (37) 29 (29) 5 (4) 3 (3) 51 (51) 39 (38)

1988 34 (33) 26 (25) 37 (37) 29 (29) 6 (5) 3 (3) 51 (50) 37 (36)

1989 32 (32) 25 (24) 35 (35) 28 (28) 4 (5) 3 (3) 53 (53) 41 (40)

1990 34 (32) 27 (24) 36 (36) 29 (29) 5 (5) 2 (2) 52 (52) 40 (39)

1991 31 (31) 25 (23) 35 (36) 28 (28) 4 (4) 2 (2) 52 (51) 40 (39)

1992 30 (29) 23 (22) 33 (33) 26 (26) 3 (3) 2 (1) 49 (48) 37 (36)

1993 28 (27) 22 (21) 31 (31) 25 (25) 4 (3) 2 (2) 45 (44) 34 (33)

1994 28 (26) 22 (19) 29 (29) 23 (23) 3 (3) 2 (1) 41 (40) 30 (29)

1995 27 (26) 21 (19) 29 (28) 23 (22) 4 (3) 2 (1) 42 (41) 30 (29)

1996 27 (26) 21 (19) 28 (28) 22 (22) 3 (3) 2 (1) 43 (42) 32 (30)

1997 26 (24) 20 (18) 26 (26) 21 (20) 3 (2) 1 (1) 41 (39) 30 (28)

1998 26 (24) 20 (18) 26 (26) 21 (20) 2 (2) 1 (1) 41 (40) 32 (30)

1999 25 (24) 19 (18) 26 (26) 21 (20) 3 (2) 1 (1) 40 (38) 29 (28)

2000 28 (26) 22 (19) 26 (26) 20 (20) 3 (2) 1 (1) 40 (38) 29 (27)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(values in parentheses represent estimates from the old imputation methodology)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 13

Table 5 shows the extent of alcohol involvement of drivers involved in fatal crashes by their age. 

Table 5 : Alcohol Involvement for Drivers Involved in Fatal Crashes by Age and 

Driver’s BAC, FARS 1982-2000*

Age 16-20 21-24 25-34 35-44 45-64 65+

BAC .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+

1982 45

(44)

32

(31)

53

(52)

42

(40)

46

(44)

38

(35)

38

(35)

31

(28)

29

(26)

23

(21)

15

(14)

11

(10)

1983 43

(42)

31

(30)

53

(51)

42

(39)

46

(44)

38

(35)

37

(34)

31

(28)

26

(25)

22

(19)

13

(12)

9

(9)

1984 40

(40)

28

(27)

52

(49)

40

(37)

44

(42)

36

(33)

35

(32)

29

(26)

25

(23)

20

(18)

14

(12)

10

(9)

1985 35

(35)

23

(24)

47

(46)

37

(35)

42

(41)

34

(32)

32

(30)

27

(24)

23

(22)

18

(17)

12

(11)

8

(8)

1986 37

(36)

25

(24)

49

(47)

38

(36)

43

(41)

35

(33)

33

(31)

27

(25)

23

(21)

18

(16)

12

(10)

7

(7)

1987 33

(33)

22

(21)

47

(45)

36

(34)

43

(42)

34

(33)

32

(31)

27

(25)

21

(21)

17

(16)

11

(10)

7

(7)

1988 33

(32)

22

(21)

47

(46)

36

(35)

42

(41)

34

(33)

32

(31)

27

(25)

21

(21)

17

(16)

11

(11)

7

(7)

1989 30

(30)

20

(20)

45

(45)

35

(35)

40

(40)

33

(32)

32

(31)

27

(25)

21

(21)

17

(17)

10

(10)

6

(7)

1990 33

(32)

22

(21)

46

(45)

36

(35)

43

(41)

35

(33)

33

(32)

28

(26)

21

(20)

17

(16)

10

(10)

7

(6)

1991 30

(30)

21

(20)

45

(44)

35

(34)

41

(40)

34

(32)

32

(31)

27

(25)

20

(20)

16

(16)

9

(10)

6

(6)

1992 27

(27)

18

(18)

42

(41)

32

(31)

40

(38)

32

(31)

31

(30)

26

(24)

20

(19)

15

(14)

10

(9)

6

(6)

1993 24

(25)

16

(16)

40

(39)

31

(31)

37

(36)

30

(29)

30

(29)

25

(23)

20

(19)

16

(14)

8

(8)

6

(5)

1994 24

(23)

15

(14)

39

(37)

30

(28)

36

(34)

29

(27)

29

(27)

24

(22)

19

(17)

15

(14)

9

(8)

6

(5)

1995 21

(21)

13

(13)

38

(37)

29

(28)

35

(34)

28

(27)

30

(29)

24

(23)

19

(18)

15

(14)

8

(7)

5

(5)

1996 23

(21)

15

(14)

38

(37)

28

(27)

34

(33)

28

(26)

29

(28)

24

(22)

19

(18)

15

(14)

9

(8)

6

(5)

1997 22

(22)

15

(14)

36

(35)

27

(26)

32

(31)

25

(24)

29

(27)

24

(22)

18

(17)

14

(13)

8

(7)

5

(5)

1998 22

(22)

15

(14)

37

(36)

29

(28)

32

(31)

25

(24)

28

(27)

23

(21)

18

(17)

14

(13)

8

(7)

5

(5)

1999 22

(21)

15

(14)

38

(36)

28

(27)

32

(30)

25

(24)

28

(27)

23

(21)

18

(17)

14

(13)

8

(7)

5

(4)

2000 24

(23)

16

(15)

38

(37)

29

(27)

33

(31)

26

(24)

30

(28)

24

(22)

19

(18)

15

(14)

8

(8)

5

(5)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(values in parentheses represent estimates from the old imputation methodology)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 14

Drivers in the age group 21-24 have the highest proportion of alcohol involvement. This trend 

was carried through 1982 to 1999. Older drivers, 65 years of age and above had the lowest 

proportion of alcohol involvement. 

