154 Transportation Research Record: Journal of the Transportation Research Board, No. 2280, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 154–161. DOI: 10.3141/2280-17 A. Borsos and C. Koren, Department of Transport Infrastructure and Municipal Engineering, Szechenyi Istvan University, Egyetem ter 1, Gyor 9026, Hungary. J. N. Ivan, Civil and Environmental Engineering, Unit 2037, and N. Ravishanker, Department of Statistics, Unit 4120, University of Connecticut, Storrs, CT 06269. Corresponding author: A. Borsos, borsosa@sze.hu. D N N P =       - 0 0003 2 23 . ( ) Later, other authors tried to validate or update the formula on the basis of newer data. Andreassen argued that the relationship that Smeed discovered should not be used as a comparative tool for different countries with different motorization levels (2), yet it helps to put accident rates into perspective. Adams stated that the “parameters of his original model do not fit the experience of every country exactly, but the model still represents a very useful generalization of the relationship between death rates and exposure” (3). He also suggested that the long-term decline in death rates is attributable to a learning process in society. The first interpretation of Smeed’s law was also later updated by Holló with a revised formula (4). A less encouraging interpretation of Smeed’s formula is that the increase in vehicle ownership leads to an increase in fatalities per population and in the total number of fatalities. D P N P =       0 0003 3 13 . ( ) Fortunately, the trend of increases in the total number of fatalities started to change toward decreases in some countries starting in the 1960s. For instance, in the United Kingdom, the Smeed prediction was moving correctly and had approximately the right magnitude until about 1966. Since 1966, the Smeed prediction continues to rise, whereas the real number of road deaths has fallen quite consis- tently. By 2000, the Smeed prediction was about 4 times too high (5). To visualize this, the Smeed prediction (Equation 3) with his observations for 20 countries from 1938 and the actual values for a few countries are plotted in Figure 1. Broughton disputed that Smeed’s formula can be regarded as a law and also suggested that the relationship is time dependent, that is, that it changes over time (6). Research carried out by Oppe found that the long-term devel- opment of traffic fatalities in the highly motorized countries follows a lawlike pattern determined by the growth of motoriza- tion and the decline of the fatality rate per vehicle kilometer of driving (7, 8). Oppe clarifies that “the development of the num- ber of fatalities over the entire range can be explained by means of two basic continuous processes, a positive growth of traffic volume and a negative growth of the fatality rate, together result- ing in the rise and fall of the number of fatalities that has been noticed” (8). Long-Term Safety Trends as a Function of Vehicle Ownership in 26 Countries Attila Borsos, Csaba Koren, John N. Ivan, and Nalini Ravishanker The objective of this paper was to model the evolution of road safety as a function of motorization level. The authors completed a country-level as well as a time-dependent analysis focusing on countries for which data were available for a long period of time (1965 to 2009). For the statisti- cal analysis, a function describing road safety trends (decline, turning, improvement) was proposed. Two coefficients in the model were esti- mated for each country and for each year, and their change over time is discussed. The results showed that the shape of the curve changed over time. In some countries, the decrease in the mortality rate became slower over time; however, a greater potential to improve road safety existed in other countries. Possible reasons for the general positive trends in road safety are the continuous improvement in engineering solutions (better infrastructure, safer cars) as well as road users who are better trained and skilled because of education and experience. In addition to the factors mentioned previously, the increased speed by which safety-related information and knowledge are disseminated contributes to the decrease in the differences in safety levels among countries. The analysis of macroscopic trends in road safety first attracted attention in the mid-20th century. In 1949, R. J. Smeed published his formula for predicting road deaths as an empirical rule relating traffic fatalities to motor vehicle registrations and population (1): D N P = ( ) 0 0003 1 2 13 . ( ) i where D = number of annual road deaths, N = number of registered vehicles, and P = population. He did his analysis when vehicle ownership rates were between 0.01 and 0.23; in some places these figures today exceed 0.8 (i.e., 800 motorized vehicles per 1,000 population). Smeed’s paper is mostly cited with the emphasis that the increase in vehicle ownership leads to a decrease in fatalities per vehicle, as it follows from Equation 1: