Accid, Anal. & Pm. Vol. 24, No. 6, pp. 643-653, Printed in Great Britain.

CWI1-4575/92 $5.00 + .OO Q I992 Pergamon Pcss Ltd.

1992

THE INFLUENCE OF SAFETY BELT LAWS ON SELFREPORTED SAFETY BELT USE IN THE UNITED STATES LUISG. ESCOBEDO, TERENCEL. CHORBA Centers for Disease Control, 1600 Clifton Road, Atlanta, GA, 30333, U.S.A. PATRICK L. REMINGTON Bureau of Community Health and Prevention, Wisconsin Department of Health and Social Services, Box 309, Madison, WI, 53701, U.S.A.

ROBERT F. ANDA, LEE SANDERSON, and AKBARA. ZAIDI Centers for Disease Control, 1600 Clifton Road, Atlanta, GA, 30333, U.S.A. (Received9 August 1991; in revisedform 10 December 1991) Abstract-We

assessed rates and trends in safety belt use by presence and type of safety belt law using data from states participating in the 1984-1989 Behavioral Risk Factor Surveillance System. State(s) with a safety belt law allowing law enforcement officers to stop vehicles for occupants’ failure to use safety belts (primary enforcement law) had greater and more rapid increases in safety belt use rates than did states with laws requiring that vehicles must first he stopped for some other violation before a citation or fine for occupants’ failure to use safety belts could he imposed (secondary enforcement law). Larger and sustained increases in safety belt use occurred when safety belt laws hecame effective or when fines were imposed for violations than when laws were first enacted. These data suggest that primary enforcement laws result in greater and more rapid increases in safety belt use than do secondary enforcement laws, and that initial increases in safety belt use following implementation of laws are sustained.

INTRODUCTION

In the United States, motor vehicle crashes are a major cause of morbidity, disability, and death (National Center for Health Statistics 1989; Rice et al. 1989). Safety belt use (and safety belt laws) can reduce crash-related injury, death, disability, and medical care expenditures (Hartunian, Smart, and Thomson 1980; Evans 1986; Partyka 1988; Orsay et al. 1988). Lap/shoulder belts reduce the risk of death by an estimated 4 1%to 47% in frontal crashes (Evans 1986; Partyka 1988), by 26% in side-impact crashes (Partyka 1988),by 35% in rear-impact crashes (Partyka 1988), and by 69% to 76% in rollover crashes (Evans 1986; Partyka 1988). Overall, lap/shoulder safety belts reduce the risk of serious injury by 40% to 70% overall in motor vehicle crashes (SAE 1984). As of July 1991, 40 of the 50 states, the District of Columbia, and Puerto Rico had safety belt use laws. In only 9 of the 40 states with safety belt laws could law enforcement officers stop vehicles for occupants’ failure to use safety belts (primary enforcement laws); in the other 3 1, a vehicle would first have to be stopped for some other traffic violation before a citation or fine for occupants’ failure to use safety belts could be imposed (secondary enforcement laws). Although population-based surveys have indicated that safety belt use varies widely from state to state (Anda et al. 1990), the contribution of safety belt laws to this variation has not been well described. Therefore, we sought to assess the relationship of the presence and type of safety belt laws to safety belt use over time at the state level. To do this, we analyzed data from states that participated in the Behavioral Risk Factor Surveillance System (BRFSS) from 1984 to 1989. METHODS

BRFSS survey design To assess rates and trends in self-reported safety belt use in relation to safety belt laws, we used data from the BRFSS from 1984 to 1989. The objective of this system is to deter643