Table 6 shows the alcohol involvement among drivers who are fatally injured. Classification of 

this population by time of day shows that a greater proportion of drivers killed in nighttime 

crashes had alcohol involvement than drivers that are killed in daytime crashes.

Table 6 : Alcohol Involvement for Drivers Killed in Fatal Crashes by Time of the Day and 

Driver’s BAC, FARS 1982-2000*

Daytime Nighttime Total

Year .01+ .10+ .01+ .10+ .01+ .10+

1982 28 (26) 22 (20) 73 (70) 62 (59) 55 (53) 46 (44)

1983 26 (25) 20 (19) 73 (70) 62 (59) 54 (51) 45 (42)

1984 25 (23) 19 (17) 71 (69) 59 (57) 51 (49) 42 (40)

1985 24 (23) 17 (17) 69 (68) 57 (56) 49 (48) 39 (39)

1986 24 (23) 18 (16) 70 (68) 58 (56) 50 (48) 40 (39)

1987 23 (22) 17 (16) 67 (66) 56 (55) 48 (47) 39 (38)

1988 22 (22) 16 (16) 67 (67) 56 (56) 47 (47) 38 (38)

1989 21 (21) 16 (15) 67 (66) 56 (56) 46 (46) 38 (37)

1990 21 (21) 16 (15) 67 (67) 57 (57) 46 (46) 38 (38)

1991 20 (19) 15 (14) 66 (65) 56 (55) 45 (44) 37 (37)

1992 19 (18) 14 (13) 64 (63) 54 (53) 43 (42) 35 (34)

1993 18 (17) 13 (12) 63 (62) 54 (52) 41 (40) 34 (33)

1994 17 (16) 13 (12) 60 (60) 51 (50) 38 (37) 31 (31)

1995 18 (17) 13 (12) 61 (59) 51 (50) 39 (38) 32 (31)

1996 17 (16) 12 (11) 61 (59) 51 (50) 38 (37) 31 (30)

1997 16 (15) 12 (11) 58 (57) 49 (48) 36 (35) 30 (28)

1998 16 (15) 12 (11) 59 (57) 49 (48) 36 (35) 30 (28)

1999 17 (15) 12 (11) 58 (56) 49 (47) 36 (35) 29 (28)

2000 17 (16) 12 (11) 58 (57) 49 (48) 37 (36) 30 (29)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

 (values in parentheses represent estimates from the old imputation methodology)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 15

Table 7 shows the trend of alcohol involvement among fatally injured drivers by the time of day 

and the type of crash, i.e., if the driver was killed in a single vehicle or a multiple vehicle crash. 

Table 7 : Alcohol Involvement for Drivers Killed in Fatal Crashes by Crash Type and Time 

of the Day and Driver’s BAC, FARS 1982-2000*

Single Vehicle Crashes Multiple Vehicle Crashes

Time Day Night Total Day Night Total

BAC .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+

1982 42

(40)

34

(32)

83

(81)

73

(71)

71

(69)

61

(60)

20

(18)

14

(12)

59

(56)

47

(43)

40

(37)

31

(28)

1983 40

(38)

33

(31)

83

(80)

73

(71)

69

(67)

60

(58)

18

(17)

13

(11)

59

(56)

47

(43)

38

(36)

29

(27)

1984 37

(36)

30

(28)

81

(79)

70

(69)

67

(65)

58

(56)

18

(16)

12

(11)

56

(54)

43

(41)

35

(34)

26

(24)

1985 37

(36)

29

(28)

80

(79)

68

(68)

65

(64)

55

(55)

17

(16)

11

(10)

54

(53)

42

(40)

33

(32)

25

(24)

1986 36

(34)

29

(27)

80

(79)

69

(67)

66

(64)

56

(54)

18

(17)

12

(11)

54

(52)

42

(40)

34

(33)

25

(24)

1987 36

(35)

29

(28)

78

(77)

67

(66)

64

(63)

55

(54)

16

(15)

10

(10)

52

(51)

40

(39)

32

(31)

24

(23)

1988 34

(34)

27

(27)

78

(78)

68

(68)

63

(63)

54

(54)

16

(15)

10

(9)

51

(51)

40

(39)

31

(31)

23

(22)

1989 34

(34)

27

(27)

77

(76)

67

(66)

62

(62)

53

(53)

15

(14)

10

(9)

52

(51)

41

(40)

30

(30)

23

(22)

1990 33

(33)

26

(27)

78

(78)

68

(68)

63

(63)

54

(54)

14

(14)

9

(9)

51

(50)

40

(40)

30

(29)

23

(22)

1991 31

(31)

25

(25)

77

(76)

67

(67)

62

(61)

53

(52)

13

(13)

9

(8)

49

(48)

39

(38)

28

(27)

21

(20)

1992 30

(29)

23

(23)

76

(74)

66

(65)

59

(58)

51

(50)

13

(12)

8

(7)

46

(45)

37

(35)

26

(25)

20

(19)

1993 29

(28)

23

(23)

74

(73)

65

(64)

58

(57)

50

(49)

12

(11)

8

(7)

46

(45)

37

(35)

25

(24)

19

(18)

1994 27

(26)

22

(21)

72

(71)

63

(62)

55

(54)

47

(46)

11

(11)

7

(7)

44

(43)

35

(34)

24

(23)

18

(17)

1995 28

(27)

22

(22)

73

(71)

63

(62)

56

(55)

48

(47)

12

(11)

8

(7)

42

(41)

34

(32)

23

(22)

18

(16)

1996 27

(26)

21

(21)

73

(71)

63

(62)

55

(54)

47

(46)

11

(11)

7

(6)

44

(42)

34

(32)

23

(22)

17

(16)

1997 26

(24)

21

(19)

70

(69)

61

(60)

53

(51)

45

(44)

11

(10)

7

(6)

42

(39)

33

(31)

22

(21)

17

(15)

1998 26

(25)

21

(20)

70

(68)

61

(60)

53

(51)

45

(44)

11

(10)

7

(6)

40

(38)

31

(29)

21

(20)

16

(14)

1999 26

(25)

20

(19)

70

(68)

60

(59)

52

(51)

44

(43)

11

(10)

7

(6)

40

(38)

31

(28)

21

(20)

15

(14)

2000 26

(25)

20

(20)

71

(69)

60

(59)

53

(51)

44

(43)

11

(10)

7

(6)

40

(39)

32

(30)

22

(21)

16

(15)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

(values in parentheses represent estimates from the old imputation methodology)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 16

The trend of alcohol involvement is similar for both methods with the nighttime single vehicle 

crashes showing the highest proportion of drivers that had some alcohol.

