bicyclists or pedestrians present to distract his attention at the regularly overcrowded intersection. The parked green van disappeared within five minutes, the two other cars that may have been important left without a trace. It is hardly possible to observe traffic behaviour under the most relevant condition of an accident occurring, because accidents are very rare events, given the large number of trips. Given the new video equipment and the recent developments in automatic incident and accident detection, it becomes more and more realistic to collect such data at not too high costs. Additional to this type of data that is most essential for a good understanding of the risk increasing factors in traffic, it also important to look at normal traffic behaviour as a reference base. The question about the possibilities and limitations of accident analysis is not lightly answered. We cannot speak unambiguously about accident analysis. Accident analysis covers a whole range of activities, each originating from a different background and based on different sources of information: national data banks, additional information from other sources, specially collected accident data, behavioural background data etc. To answer the question about the possibilities and limitations, we first have to look at the cycle of activities in the area of traffic safety. Some of these activities are mainly concerned with the safety management of the traffic system, some others are primarily research activities. The following steps should be distinguished: - detection of new or remaining safety problems; - description of the problem and its main characteristics;
- the analysis of the problem, its causes and suggestions for improvement; - selection and implementation of safety measures; - evaluation of measures taken.
Although this cycle can be carried out by the same person or group of persons, the problem has a different (political/managerial or scientific) background at each stage. We will describe the phases in which accident analysis is used. It is important to make this distinction. Many fruitless discussions about the method of analysis result from ignoring this distinction. Politicians, or road managers are not primarily interested in individual accidents. From their perspective accidents are often treated equally, because the total outcome is much more important than the whole chain of events leading to each individual accident. Therefore, each accident counts as one and they add up all together to a final safety result.
Researchers are much more interested in the chain of events leading to an individual accident. They want to get detailed information about each accident, to detect its causes and the relevant conditions. The politician wants only those details that direct his actions. At the highest level this is the decrease in the total number of accidents. The main source of information is the national database and its statistical treatment. For him, accident analysis is looking at (subgroups of)
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accident numbers and their statistical fluctuations. This is the main stream of accident analysis as applied in the area of traffic safety. Therefore, we will first describe these aspects of accidents.
2. The nature of accidents and their statistical characteristics.
The basic notion is that accidents, whatever there cause, appear according to a chance process. Two simple assumptions are usually made to describe this process for (traffic) accidents: - the probability of an accident to occur is independent from the occurrence of previous accidents;
-the occurrence of accidents is homogeneous in time.
If these two assumptions hold, then accidents are Poisson distributed. The first assumption does not meet much criticism. Accidents are rare events and therefore not easily influenced by previous accidents. In some cases where there is a direct causal chain (e.g. , when a number of cars run into each other) the series of accidents may be regarded as one complicated accident with many cars involved.The assumption does not apply to casualties. Casualties are often related to the same accident and therefore the independency assumption does not hold. The second assumption seems less obvious at first sight. The occurrence of accidents through time or on different locations are not equally likely. However, the assumption need not hold over long time periods. It is a rather theoretical assumption in its nature. If it holds for short periods of time, then it also holds for long periods, because the sum of Poisson distributed variables, even if their Poisson rates are different, is also Poisson distributed. The Poisson rate for the sum of these periods is then equal to the sum of the Poisson rates for these parts.
The assumption that really counts for a comparison of (composite) situations, is whether two outcomes from an aggregation of situations in time and/or space, have a comparable mix of basic situations. E.g. , the comparison of the number of accidents on one particular day of the year, as compared to another day (the next day, or the same day of the next week etc.). If the conditions are assumed to be the same (same duration, same mix of traffic and situations, same weather conditions etc.) then the resulting numbers of accidents are the outcomes of the same Poisson process. This assumption can be tested by estimating the rate parameter on the basis of the two observed values (the estimate being the average of the two values). Probability theory can be used to compute the likelihood of the equality assumption, given the two observations and their mean. This statistical procedure is rather powerful. The Poisson assumption is investigated many times and turns out to be supported by a vast body of empirical evidence. It has been applied in numerous situations to find out whether differences in observed numbers of accidents suggest real differences in safety. The main purpose of this procedure is to detect differences in safety. This may be a difference over time, or between different places or between different conditions. Such differences may guide the process of improvement. Because the main concern is to reduce the
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number of accidents, such an analysis may lead to the most promising areas for treatment. A necessary condition for the application of such a test is, that the numbers of accidents to be compared are large enough to show existing differences. In many local cases an application is not possible. Accident black-spot analysis is often hindered by this limitation, e.g., if such a test is applied to find out whether the number of accidents at a particular location is higher than average. The procedure described can also be used if the accidents are classified according to a number of characteristics to find promising safety targets. Not only with aggregation, but also with
disaggregation the Poisson assumption holds, and the accident numbers can be tested against each other on the basis of the Poisson assumptions. Such a test is rather cumbersome, because for each particular case, i.e. for each different Poisson parameter, the probabilities for all possible outcomes must be computed to apply the test. In practice, this is not necessary when the numbers are large. Then the Poisson distribution can be approximated by a Normal distribution, with mean and variance equal to the Poisson parameter. Once the mean value and the variance of a Normal distribution are given, all tests can be rephrased in terms of the standard Normal distribution with zero mean and variance one. No computations are necessary any more, but test statistics can be drawn from tables.