644

L. G. ESCOBEDO et al.

mine the prevalence of behavioral risks in adult populations in each state that are associated with the leading causes of death and morbidity. The number of states participating in these surveys has increased from 15 in 1984 (when monthly surveys were initiated) to 39 (and the District of Columbia) in 1989. Operation of this system is performed jointly by participating state health departments and the Centers for Disease Control. Details of these surveys’ sample design, plan of operation, selection process, and data collection have been published elsewhere (Marks, Hogelin, and Gentry et al. 1985; Remington et al. 1988). Briefly, respondents for these surveys are selected by using a probability sample of adult residents with telephones in each state. Telephone numbers are randomly selected using a three-stage cluster design based on the Waksberg method (Waksberg 1978). A trained interviewer reaches a representative household, randomly selects one adult aged 18 years or older and administers a standard questionnaire. Interviews last approximately lo- 15 minutes. Of contacts made with eligible respondents, the median annual response rates for 1984 to 1989 ranged from 83% to 85%. Interviews are conducted monthly during a specified 7- to lo-day interview period. In each state, interviews are conducted during the same period, and the number of interviews conducted each month are approximately the same. Each respondent is asked about safety belt use: “How often do you use seatbelts when you drive or ride in a car? Would you say: always, nearly always, sometimes, seldom, or never?’ For this analysis, safety belt use was defined as “always” using “seatbelts.” Cross-sectional analysis

To describe the cross-sectional relationship between safety belt use and the presence and type of safety belt law (none, secondary, or primary), we calculated state-specific safety belt use rates for the District of Columbia and 37 states that participated in the 1989 Behavioral Risk Factor Surveillance System (North Dakota and South Carolina were excluded from this analysis, since their safety belt laws were enacted during 1989). For this analysis, a total of 59,856 respondents was included. We excluded 3,539 respondents who were Asian, Native American, or “other races”-because their population distributions for the 1980 census were not available by sex and educational attainment for purposes of standardization of safety belt use rates-or who had missing information regarding safety belt use or educational attainment. To calculate safety belt use rates representative of the population of each of the 37 states and the District of Columbia, we used SESUDAAN, a procedure for analyzing complex sample survey data (Shah 1981). To compare safety belt use between states, we standardized the safety belt use rates to the 1980 U.S. Census distribution of age, race, sex, and educational attainment (Shah 198 1; Rothman 1986). Because safety belt use rates by state were not normally distributed, we used the Wilcoxon Rank Sum test to determine whether the distribution of safety belt use rates varied by level of enforcement allowed (Colton 1974). Trend analysis

For this analysis, we included 136,166 persons interviewed in fifteen states that collected data continuously from 1984 to 1989. We excluded 1,964 ( 1.4%)persons with missing information regarding safety belt use or educational attainment and 3,773 (2.8%) who were Asian, Native American, or from “other races.” Thus, we included responses from 130,429 persons for trend analyses. First, to assess the overall trend in safety belt use by presence and type of safety belt law (none, secondary, or primary), we aggregated data from the 15 states (3 had no safety belt laws, 11 had enacted a secondary enforcement law, and 1 had a primary enforcement law) included for the trend analysis. We then calculated monthly and period (1984- 1985, 1986, and 1987-1989) safety belt use rates by presence and type of safety belt law based on calendar dates of interview. We used SESUDAAN to calculate rates, standard errors, and 95% confidence intervals for each period (Shah 1981). Second, to assess changes in safety belt use rates before or after secondary enforcement laws became effective, it was necessary to shift calendar dates of respondent inter-

645

Influence of safety belt laws

views relative to dates before or after secondary enforcement laws became effective (since the 11 states that enacted secondary enforcement laws did so at different times). With this procedure, dates when each of the 11 secondary enforcement laws became effective were used to define an arbitrary central date for all states (a “time zero”) and dates before or after each of the eleven secondary enforcement laws became effective were “transposed” to dates before or after this central date. Because the magnitude of this shift was based on the time interval from the date when the law became effective to the central date, South Carolina contributed 66 months (from January 1984 to July 1989 the month when the law became effective) and Illinois contributed 53 months (from July 1985 when the law became effective to December 1989) for a total of 120 transposed data points (one additonal point for the month when laws became effective). We then aggregated data from these 11 states to calculate “transposed” monthly and period (prelaw and postlaw) safety belt use rates. We used SESUDAAN to calculate rates, standard errors, and 95% confidence intervals for each period (Shah 1981).