Table 8: Alcohol Involvement for Drivers Killed in Fatal Crashes by Time of the Day and 

Day of the Week and Driver’s BAC, FARS 1982-2000*

Weekday Weekend

Time Day Night Total Day Night Total

BAC .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+

1982 24

(22)

19

(16)

69

(66)

58

(56)

46

(43)

38

(35)

38

(37)

30

(28)

76

(74)

65

(62)

67

(65)

56

(54)

1983 22

(21)

17

(15)

69

(67)

59

(56)

44

(42)

36

(34)

38

(35)

30

(27)

76

(73)

65

(62)

66

(63)

56

(53)

1984 21

(19)

15

(14)

66

(63)

55

(53)

41

(39)

33

(31)

35

(34)

27

(26)

75

(73)

62

(61)

64

(62)

53

(51)

1985 20

(19)

14

(13)

64

(63)

53

(53)

39

(38)

31

(30)

36

(35)

27

(26)

73

(72)

60

(60)

62

(61)

51

(50)

1986 21

(19)

15

(14)

65

(63)

54

(53)

41

(39)

32

(31)

34

(32)

25

(23)

73

(71)

60

(59)

62

(60)

50

(49)

1987 19

(18)

14

(13)

63

(62)

52

(51)

38

(37)

30

(29)

34

(33)

26

(25)

71

(70)

59

(58)

60

(59)

49

(48)

1988 18

(18)

13

(13)

62

(62)

52

(52)

37

(37)

30

(29)

33

(32)

25

(24)

71

(71)

60

(59)

60

(60)

50

(49)

1989 17

(17)

12

(12)

62

(61)

52

(52)

35

(35)

29

(29)

33

(32)

25

(24)

71

(70)

59

(59)

60

(59)

50

(49)

1990 17

(17)

12

(12)

62

(62)

53

(52)

36

(35)

29

(29)

31

(31)

24

(24)

71

(70)

60

(60)

60

(59)

50

(50)

1991 16

(16)

12

(11)

62

(61)

53

(52)

35

(34)

29

(28)

30

(29)

24

(23)

70

(69)

59

(58)

58

(57)

49

(48)

1992 16

(15)

11

(10)

58

(58)

49

(49)

33

(32)

26

(26)

29

(27)

22

(20)

69

(67)

58

(57)

57

(55)

47

(46)

1993 15

(14)

11

(10)

57

(56)

48

(48)

31

(30)

25

(25)

27

(26)

20

(19)

68

(66)

58

(56)

55

(53)

46

(44)

1994 14

(13)

10

(9)

53

(52)

44

(43)

28

(27)

22

(22)

25

(24)

20

(19)

67

(65)

57

(56)

53

(52)

45

(43)

1995 14

(14)

10

(10)

54

(53)

46

(45)

29

(29)

24

(23)

27

(25)

20

(19)

66

(64)

56

(54)

53

(51)

44

(42)

1996 14

(13)

10

(9)

54

(53)

45

(44)

29

(28)

23

(22)

26

(24)

20

(18)

67

(65)

56

(55)

53

(51)

44

(42)

1997 13

(12)

9

(8)

51

(50)

43

(42)

27

(26)

22

(21)

25

(23)

19

(17)

64

(62)

54

(53)

51

(48)

42

(40)

1998 13

(12)

10

(9)

52

(50)

43

(42)

27

(26)

22

(21)

24

(23)

19

(17)

65

(62)

55

(53)

50

(48)

42

(40)

1999 13

(12)

9

(8)

51

(50)

43

(42)

27

(26)

21

(20)

27

(25)

20

(18)

64

(61)

53

(51)

50

(48)

41

(39)

2000 13

(13)

9

(9)

51

(50)

42

(41)

27

(26)

21

(21)

25

(23)

19

(18)

65

(63)

54

(53)

51

(49)

42

(40)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 17

Table 9 shows the level of alcohol involvement among fatally injured drivers by their restraint 

use. Restraint usage has been observed to be correlated with the level of alcohol involvement 

and is also used as a covariate in both the models.

Table 9: Alcohol Involvement of Unbelted, Fatally Injured Drivers of Passenger Cars, 

Light Trucks and Vans and Driver’s BAC, FARS 1982-2000*

BAC=.01+ BAC=.10+

Year Multiple 

Imputation

Discriminant 

Analysis

Multiple 

Imputation

Discriminant 

Analysis

1982 58 55 49 47

1983 55 53 48 45

1984 53 51 45 43

1985 52 51 43 42

1986 55 53 46 44

1987 54 53 45 44

1988 55 55 46 46

1989 53 53 45 45

1990 55 54 46 46

1991 54 53 46 45

1992 52 51 44 43

1993 51 49 44 42

1994 49 48 42 41

1995 50 48 42 41

1996 50 48 42 40

1997 48 46 41 39

1998 48 46 41 39

1999 47 45 40 38

2000 49 47 41 39

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)
______________________________________________________________________________

 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 18

Table 10 shows the level of alcohol involvement among fatally injured drivers who had prior 

convictions such as previously recorded crashes, DWI convictions, Speeding and License

suspensions. Drivers who had previous DWI convictions who were killed in crashes were more 

likely to have alcohol compared to drivers with a history of other types of infractions.