3. The use of accident statistics for traffic safety policy.
The testing procedure described has its merits for those types of analysis that are based on the assumptions mentioned. The best example of such an application is the monitoring of safety for a country or region over a year, using the total number of accidents (eventually of a particular type, such as fatal accidents), in order to compare this number with the outcome of the year before. If sequences of accidents are given over several years, then trends in the developments can be detected and accident numbers predicted for following years. Once such a trend is established, then the value for the next year or years can be predicted, together with its error bounds. Deviations from a given trend can also be tested afterwards, and new actions planned. The most famous one is carried out by Smeed 1949. We will discuss this type of accident analysis in more detail later.
1. The application of the Chi-square test for interaction is generalised to higher order classifications. Foldvary and Lane (1974), in measuring the effect of compulsory wearing of seat belts, were among the first who applied the partitioning of the total Chi-square in values for the higher order interactions of four-way tables.
2. Tests are not restricted to overall effects, but Chi-square values can be decomposed regarding sub-hypotheses within the model. Also in the two-way table, the total Chisquare can be decomposed into interaction effects of part tables. The advantage of 1. and 2. over previous situations is, that large numbers of Chi-square tests on many interrelated (sub)tables and
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corresponding Chi-squares were replaced by one analysis with an exact portioning of one Chi-square.
3. More attention is put to parameter estimation. E.g., the partitioning of the Chi-square made it possible to test for linear or quadratic restraints on the row-parameters or for discontinuities in trends.
4. The unit of analysis is generalised from counts to weighted counts. This is especially advantageous for road safety analyses, where corrections for period of time, number of road users, number of locations or number of vehicle kilometres is often necessary. The last option is not found in many statistical packages. Andersen 1977 gives an example for road safety analysis in a two-way table. A computer programme WPM, developed for this type of analysis of multi-way tables, is available at SWOV (see: De Leeuw and Oppe 1976). The accident analysis at this level is not explanatory. It tries to detect safety problems that need special attention. The basic information needed consists of accident numbers, to describe the total amount of unsafety, and exposure data to calculate risks and to find situations or (groups of) road users with a high level of risk.
4. Accident analysis for research purposes.
Traffic safety research is concerned with the occurrence of accidents and their consequences. Therefore, one might say that the object of research is the accident. The researchers interest however is less focused at this final outcome itself, but much more at the process that results (or does not result) in accidents. Therefore, it is better to regard the critical event in traffic as his object of study. One of the major problems in the study of the traffic process that results in accidents is, that the actual occurrence is hardly ever observed by the researcher.
Investigating a traffic accident, he will try to reconstruct the event from indirect sources such as the information given by the road users involved, or by eye-witnesses, about the circumstances, the characteristics of the vehicles, the road and the drivers. As such this is not unique in science, there are more examples of an indirect study of the object of research. However, a second difficulty is, that the object of research cannot be evoked. Systematic research by means of controlled experiments is only possible for aspects of the problem, not for the problem itself.
The combination of indirect observation and lack of systematic control make it very difficult for the investigator to detect which factors, under what circumstances cause an accident. Although the researcher is primarily interested in the process leading to accidents, he has almost exclusively information about the consequences, the product of it, the accident. Furthermore, the context of accidents is complicated. Generally speaking, the following aspects can be distinguished: - Given the state of the traffic system, traffic volume and composition, the manoeuvres of the road users, their speeds, the weather conditions, the condition of the road, the vehicles, the road users
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and their interactions, accidents can or cannot be prevented.
- Given an accident, also depending on a large number of factors, such as the speed and mass of vehicles, the collision angle, the protection of road users and their vulnerability, the location of impact etc., injuries are more or less severe or the material damage is more or less substantial. Although these aspects cannot be studied independently, from a theoretical point of view it has advantages to distinguish the number of situations in traffic that are potentially dangerous, from the probability of having an accident given such a potentially dangerous situation and also from the resulting outcome, given a particular accident.
This conceptual framework is the general basis for the formulation of risk regarding the decisions of individual road users as well as the decisions of controllers at higher levels. In the mathematical formulation of risk we need an explicit description of our probability space, consisting of the elementary events (the situations) that may result in accidents, the probability for each type of event to end up in an accident, and finally the particular outcome, the loss, given that type of accident.
A different approach is to look at combinations of accident characteristics, to find critical factors. This type of analysis may be carried out at the total group of accidents or at subgroups. The accident itself may be the unit of research, but also a road, a road location, a road design (e.g. a roundabout) etc.
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