Table I. Percentage annual self-reported safety belt use in selected states, by mandatory safety belt use laws-BRFSS, United States, 1989 Safety belt use ( + 95% cI)* State?

Sample size*

Crude

Hawaii North Carolina Texas New Mexico New York Connecticut Iowa Washington Virginia California Maryland District of co Michigan Florida Tennessee Ohio Georgia Missouri Oklahoma Minnesota Illinois Indiana Pennsylvania Wisconsin Montana Idaho Utah Arizona Rhode Island Oregon Maine Kentucky Alabama New Hampshire West Virginia Massachusetts Nebraska South Dakota

147 1708 1415 1106 1197 1299 1262 1442 1371 1961 1631 1399 2280 1632 2337 1395 1573 1464 1114 3336 1690 2132 1767 1242 1140 1690 1734 1400 1718 1625 1231 1756 1768 1330 1692 1178 1391 1703

85 (2) 70 (3) 67 (3) 66 (3) 65 (3) 62 (3) 52 (3) 68 (3) 68 (3) 67 (2) 67 (3) 59 (30) 62 (2) 64 (3) 54 (2) 54 (3) 53 (3) 51 (3) 50 (3) 54 (2) 50 (3) 47 (2) 48 (3) 50 (3) 43 (3) 42 (3) 39 (3) 47 (3) 42 (3) 44 (3) 39 (3) 36 (3) 33 (2) 37 (3) 32 (3) 36 (3) 26 (2) 18 (2)

Standardized5 85 (3) 70 (3) 65 (3) 64 (3) 62 (4) 58 (3) 50 (3) 65 (3) 65 (3) 63 (3) 63 (3) 61 (6) 60 (2) 60 (3) 53 (2) 51 (3) 50 (3) 49 (3) 49 (3) 48 (2) 47 (3) 46 (2) 46 (3) 45 (3) 39 (3) 39 (3) 37 (3) 44 (4) 38 (3) 38 (3) 36 (3) 35 (3) 32 (3) 31 (3) 31 (3) 31 (3) 24 (3) 17 (2)

Type of safety belt law Primary Primary Primary Primary Primary Primary Primary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary Secondary None None None None None None None None None None None

*95% confidence interval. tRanked by presence and type of safety belt law and in descending order of standardized rates. @ample size for standardized rates. #Standardized for the distribution of age, race, sex, and educational attainment of the 1980 U.S. population.

L. G. ESCOBEDOet al.

646

Third, for the 12 states that had enacted laws, we developed time series models for each state to test the significance of changes in safety belt use during the period before laws became effective in each state (See Appendix). These time series models were necessary to develop “intervention” models to assess the statistical significance of changes in safety belt use at the state level after (i) laws were enacted, (ii) laws became effective, (iii) fines were imposed, or (iv) the simultaneous occurrence of two or all interventions. All models were created using exponentially weighted moving average (EWMA) methods (See Appendix), (Box and Jenkins 1970). RESULTS The 1989 self-reported safety belt use rates varied considerably from state to state; these rates ranged from 17% in South Dakota to 85% in Hawaii (Table 1). States with primary enforcement laws had significantly higher use rates than states with secondary enforcement laws, and states with secondary enforcement laws had significantly higher use rates than states without safety belt laws (Fig. 1) (r, < 0.01 in both instances; Wilcoxon rank sum test). Figure 2 shows that North Carolina (the only state participating in the surveys since 1984 that enacted a primary enforcement law) had the greatest increase in safety belt use, followed by states that had enacted secondary enforcement laws and states without safety belt laws. Between January 1984 and December 1989, increase in safety belt use was approximately 20 percentage points in states without safety belt laws (from approximately 20% to 40%), 35 percentage points in states with secondary enforcement laws (from approximately 20% to 55%) and 50 percentage points in North Carolina (from approximately 20% to 70%). In North Carolina, safety belt use increased from 21% to 52% the month after the law became effective. A second increase in safety belt use (from 43% in December 1986 to 73% in January 1987) occurred in North Carolina when the state imposed a $25 fine for violations. Increases in safety belt use occurred in states with secondary enforcement laws during the time when these laws became effective.