Table 10: Previous Driving Records of Drivers Killed in Traffic Crashes, FARS 1982-2000*

Recorded Crashes DWI Convictions Speeding 

Convictions

Recorded 

Suspensions

Year .01+ .10+ .01+ .10+ .01+ .10+ .01+ .10+

1982 62 (59) 52 (50) 85 (83) 76 (74) 64 (61) 53 (50) 77 (75) 67 (65)

1983 60 (58) 51 (48) 84 (82) 74 (73) 62 (60) 52 (49) 75 (73) 65 (63)

1984 59 (58) 48 (47) 83 (82) 73 (72) 59 (57) 48 (46) 72 (69) 61 (59)

1985 54 (53) 44 (44) 82 (81) 73 (72) 56 (56) 46 (45) 73 (71) 63 (62)

1986 55 (54) 44 (43) 83 (82) 74 (73) 57 (56) 46 (45) 75 (73) 64 (62)

1987 52 (52) 42 (41) 82 (81) 74 (73) 54 (54) 44 (43) 71 (70) 61 (60)

1988 52 (52) 43 (43) 83 (83) 75 (75) 55 (55) 45 (45) 70 (70) 60 (60)

1989 51 (51) 42 (42) 82 (82) 74 (73) 54 (53) 43 (43) 69 (69) 60 (60)

1990 50 (50) 41 (41) 83 (83) 76 (76) 53 (53) 44 (44) 70 (70) 60 (60)

1991 50 (49) 42 (41) 84 (83) 77 (76) 54 (53) 44 (44) 70 (69) 61 (60)

1992 46 (46) 38 (38) 84 (84) 76 (76) 49 (48) 40 (39) 68 (67) 59 (58)

1993 45 (44) 37 (36) 80 (79) 73 (72) 47 (46) 39 (38) 67 (66) 58 (58)

1994 41 (40) 33 (32) 81 (81) 74 (73) 44 (43) 35 (34) 64 (63) 55 (54)

1995 41 (41) 34 (33) 81 (80) 74 (74) 46 (45) 37 (36) 64 (63) 55 (54)

1996 40 (40) 32 (32) 79 (79) 72 (71) 45 (44) 36 (35) 63 (62) 54 (53)

1997 40 (39) 32 (31) 78 (77) 70 (69) 43 (42) 35 (34) 63 (62) 55 (53)

1998 40 (38) 32 (31) 76 (75) 69 (68) 43 (42) 34 (33) 62 (60) 53 (52)

1999 37 (36) 31 (30) 78 (78) 70 (69) 43 (41) 34 (33) 61 (60) 52 (51)

2000 40 (38) 32 (31) 79 (77) 70 (70) 42 (41) 34 (33) 62 (60) 52 (50)

(values in parentheses represent estimates from the old imputation methodology)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 19

Table 11 shows the level of alcohol involvement among fatally injured nonoccupants

(pedestrians and pedalcyclists).

Table 11 : Pedestrians and Pedalcyclists Killed in Traffic Crashes by BAC of the 

Pedestrian or Pedalcyclist, FARS 1982-2000*

Pedestrians Pedalcyclists

Year .01+ .10+ .01+ .10+

1982 42 (41) 36 (34) 22 (20) 16 (14)

1983 42 (40) 36 (33) 18 (20) 14 (14)

1984 40 (39) 34 (33) 18 (18) 13 (13)

1985 40 (39) 33 (32) 15 (18) 11 (12)

1986 39 (39) 33 (32) 17 (18) 13 (12)

1987 38 (38) 31 (31) 19 (21) 14 (14)

1988 37 (37) 31 (30) 18 (19) 14 (14)

1989 39 (39) 32 (32) 18 (19) 14 (14)

1990 38 (38) 32 (32) 20 (21) 16 (16)

1991 38 (38) 32 (32) 24 (24) 18 (17)

1992 39 (38) 33 (32) 20 (22) 15 (16)

1993 38 (37) 32 (32) 22 (23) 17 (17)

1994 36 (36) 30 (30) 20 (21) 16 (16)

1995 37 (37) 31 (30) 23 (24) 19 (19)

1996 38 (38) 32 (32) 22 (23) 17 (17)

1997 35 (34) 30 (29) 22 (23) 17 (17)

1998 38 (37) 31 (30) 24 (24) 19 (19)

1999 38 (37) 32 (31) 26 (26) 23 (22)

2000 38 (37) 32 (30) 25 (26) 21 (21)

(values in parentheses represent estimates from the old imputation methodology)

(*Based on 1982-1999 Final and 2000 Annual Report (AR) Files)

Table 12 compares the estimates from the two methods for all traffic fatalities by state and the 

highest BAC in the crash for 2000.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 20

Table 12 : Percentage Alcohol Involvement in Traffic Fatalities by State and 

Highest BAC in the Crash, FARS 2000*

State BAC=.01+ BAC=.10+ State BAC=.01+ BAC=.10+

Alabama 43 (40) 35 (33) Montana 49 (46) 42 (39)

Alaska 54 (52) 45 (43) Nebraska 38 (37) 26 (25)

Arizona 45 (44) 36 (34) Nevada 43 (45) 35 (35)

Arkansas 34 (31) 25 (21) New Hampshire 37 (39) 30 (31)

California 39 (37) 30 (28) New Jersey 44 (44) 35 (32)

Colorado 40 (38) 31 (29) New Mexico 49 (48) 39 (37)

Connecticut 47 (46) 38 (35) New York 32 (29) 23 (20)

Delaware 50 (49) 41 (40) North Carolina 39 (36) 32 (28)

DC 38 (39) 31 (29) North Dakota 49 (48) 43 (42)

Florida 43 (40) 34 (31) Ohio 41 (38) 34 (30)

Georgia 38 (37) 30 (28) Oklahoma 36 (34) 28 (26)

Hawaii 43 (41) 31 (28) Oregon 41 (42) 29 (29)

Idaho 43 (41) 30 (29) Pennsylvania 43 (41) 36 (34)

Illinois 44 (43) 35 (34) Rhode Island 52 (51) 40 (38)

Indiana 34 (31) 27 (24) South Carolina 41 (40) 34 (31)

Iowa 30 (28) 25 (22) South Dakota 48 (47) 39 (38)

Kansas 35 (33) 27 (26) Tennessee 43 (39) 34 (31)