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Range- 37-65

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0

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Type of Safety Belt Law Fig. I. Safety belt use in 37 states and the District of Columbia by presence and type of safety belt law, 1989 Behavioral Risk Factor Surveillance System.

Influence of safety belt laws

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Table 2. Safety belt use in 15 states aggregated by period and presence and type of safety belt law, 1984- 1989 BRPSS. Percent safety belt use* (95% CIt) Enforcement allowed

1984-1985

1986

1987-1989

Primary Secondary None

21(19-23) 22 (21-23) 2 1(20-22)

45 (42-48) 40 (39-42) 29 (27-3 I)

70 (68-7 1) 49 (48-50) 35 (34-37)

*Standardized for the distribution of age, race, sex, and educational attainment of the 1980 U.S. population. t95% confidence interval.

When we examined safety belt use rates by presence and type of safety belt law in three distinct periods, we found significant increases in safety belt use from the approximately prelaw period (1984-1985) through an intermediate period (1986) to a later period in 1987- 1989 (when many safety belt laws had become effective or were being implemented) for all three groups of states (Table 2). During 1987- 1989, safety belt use rates were substantially greater for the state with a primary enforcement law (North Carolina) than states with secondary enforcement laws, which in turn were greater than states without safety belt laws. Examination of safety belt use rates based on dates transposed before or after secondary belt laws became effective (an arbitrary date for all states rather than unique calendar dates for each state) showed that after secondary enforcement laws became effective, safety belt use increased dramatically (Fig. 3). Overall, from several months before secondary enforcement laws became effective to several months after, safety belt use increased approximately 30 percentage points (from approximately 25% to 55%). Table 3 shows results of the intervention models. In North Carolina, safety belt use increased 6 percentage points after the law was enacted, 25 percentage points after the law became effective, and another 23 percentage points after the fine was imposed. For states with secondary enforcement laws, total increases in safety belt use ranged from slight increases at the time of interventions in Utah (which were not statistically significant) to a 25 percentage point increase after interventions occurred simultaneously in Wisconsin. Overall, intervention models showed substantially greater increases in safety belt use when safety belt laws first became effective, or when fines were first imposed for violations, or both, than when safety belt laws were enacted alone. DISCUSSION

To improve safety belt use rates and occupant protection, many nations and states have enacted laws requiring vehicle occupants to wear safety belts. Multiple studies have found that safety belt laws have resulted in increases in safety belt use and reductions in crash-related injury and death (Campbell, Stewart, and Campbell 1986; Wagenaar and Wiviott 1986; Williams and Lund 1986; Latimer and Lave 1987; Lund, Pollner, and Williams 1987; Williams et al. 1987a; Williams, Wells, and Lund 1987b; Chorba, Reinfurt, and Hulka 1988; Reinfurt et al. 1988; Streff, Wagenaar and Schultz 1990; Reinfurt et al. 1990; States et al. 1990; Wagenaar and Margolis 1990; Lestina et al. 199l), especially in jurisdictions with primary enforcement laws (Campbell 1988; Campbell and Campbell 1988; Wagenaar, Maybee, and Sullivan 1988; Williams and Lund 1988; Tipton, Camp, and Hsu 1990; Evans and Graham 1991). These increases reportedly have been considerably higher in several other countries than in most U.S. jurisdictions (Campbell and Campbell 1986; Hedlund 1990). However, BRFSS provides new information with respect to changes in safety belt use in response to legislation in the United States. This system is the one source of state-based safety belt use data gathered uniformly, continuously, and with a survey methodology that permits reliable comparisons of changes in safety belt use after laws were or were not enacted in a large number of states.

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Aggregate safety @It use in 11 states.with

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secondary laws, with dates of interview in relation to before or after laws became effktive, 1984-1989 Behavioral Risk Factor Surveillance SystetII.

MonthsBefore or After SecondaryLaws Became Eiffective

-1

t

-66 -61 -56 -51 -46 -41 -36 -31 -26 -21 -16 -11 -6

I

54 (!M-55)

I

1

_ Postlaw Paiod

Percent Belt Use (95% confudeace Wmml) Pfelaw Period 25 (24-25)

I

Fig.3.

0

20

40

60

80

100

L. G. ESCOBED~et al.

650

Table 3. Increase in safety belt use after safety belt law intervention(s) for states hased on time series intervention models, BRFSS, United States, 1984-89. Percent belt use increase (SE*) State Primary Law North Carolina Secondary Law California Idaho Illinois Indiana Minnesota Montana Ohio S. Carolina Tennessee Utah Wisconsin

Law enacted

6 (3)$

Law effective

Fine imposed

25 (3)$

23 (3)$

9 (3)$

22 (3)$ 10 (4)* 26 (3)$ 23 (4)$

11(4)$ 2 (3) 5 (3)

11cm

10cm

6 (3)$ 7 (4)

13 (9)$ 15 (6)$

11(4)$

6 (6)

none 15 (3)$ 4 (3)

6 (6)

Simultaneouslyt

15 (I)$ 5 (4) 8 (4)$ 15 (3)$ 25 (4)$

*Standard error. tInstances in which the dates the laws were enacted, became effective, or fines were imposed for violations occurred simultaneously. $P 4 0.05 relative to the prelaw safety belt use rates.

The greatest and most rapid increases in safety belt use rates were in state(s) with primary enforcement laws. Although these increases cannot be attributed solely to having a primary enforcement law, increases in safety belt use when the primary enforcement law in North Carolina was implemented suggest that primary laws, in addition to enforcement (Campbell 1988) and publicity (Williams et al. 1987a), have an important role in increasing safety belt use. The economic costs in implementing safety belt laws are minimal (Chorba and Vinicor 1990), and are considerably less than those that have been spent on less effective educational strategies aimed at increasing safety belt use (Robertson et al., 1974). Safety belt use increased in all states regardless of presence of safety belt laws, suggesting increased general acceptance of safety belt use. However, a large sustained increase in safety belt use was augmented when laws became effective and again when fines were imposed for violations, resulting in even greater overall increases for states with safety belt laws. In the United States, it has been estimated that from 1984 through 1989, more than 14,000 lives were saved as a result of enactment of safety belt laws (National Center for Statistics and Analysis 1990). To further the effectiveness of safety belt laws, the factors that are associated with increased belt use after enactment of safety belt laws need to be investigated. Examples of such factors include level of enforcement (Campbell 1988), magnitude of penalties for violations, publicity associated with safety belt laws (Williams et al. 1987a), and negligence considerations in mitigating damages associated with noncompliance with safety belt laws in different jurisdictions (Gallub 1986; Bohan and Teret 1990). Though the Behavioral Risk Factor Surveillance System provides information on safety belt use by time, place, and personal characteristics that is unavailable from observational surveys (Goldbaum et al. 1986; Anda et al. 1990; Escobedo et al. 199 l), selfreports of safety belt use exceed observed safety belt use (Chorba et al. 1988; Streff and Wagenaar 1989). However, in past analyses, self-reports of “always” using safety belts have exceeded observed rates by about 8% (Streff and Wagenaar 1989; Centers for Disease Control 1987), suggesting generally good agreement between self-reported and observed safety belt use. Moreover, overreporting of safety belt use has been similar in jurisdictions with and without safety belt laws (Streff and Wagenaar 1989). Thus, respondents’ desire to appear compliant with safety belt laws is unlikely to explain the observed increases in safety belt use after implementation of safety belt laws. Despite the increasing availability of cars with automatic restraints, universal use of safety belts is desirable. Many people will continue to drive cars from model years lacking