Kentucky 34 (31) 27 (25) Texas 49 (50) 40 (38)

Louisiana 49 (48) 39 (38) Utah 28 (24) 22 (18)

Maine 31 (30) 23 (22) Vermont 41 (39) 36 (34)

Maryland 40 (38) 30 (27) Virginia 38 (37) 29 (28)

Massachusetts 49 (50) 38 (35) Washington 45 (44) 36 (34)

Michigan 38 (37) 30 (29) West Virginia 45 (43) 38 (36)

Minnesota 41 (41) 33 (33) Wisconsin 44 (43) 37 (36)

Mississippi 41 (40) 32 (30) Wyoming 32 (30) 28 (26)

Missouri 44 (44) 36 (33) U.S. Total 41 (40) 33 (31)

(values in parentheses represent estimates from the old imputation methodology)

(*Based on 2000 Annual Report (AR) File)
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 21

6. Conclusions

NHTSA is adopting the Multiple Imputation procedure for estimating missing BAC values for 

the significant analytical advantages it provides over the Discriminant Analysis. There is a 

discrepancy in the estimates between the two methods with the estimates from Multiple

Imputation providing estimates that are up to 2 percent higher than those provided by

Discriminant Analysis. The overall trend of alcohol involvement tracks very similarly for the 

estimates from both methods. The historical revision of estimates using Multiple Imputation up 

to 1982 will preserve the overall trend of alcohol involvement. The discrepancy between the two 

methods can be attributed to the fact that Multiple Imputation uses the logit model as compared 

to the linear discriminant model of the old method. Fundamental differences in the assumptions 

involved in the two methods can be one of the main reasons for the shift in estimates.

This underscores the importance of providing meaningful estimates of uncertainty (e.g. standard 

errors) for statistics related to BAC. The standard errors now available from Multiple Imputation 

will enable NCSA to provide measures of uncertainty. Also, the BAC values arrived at through 

Multiple Imputation can now be used as a factor in analytical models. 

7. Transitioning Schedule

NCSA will use the old method to report alcohol involvement for the 2001 Early Assessment.

NCSA will use Multiple Imputation to report alcohol involvement for the 2001 FARS Annual 

Report. 

The new estimates will be used in NCSA’s Annual Publications (Traffic Safety Facts, 

Fact Sheets etc.), as well as related Reports and Research Notes that use the 2001 FARS 

data. 

All historical series of alcohol involvement in these publications will be revised back to 

the 1982 data year to reflect the estimates from the new methodology.

The revised alcohol estimates for prior years will differ from the estimates that are in previously 

published reports for those years, the extent of which has been documented in this report.

NCSA will also make the new datasets available on its website to enable non-NCSA users to 

generate estimated alcohol involvement along various categories of interest. 

A web-interface to the new estimates is being implemented and should be online by the time the 

public-use datasets are released.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 22

8. References

1. De Wolf, V.A. (1988) Panel Meeting on the Imputation of Missing Data in FARS: Summary 

and Recommendations, National Highway Traffic Safety Administration, Department of

Transportation.

2. Huberty, C.J. and Wisenbaker, J.M. (1987) On Estimating Missing BAC Measures in the 1985 

FARS Data Set, National Highway Traffic Safety Administration, Department of Transportation.

3. Kalton G. (1988) Comments on Imputation for Missing Data in the Fatal Accident Reporting 

System, National Highway Traffic Safety Administration, Department of Transportation.

4. Klein, T.M., (1986) A Method for estimating Posterior BAC distributions for persons involved 

in fatal traffic accidents. Report DOT-HS-807-094, National Highway Traffic Safety

Administration, Department of Transportation.

5. Little, R. (1987) Imputation Methodology for the Fatal Accident Reporting System, National 

Highway Traffic Safety Administration, Department of Transportation.

6. Rubin, D.B. (1987) Multiple Imputation of Nonresponse in Surveys. J.Wiley and Sons, New 

York.

7. Rubin, D.B. (1987) Imputation of Missing Data in FARS: Suggestions and Comments on 

Papers and Presentations, National Highway Traffic Safety Administration, Department of 

Transportation.

8. Rubin,D.B, Shafer, J.L. and Subramanian, R. (1998) Multiple Imputation of Missing Blood 

Alcohol Concentration (BAC) values in FARS. Report DOT-HS-808-816, National Highway 

Traffic Safety Administration, Department of Transportation.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 23

Appendix A: FAQ on the Multiply-Imputed Datasets of Missing BAC in FARS

1. What is imputation?

A. Imputation is the practice of ‘filling in’ missing data with plausible values. It solves 

the missing-data problem at the beginning of the analysis.

2. Why impute Missing BAC in FARS?

A. On an average, approximately 60 percent of the BAC values are missing/unknown in 

FARS each year. Invalid inferences can be drawn on the level of alcohol

involvement for cases where the BAC is missing as the characteristics of the persons 

with unknown BACs can be significantly different from those with known BACs. In 

order to perform complete-data analysis of FARS data with respect to alcohol

involvement, the missing BACs need to be simulated (imputation!)

3. What is Multiple Imputation (MI)?

A. MI is a technique in which each missing value is replaced by m>1 simulated versions 

and these simulated complete datasets are analyzed by standard methods. These 

simulated values are actual values of BAC in the plausible range (.00<=BAC<=.94).

4. Why Multiple Imputation of BAC in FARS?

A. Multiple Imputation is the state-of-the-art technique to impute missing values. Each 

missing BAC value is replaced by ten simulated values of BAC using rigorous 

statistical techniques that consider the interaction of all the characteristics of the case. 

MI allows for the computation of Standard Errors and Confidence Intervals. 

5. Can MI estimates be used in analysis (regression etc.)?

A. Yes, the multiply-imputed values can be used in analysis. The regression coefficients 

will have to be averaged out over the ten imputed values of BAC.

6. How do I combine the results across the multiply imputed datasets?

A. The data analysis for the quantity of interest (e.g., Percent Alcohol Involvement for 

Drivers involved in Fatal Crashes), or Dinv , should be performed ten times, once for 

each of the ten imputed datasets, to obtain a single set of results.

From each analysis, suppose that D

j

inv is the percent of alcohol involvement for 

drivers involved from the jth imputed dataset. The overall estimate for drivers 

involved will be average of the individual estimate from the ten datasets.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 24

∑=

=

10

1

1

j

j

inv

Dinv

m D

7. Why not just impute once?

A. If the proportion of missing values is small, then single imputation may be quite 

reasonable. Without special corrective measures, single-imputation inference tends to 

overstate precision because it omits the between-imputation component of variability 

which is the error in estimating the missing value. When the fraction of missing 

information is small (say, less than 5%) then single-imputation inferences may be 

fairly accurate, which is not the case with FARS, where more than 50 percent of the 

BAC values are missing. For joint inferences about multiple variables, however, 

even small rates of missing information may seriously impair a single-imputation 

procedure.

8. Will the alcohol involvement estimates change from those of the previous method?

A. Yes, there will be minor differences between the estimates of alcohol involvement 

between the earlier method (Discriminant Analysis) and Multiple Imputation. The 

MI estimates are overall between 0 to 2 percent higher than the estimates from the old 

methodology. 

9. Why are there differences between the results from the two methods?

A. The imputation methodologies have different statistical models to estimate missing 

BAC values that could lead to the observed differences in the estimates. The old 

method computes probabilities of involvement along definite categories of BAC

while MI imputes actual values of BAC. 

10. Are there sample programs that analyze the multiply imputed datasets?

A. Yes, there are sample programs written in the SAS programming language that 

compute point-estimates and the standard errors which are documented in the

following section. Also, SAS® has released a trial version of PROC MIANALYZE® 

to analyze multiply-imputed datasets. This procedure should have packaged routines 

to generate descriptive statistics and point-estimates from the multiply-imputed 

datasets.
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 25

Appendix B: Sample SAS programs to analyze the Multiply-imputed Datasets in FARS

Example 1: Program to determine the extent of alcohol involvement in fatalities

(1) This section of code creates a dataset CRASHES which is a result of a merge between the crash 

level file for 1999 and the multiple imputation dataset (MIACC99). The dataset retains the ten 

imputations (A1 to A10) and FATALS which will be used later in the tabulation procedures. 

DATA CRASHES;

 MERGE FARS99.ACCIDENT (IN=A KEEP=ST_CASE FATALS) FARS99.MIACC99 (IN=B);

IF A AND B;

BY ST_CASE;

OUTPUT;

RUN;

(2) The first step in the next segment is the creation of CRASHBAC that has for every record 

fpc1..fpc10, spc1..spc10 and tpc1..tpc10. fpc is the indicator variable for the first 

category namely, BAC=0. Hence if the first imputation is equal to 0 then fpc1 is set to 1, or, if 

the first imputation is 8 then spc1 is set to 1, or, if the first imputation is equal to 15 then tpc1 is 

set to 1. The macro mi runs through each of the ten imputations and sets the value s of fpc&i, 

spc&i and tpc&i to 0 or 1 depending upon the value of the imputation. Note that the imputed 

values are scaled values of BAC by a factor of 100, i.e., 10 actually corresponds to a BAC value 

of .10.

data CRASHBAC;

set CRASHES;

%macro mi;;

%do i=1 %to 10;;

if A&i=0 then fpc&i=1;;

else fpc&i=0;;

if (1<=A&i<=9) then spc&i=1;; /* Use (1<=A&i<=7) for .08 Analyses */

else spc&i=0;;

if (A&i>=10) then tpc&i=1;; /* Use (A&i>=8) for .08 Analyses */

else tpc&i=0;;

%end;;

%mend mi;

%mi;

RUN;
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 26

(4) The next segment is the procedure means that computes the sum of fpc&i,spc&i and 

tpc&i and stores them in a dataset case&i for every imputation. Thus ten temporary datasets are 

created containing the sums fsbac&i, ssbac&i and tsbac&i.

%macro DO_MEANS;;

%do i=1 %to 10;;

proc means noprint data=crashbac;

var fpc&i spc&i tpc&i;

freq FATALS; /* WEIGH EACH CRASH BY NUMBER OF FATALITIES */

output out=case&i n=total sum=fsbac&i ssbac&i tsbac&i;

run;

%end;;

%mend DO_MEANS;

%DO_MEANS;

run;

(5) The next section of the code combines the ten datasets case1..case10 and computes the 

Multiple-imputation point estimate P for each interval of study. For example, pcnt0 is the P for 

the first interval of study, namely BAC=0.

data mi_est;

%macro AVG_EST;;

%do i=1 %to 10;;

set case&i;

sbac0=mean(fsbac1,fsbac2,fsbac3,fsbac4,fsbac5,fsbac6,fsbac7,fsbac8,fsbac9,fsb

ac10);

sbac1=mean(ssbac1,ssbac2,ssbac3,ssbac4,ssbac5,ssbac6,ssbac7,ssbac8,ssbac9,ssb

ac10);

sbac2=mean(tsbac1,tsbac2,tsbac3,tsbac4,tsbac5,tsbac6,tsbac7,tsbac8,tsbac9,tsb

ac10);

sbac3=sbac1+sbac2;

%end;;

%mend AVG_EST;

%AVG_EST;

run;
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 27

(6) The next section of code tabulates the alcohol involvement percentages across the three 

categories and prints them to the output.

PROC TABULATE DATA=MI_EST FORMAT=COMMA10.0 MISSING;;

VAR SBAC0 SBAC1 SBAC2 SBAC3 TOTAL;

TABLE (SBAC0='BAC=.00' SBAC1='BAC=.01-.09' SBAC2='BAC=.10+'

TOTAL='Total Fatalities'

SBAC3='Alcohol-Related Fatalities (0.01+)')*

(SUM PCTSUM<TOTAL>) / RTS=15;;

KEYLABEL N=' ' ALL='Total' SUM='Number' PCTSUM='Percent';;

TITLE1 'FATALITIES BY EXTENT OF ALCOHOL INVOLVEMENT';;

TITLE2 'FARS 1999';;

RUN;;
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 28

The TABULATE procedure outputs a Table as shown below.