Influence of safety belt laws

651

automatic restraints, and many cars with automatic shoulder belts have manual lap belt components. Because airbags are designed to deploy only in frontal, or near frontal, crashes and tend not to influence the risk of ejection (Evans 199l), the use of a safety belt generally provides greater overall crash protection than does the presence of an airbag (Williams and Lund 1986). Therefore, these data suggest that strengthening current safety belt laws and enacting new ones remain important approaches to reducing the burden of crash-related injury and death. Acknowledgements-We

acknowledge the collaboration of ah state BRFSS coordinators who have contributed greatly to the usefulness ofthis System. We also acknowledge the assistance and encouragement ofJohn Eberhard and Robert Schweitz of the Office of Driver and Pedestrian Research, National Highway Traffic Safety Administration. Finally, we thank James A. Mercy, Adele L. Franks, and Audrey L. Pinto, of the Centers for Disease Control, and John D. States, of the University of Rochester, for their valuable comments in the preparation of this manuscript. REFERENCES Anda, R. F. et al. Behavioral Risk Factor Surveillance System (BRFSS), 1988. SS-2, Surveillance Summary Series. MMWR 39:1-21; 1990. Bohan BF, Teret SP. Seat belts and the law: Mandatory use laws and the legal consequences of non-use. Washington, DC: National Highway Traffic Safety Administration; Department of Transportation publication no. HS 807-576, 1990. Box, G. E. P.; Jenkins, G. M. Time series analysis: Forecasting and control. San Francisco: Holden-Day Inc; 1970. Campbell, B. J. The association between enforcement and seat belt use. J. Safety Res. 19: 159-163; 1988. Campbell, B. J.; Campbell, F. A. Seat belt experience in four foreign countries compared to the United States. Chapel Hill: University of North Carolina Highway Safety Research Center; December 1986. Campbell, B. J.; Campbell, F. A. Injury reduction and belt use associated with occupant restraint laws. In: Graham, J. D., editor. Preventing automobile injury. Dover: Auburn House Publishing Company; 1988:24-50. Campbell, B. J.; Stewart, J. R.; Campbell, F. A. Early results ofseat belt legislation in the United SatesofAmerica. Publication no. PR 123. Chapel Hill, NC: University of North Carolina Highway Safety Research Center, July 1986. Centers for Disease Control. Comparison of observed and self-reported seat belt use rates-United States. MMWR 37:549-551; 1987. Chorba, T. L.; Reinfurt, D.; Hulka, B. S. Efficacy of mandatory seat-belt use legislation: The North Carolina experience from 1983 through 1987. JAMA 260:3593-3597; 1988. Chorba, T.; Vinicor, F. Enactment of mandatory seatbelt-use legislation: An analysis of the political process in North Carolina. N. C. Med. J. 5 I :599-607; 1990. Colton, T. Statistics in medicine. Boston: Little Brown & Company; 1974:2 19-227. Escobedo, L. G.; Chorba, T. L.; Remington, P. L.; An&, R. F.; Sanderson, L.; Zaidi, A. A. State laws and the use ofcar safety seat belts. N. Engl. J. Med. 325:1586-1587; 1991. Evans, L. The effectiveness of seat belts in preventing fatalities. Accid. Anal. Prev. 18:229-241; 1986. Evans, L. Traffic safety and the driver. New York: Van Nostrand Reinhold; 199 I:2 19-250. Evans, W. N.; Graham, J. D. Risk reduction or risk compensation? The case of mandatory safety-belt use. Journal of Risk and Uncertainty 4:6 l-73; 1991. Gallub, M. B. A compromise between mitigation and comparative fault: A critical assessment of the seat belt controversy and a proposal for reform. Hofstra Law Review 14:3 19-55; 1986. Goldbaum, G. M.; Remington, P. L.; Powell, K. E.; Hogelin, G. C.; Gentry, E. M. Failure to use seat belts in the United States. JAMA 255:2459-2462; 1986. Hartunian, N. S.; Smart, C. N.; Thompson, M. S. The incidence and economic costs of cancer, motor vehicle injuries, coronary heart disease, and stroke: A comparative analysis. Am. J. Public Health 70: 1249-1260; 1980. Hedlund, J. Casualty reductions resulting from safety belt use laws. In: Effectiveness of safety belt use laws: A multinational examination. Department of Transportation publication no. HS 807-018. Washington, DC: National Traffic Safety Administration; October 1990. Latimer, E. A.; Lave, L. B. Initial effects ofthe New York State auto safety belt law. Am. J. Public Health 77: I83186; 1987. Lestina, D. C.; Williams, A. F.; Lund, A.D.; Zador, P.; Kuhlmann, T. P. Motor vehicle crash injury pattemsand theVirginiaSeat Belt Law. JAMA 265:1409-1413; 1991. Lund, A. K.; Pollner, J.; Williams, A. F. Preliminary estimates of the effects of mandatory seat belt use laws. Accid. Anal. Prev. 19:219-223; 1987. Marks, J. S.; Hogelin, G. C.; Gentry, E. M. et al. The Behavioral Risk Factor Surveys: I. State-specific prevalence estimates of behavioral risk factors. Am. J. Prev. Med. 1: 1-8; 1985. National Center for Health Statistics. Health, United States, 1990. DHHS publication no. PHS 9 I - 1232. Hyattsville, MD: National Center for Health Statistics 1990. National Center for Statistics and Analysis. 1989 traffic fatality facts. Washington, DC National Highway Traffic Safety Administration; October 1990. Orsay, E. M.; Turnbull, T. L.; Dunne, M.; Barrett, J. A,; Lange&erg, P.; Orsay, C. P. Prospective study of the effect of safety belts on morbidity and health care costs in motor-vehicle accidents. JAMA 260:3598-3603; 1988.

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Partyka, S. C. Papers on adult seat belts-effectiveness and use. Department of Transportation publication no. HS 807-286. Washington, DC National Highway TratIic Safety Administration; 1988. Reinfurt, D. W.; Campbell, B. J.; Stewart, J. R.; Stutts, J. C. North Carolina’s occupant restraint law: A three vear evahtation. Publication no. PR 158 Chaoel Hilk Universitv of North Carolina Hiiwav Safetv Research VI. kenter; October 1988. Reinfurt, D. W.; Campbell, B. J.; Stewart, J. R.; Stutts, J. C. Evaluating the North Carolina safety belt wearing law. Accid. Anal. Prev. 22:197-210; 1990. Remington, P. L.; Smith, M. Y.; Williamson, D. F.; Anda, R. F.; Gentry, E. M.; Hogelin, G. C. Des&n, characteristics, and usefulness of state-based Behavioral Risk Factor Surveillance: 1981-87. Public Health Rep. 103:366-375; 1988. Rice, D. P.; MacKenzie, E. J.; and associates. Cost of injury in the United States: a report to Congress. San Francisco: Institute for Health and Aging, University of California, and Injury Prevention Center, The Johns Hop kins University, 1989. Robertson, L. S.; -Kelley, A. B.; O’Neill, B.; Wixom, C. W.; Eiswirth, R. S.; Haddon, W. A controlled study of the effect of television messaaes on satetv belt use. Am. J. Public Health 64: 107 l- 1080: 1974. Rothman, K. J. Modern epideAology. Boston/Toronto: Little Brown & Company; 1986:41-49. SAE. Advances in belt restraint systems: Design, performance, and usage. Special publication SP- 14 I. Warrendale, PA: SAE; 1984. Shah, B. U. SESUDAAN: Standard errors program for imputing of standardized rates from sample survey data. Research Triangle Park, NC: Research Triangle Institute; 198 1. States, 3. D.; Annechiarico, R. P.; Good, R. G.; Lieou, J.; Andrews, M.; Cushman, L.; Ingersoll, G. A time comparison study of the New York State safety belt use law utilizing hospital admission and police accident report information. Accid. Anal. Prev. 22:509-52 1; 1990. St&, F. M.; Wagenaar, A. C. Are there really shortcuts? Estimating seat belt use with self-report measures, Accid. Anal. Prev. 21:509-516; 1989. Streff, F. M.; Wagenaar, A. C.; Schultz, R. Reductions in police-reported injuries associated with Michigan’s safety belt law. J. Safety Res. 2 1:9- 18; 1990. Tipton, R. M.; Camp, C. C.; Hsu, K. The effects of mandatory seat belt legislation on self-reported seat beh use among male and female college students. Accid. Anal. Prev. 22:543-548; 1990. Wagenaar, A. C.; Margolis, L. H. Effects of a mandatory safety belt law on hospital admissions. Accid. Anal. Prev. 22:253-261; 1990. Wagenaar, A. C.; Maybee, R. G.; Sullivan, K. P. Mandatory seat belt laws in eight states: A time-seriesevaluation. J. Safety Res. 1951-70; 1988. Wagenaar, A. C.; Wiviott, M. B. T. Effects of man~ting stilt use: A series of surveys on compliance in Michigan. Public Health Rep 101:505-13; 1986. Waksberg, J. Sampling methods for random digit dialing. J. Am. Stat. Assoc. 7340-46; 1978. Williams, A. F.; Lund, A. K. Seat belt use laws and occupant crash protection in the United States. Am. J. Public Health 76:1438-1442; 1986. Williams, A. F.; Lund, A. K. Mandatory seat belt use laws and occupant crash protection in the United States: Present status and future prospects. In: Graham, J. D., editor. Preventing automobile injury. Dover, MA: Auburn House Publishing Company; 19885 l-72. Withams, A. F.; Preusser, D. F.; Blomberg, R. D.; Lund, A. K. Seat belt use law enfor~ment and pubhcity in Elmira, New York: A reminder campaign. Am. J. Public Health 7731450-146 1; 1987a. Williams, A. F.; Wells, J. D.; Lund, A. K. Shoulder belt use in four states with belt use laws. Accid. Anal. Prev. 19:251-260; 1987b.