FATALITIES BY EXTENT OF ALCOHOL INVOLVEMENT

 FARS 1999

BAC=.00 BAC=.01-.09 BAC=.10+ Total Fatalities Alcohol-Related Fatalities (0.01+)

Number Percent Number Percent Number Percent Number Percent Number Percent

25,145 60 3,391 8 13,181 32 41,717 100 16,572 40
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 National Center for Statistics and Analysis, 400 Seventh St., S.W., Washington, DC 20590 29

Appendix B: Sample SAS programs to analyze the Multiply-imputed Datasets in FARS

Example 2: Program to determine alcohol involvement for drivers involved in fatal crashes 

in FARS by the sex of the driver

(1) This section of code creates a dataset DRVINV which is a result of a merge between the person 

level file for 1999 and the multiple imputation dataset (MIPER99). The dataset retains the ten 

imputations (P1 to P10) and SEX which will be used later in the tabulation procedures. SEX is 1 

in the case of a male driver and 2 for a female driver and 9 when it is not known.

DATA DRVINV;

MERGE FARS99.PERSON (IN=A KEEP=ST_CASE VEH_NO PER_NO SEX PER_TYP) 

FARS99.MIPER99 (IN=B);

IF A AND B;

IF PER_TYP=1;

BY ST_CASE VEH_NO PER_NO;

OUTPUT;

RUN;

(2) The first step in the next segment is the creation of DRVBAC that has for every record 

fpc1..fpc10, spc1..spc10 and tpc1..tpc10. fpc is the indicator variable for the first 

category namely, BAC=0. Hence if the first imputation is equal to 0 then fpc1 is set to 1, or, if 

the the first imputation is 8 then spc1 is set to 1, or, if the first imputation is equal to 15 then 

tpc1 is set to 1. The macro mi runs through each of the ten imputations and sets the values of 

fpc&i, spc&i and tpc&i to 0 or 1 depending upon the value of the imputation. Note that the 

imputed values are scaled values of BAC by a factor of 100, i.e., 10 actually corresponds to a 

BAC value of .10.

data DRVBAC;

set DRVINV;

%macro mi;;

%do i=1 %to 10;;

if P&i=0 then fpc&i=1;;

else fpc&i=0;;

if (1<=P&i<=9) then spc&i=1;; /* Use (1<=P&i<=7) for .08 Analyses */

else spc&i=0;;

if (P&i>=10) then tpc&i=1;; /* Use (P&i>=8) for .08 Analyses */

else tpc&i=0;;

%end;;

%mend mi;

%mi;

RUN;
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30

(4) The next segment is the procedure means that computes the sum of fpc&i,spc&i and 

tpc&i and stores them in a dataset case&i for every imputation. Thus ten temporary datasets are 

created containing the sums fsbac&i, ssbac&i and tsbac&i. The dataset drvbac should first 

be sorted by sex.

proc sort data=drvbac;

by SEX;

run;

%macro DO_MEANS;;

%do i=1 %to 10;;

proc means noprint data=drvbac;

var fpc&i spc&i tpc&i;

by SEX;

output out=case&i n=total sum=fsbac&i ssbac&i tsbac&i;

run;

%end;;

%mend DO_MEANS;

%DO_MEANS;

run;

(5) The next section of the code combines the ten datasets case1..case10 and computes the 

Multiple-imputation point estimate P for each interval of study. For example, pcnt0 is the P for 

the first interval of study, namely BAC=0.

data mi_est;

%macro AVG_EST;;

%do i=1 %to 10;;

set case&i;

sbac0=mean(fsbac1,fsbac2,fsbac3,fsbac4,fsbac5,fsbac6,fsbac7,fsbac8,fsbac9,fsb

ac10);

sbac1=mean(ssbac1,ssbac2,ssbac3,ssbac4,ssbac5,ssbac6,ssbac7,ssbac8,ssbac9,ssb

ac10);

sbac2=mean(tsbac1,tsbac2,tsbac3,tsbac4,tsbac5,tsbac6,tsbac7,tsbac8,tsbac9,tsb

ac10);

sbac3=sbac1+sbac2;

%end;;

%mend AVG_EST;

%AVG_EST;

run;
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31

(6) The next section of code tabulates the alcohol involvement percentages across the three 

categories and prints them to the output.

PROC TABULATE DATA=MI_EST FORMAT=COMMA10.0 MISSING;;

WHERE SEX IN (1,,2,,9);

CLASS SEX;

VAR SBAC0 SBAC1 SBAC2 SBAC3 TOTAL;

TABLE SEX='Sex' ALL, (SBAC0='BAC=.00' SBAC1='BAC=.01-.09' SBAC2='BAC=.10+'

TOTAL='Total Drivers Involved'

SBAC3='Total Drivers w/Alcohol')*

(SUM PCTSUM<TOTAL>) / RTS=15;;

KEYLABEL N=' ' ALL='Total' SUM='Number' PCTSUM='Percent';;

TITLE1 'DRIVERS INVOLVED IN FATAL CRASHES, BY SEX';;

TITLE2 'FARS 1999';;

RUN;;
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32

The routines tabulate an output as seen in Exhibit 3. 

DRIVERS INVOLVED IN FATAL CRASHES, BY SEX

 FARS 1999

BAC=.00 BAC=.01-.09 BAC=.10+ Total Drivers Involved Total Drivers w/Alcohol

Number Percent Number Percent Number Percent Number Percent Number Percent

Sex

Male 29,614 72 2,617 6 8,782 21 41,012 100 11,399 28

Female 12,720 86 528 4 1,588 11 14,835 100 2,116 14

Unknown 525 80 29 4 100 15 655 100 130 20

Total 42,858 76 3,174 6 10,470 19 56,502 100 13,644 24
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33

Appendix B: Sample SAS programs to analyze the Multiply-imputed Datasets in FARS

Example 3: Program to determine 95% Confidence Interval and Standard Error of

Estimate for the estimated Alcohol Involvement in Fatal Crashes

(1) Assign crash-level BAC into relevant categories. Of interest are the confidence intervals and 

standard error associated with the estimated alcohol involvement in fatal crashes, i.e., crashes 

where the crash BAC was 0.01 or greater.