APPENDIX MATHEMATICAL INTERVENTION

FUNCTIONS ANALYSIS

UNDERLYING MODELS USED

TIME SERIES AND IN THIS REPORT

Time series model The time series models underlying safety belt use trends are represented by the following mathematical function: z, = (1 - a) z*-, + a(1 -a)zt_2+tu*(l

-ffafzl_~+..*a”(l

-a)z,_(,+t~+u,

where z, is the safety belt use rate in month (t); z,-i, zl+ z,-3. . . . z,-(,+~)arethe preceding rates beginning with the previous month (t - 1) and ending with the first month [t - (n + l)] in the series; a! is the moving average parameter; and u, is the random error term with zero mean and constant variance. The moving average parameter is used to generate coefficients (weights) for each rate in the series. These coefficients are used to predict zt and determine whether rates increased, decreased, or did not change over time. This function describes an exponentially weighted moving average (EWMA) model.

~~te~entio~ model To model the intervention effect, we introduced intervention variables 1,(t), [r(t), . . . I&) into the above model: zt = w,l&) +

@212(l)

+

w&l)

+

w4140)

+

OM)

+

W616(0

+

(1

-

a) &-I

+a(l-ff)z1_2+(u2fl-~)Zt_~+.~.a~(l-a)Zt_(”~,f+u~

Influence of safety belt laws

653

where z, is the safety belt use rate at month (t); 01, 02, . . . WCare the ubsolufe percent increases relatui to the six diIferent variationsofs&ty belt law interventions; 1,(t). I&), . . . 1((f)arcindicator variables which indicate when each of these safety belt law interventions occuned (the indicator variable has a value of 0 before the intervention occurred and 1after the intervention); and the other terms are from the time series tinction above. Six different safety belt law interventions wem observed and are based on the diEbrent dates when safety belt laws were enacted, when these laws became efkctive, and when fines were implemented for violations (or various combinations of these) in each state. The six intervention coefficients pertain to the date when safety belt laws were enacted (w,), were enacted and became e&ctive (y), were enacted and became e5ktive and fines were impla mented (or), became eIktive (u,), became eiktive and fines were implemented (US),and when fines were impkmented (We).For example, in one state (Wisconsin) all s&y belt law interventions were effective on one date; therefore the etkct of this intervention is given by the value of the third intervention coefficient, wj.