DATA FIRST;

SET FARS&YR..ACC&YR;

%MACRO CATEGORIZE;

%DO I=1 %TO 10;

IF A&I=0 THEN FPC&I=1; /*(BAC = 0.00) */

ELSE FPC&I=0;

IF (1<=A&I<=9) THEN SPC&I=1; /*(0.01<=BAC<=0.09) */

ELSE SPC&I=0;

IF (A&I>=10) THEN TPC&I=1; /*(BAC>=0.10) */

ELSE TPC&I=0;

IF (A&I>=1) THEN ZPC&I=1;

ELSE ZPC&I=0;

%END;

%MEND CATEGORIZE;

%CATEGORIZE;

RUN;

(2) This part of the code computes the proportions for each imputation. Of interest is ZS_PP, 

which if the proportion of crashes for which the crash BAC is 0.01+.

%MACRO STATS;

%DO I=1 %TO 10;

PROC MEANS NOPRINT DATA=NULL1;

VAR FPC&I SPC&I TPC&I ZPC&I;

OUTPUT OUT=CASE&I N=TOTAL SUM=FSBAC&I SSBAC&I TSBAC&I ZSBAC&I 

MEAN=FS_PP&I SS_PP&I TS_PP&I ZS_PP&I;

RUN;

%END;

%MEND STATS;

%STATS;
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34

DATA CALC3; /* calculate variances for each imputation */

%MACRO VARIANCE;

%DO I=1 %TO 10;

SET CASE&I;

FS_VA&I=FS_PP&I*(1-FS_PP&I)/TOTAL;

SS_VA&I=SS_PP&I*(1-SS_PP&I)/TOTAL;

TS_VA&I=TS_PP&I*(1-TS_PP&I)/TOTAL;

ZS_VA&I=ZS_PP&I*(1-ZS_PP&I)/TOTAL;

%END;

%MEND VARIANCE;

%VARIANCE;

RUN;

(3) This section computes the parameters needed to evaluate the total variance of the estimates 

for the .01+ category. The variance estimate associated with the estimate has two components. 

The within-imputation variance is the average of the complete-data variance estimates,

∑=

=

10

1

( )

10

1

t

t U U (1)

and the between-imputation variance is the variance of the complete-data point estimates,

∑=

= −

10

1

( ) 2

)

ˆ

(

9

1

t

t

B Q Q (2)

The total-variance is defined as

T U (1 m )B

−1

= + + (3)

where m is the number of imputations.

DATA P (KEEP=ZS_PP1-ZS_PP10 ); /*KEEPS THE TEN PROPORTIONS TO ESTIMATE TO */

SET CALC3; /* ESTIMATE ‘B’ IN (2) */

RUN;

PROC TRANSPOSE DATA=P OUT=PBAR;

RUN;

PROC MEANS DATA=PBAR noprint; /*ESTIMATES ‘B’ AS IN (2) */

VAR COL1;

OUTPUT OUT=PBAR_B MEAN=PBAR VAR=B;

RUN;
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35

DATA U (KEEP=ZS_VA1-ZS_VA10 ); /*KEEPS THE TEN VARIANCES TO ESTIMATE */

SET CALC3; /* ESTIMATE U IN (1) */

RUN;

PROC TRANSPOSE DATA=U OUT=UBAR;

RUN;

PROC MEANS DATA=UBAR noprint; /*COMPUTES THE AVERAGE OF THE VARIANCES TO */

VAR COL1; /*DERIVE U AS IN (1)

OUTPUT OUT=UBAR MEAN=UBAR;

RUN;

(4) This section combines the results according to Rubin (1987) to determine the total-variance 

and the 95% confidence intervals.

DATA STATS;

MERGE PBAR_B UBAR;

RUN;

The inferences are based on the approximation

T Q Q tn( ) ~

1/ 2

−

−

(4)

where the degrees of freedom < are given by

]

(1 1)

[1

2

( 1)

m B

U

m

+ −

n = − + (5)

Thus a 100(1-")% interval estimate for the estimate is given by 

Q ± tn ,1−a / 2 T (6)

The t distribution is evaluated in the code below using the TINV function whose arguments are <

(NU) and 1-"/2 (1-.05/2 = 1-.025 = .975). The total variance TM is computed as in (1). The 

lower and upper bounds of the 95% confidence intervals are evaluated in LOW and HIGH, 

respectively in the code below.
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36

DATA STATS;

SET STATS;

TM=UBAR+(1.1)*B; /* T=U+(1+1/m)*B */

RM=(1.1)*B/UBAR;

NU=9*(1+(1/RM))**2;

LOW=PBAR-TINV(.975,NU)*SQRT(TM);

HIGH=PBAR+TINV(.975,NU)*SQRT(TM);

RUN;

PROC TABULATE DATA=ALLSTATS out=test;

VAR LOW PBAR HIGH SE;

TABLE (LOW*F=5.4 PBAR='Estimate'*F=5.4 HIGH*F=5.4 SE='Std. Error'*f=10.8);

TITLE1 ‘95% CONFIDENCE INTERVALS AND STANDARD ERROR OF ESTIMATE’;

TITLE2 ‘ESTIMATE OF ALCOHOL RELATED CRASHES, FARS 1999’;

RUN;

95% CONFIDENCE INTERVALS AND STANDARD ERROR OF ESTIMATE

ESTIMATE OF ALCOHOL RELATED CRASHES, FARS 1999

LOW Estimate HIGH Std. Error

Sum Sum Sum Sum

.3922 .3977 .4032 0.00278626

LOW and HIGH are the lower and upper bounds of the 95 percent Confidence Interval 

associated with the estimate. The estimated proportion of crashes that are alcohol-related is .398 

or 39.8%. The Standard error of estimate is 0.002786 or 0.2786%.