Accid. AnaL & Prev. Vol. 24, No. 6, pp. 667-672, 1992 Rimed in Gm.at Britain.

ooOl-4SW92 SS.00 + MI O1!392PcrgmonFvcsLtd.

MACRO MODEL PREDICTION OF ELDERLY PEOPLE’S INJURY AND DEATH IN ROAD TRAFFIC

ACCIDENTS IN CROATIA

ARIANA VORKO-JOVIC “Andrija Stampar” School of Public Health, University of Zagreb, 41000 Zagreb,

Rockefellerova 4, Croatia

and

FRANJO JOVIC Faculty of Electrotechnics, University of Osijek, 54000 Osijek, Istarska 3, Croatia

(Received 1 February 1991; in revised form 27 July 1991)

Abstract-The case of elderly people injured and killed in traffic accidents in Croatia is used to illustrate a prediction method. This method consists of several steps. First, the most important variables are selected. Second, to overcome intercorrelation, new variables are constructed that include the old ones. Third, the new variables and its first derivatives are used in a rank correlation method. The results show good predictive capabilities.

INTRODUCTION

With the development of medical and technical sciences and the bettering of socioeco- nomic conditions, the human life span is becoming longer and longer. Thus, there are more elderly people, especially in developed countries, but the rapid growth of their number is also encountered in developing countries.

Old age brings different problems: illness; invalidism; social, psychological, and existential problems (loneliness, helplessness, environmental discomfort, questionable dwelling) (Durakovic 1990). Closely connected to illness and invalidity problems are injuring and mortality as consequences of accidents. Elderly people are accident victims mostly at home or in traffic. The ratio of elderly people killed in road traffic accidents to their mortality from all accidents was 16.9% in Yugoslavia in 1986. This is a significant proportion with respect to the part of elderly people who never leave their homes (Statisticki bilten “13. maj”, 1978-1986.).

The mortality analysis of elderly people in road traffic accidents in 22 countries has shown that in 1985 Yugoslavia was leading with the mortality rate of 51.7 per 100,000 inhabitants, followed by Poland with 47.0 per 100,000, Greece with 46.1 per 100,000, and Japan with 45.1 per 100,000. The mortality of elderly women in road traffic accidents is 2 to 3 times lower than the mortality of men according to World Health Statistics Annual 1987 (Norman 1962).

The mortality of elderly pedestrians was 2.5 times higher than the mortality of middle-aged pedestrians and children in Croatia in the 1970-1985 period. However, this ratio and the absolute number of elderly people injured and killed in road traffic accidents is by no means a constant. It was highest in the 1977-1981 period according to statistics given in the official road accident statistical bulletin in Beograd from 1974-1978 (Saob- ra&ajne nezgode na putevima 1974-1978) and in Zagreb from 1970-l 986. Analysing dif- ferent traffic parameters and conditions, a definite dependence of many factors can be obtained and arranged in a mathematical model.

In this study such mathematical models were constructed in order to allow a possible prediction of the injury and death process among elderly people in road traffic accidents in the territory of Croatia.

MACRO MODEL VARIABLES

Among many traffic process parameters, some exhibit higher influences on accidents than the others: (a) state of the weather; (b) season, month, type of day; (c) fuel

667

668 Brief Communications and Research Notes

consumption; (d) length of roads; (e) number of registered motor vehicles; (f) number of inhabitants; (g) traflic density; (h) number of crossings per kilometer of road, some where chosen and tested by a standard regression analysis method for significance in the modelling procedure. The following were found most sign&ant with the correlation coef- ficients R squared typically between 0.92 and 0.96 (Table 1): fuel consumption (t), length of roads (km), number of registered motor vehicles, number of inhabitants.

Since the variables chosen showed typical correlation features regarding the number of injured and dead elderly people in road traffic accidents, the following procedure was adopted to increase the sensitivity of the approach: minimizing of the number of variables by choosing compound variables, crossnormalization tuning of variables which depen- dently contribute to the accident generation. Two compound process variables were formed: specific traffic density, G, represented as the ratio of fuel consumption for motor vehicles in a year to the length of road (t/km), and specific motorization level, F, represented as the ratio of the number of registered motor vehicles to the number of inhabitants (Stat. Bull. “13.may” 1978-1986; World Health Statistics Annual 1987).

These variables were compared to the total of injured and dead elderly people in road traffic accidents in Croatia for the 1970- 1985 period (Fig. 1).

The Spearman rank correlation coefficient equals:

for specific traffic density p = 0.5893, (1)

for specific motorization level p = 0.0753. (2)

MACROMODELLING

The goal of macromodelling was to find out the regularity of model variables mostly congruent with the outcome, injury and death of elderly people in road traffic accidents, thus allowing prediction and the implementation of prevention methods. The values of input compound variables F and G are expressed in ranks for the territory of Croatia (56,000 km*) for the 1971-1985 period; the output variable is the number of injured and dead elderly people in road traffic accidents, all presented in Fig. 2.

The following steps in the model synthesis were calculated:

Sl. : I + D :: G (3)

S2. : I + D :: G - 1.5 G’ (4)

S3. : I + D :: G - 1.25 G’ + 170,000

F

Table 1. Most significant process variables

(5)

Years

1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986

Number of Number of inhabitants registered in Croatia motor vehicles

4.426.221 362.516 4.4.50.000 380.715 4.472.000 403.132 4.494.000 443.788 4.514.000 480.884 4.536.000 511.821 4.559.ooo 618.655 4.580.000 733.244 4.598.000 770.465 4.584.000 855.139 4.601.469 931.350 4.623.000 1.005.738 4.633.000 989.718 4648.000 1.034.824 4.655.000 1.014.953 4665.000 1.077.213

Fuel consumption in OOOt

752 803 866 901 999

1.073 1.181 1.335 1.453 1.358 1.373 1.349 1.173 1.186 1.309 1.444

Number of injured Road length and dead

in km elderly people

24.436 509 24.436 558 25.531 566 25.542 551 25.688 574 25.688 527 25.606 640 26.780 665 26.029 687 26.860 719 27.340 603 27.822 602 27.263 492 27.640 495 28.311 486 28.594 590

Brief Communications and Research Notes

. /*. .’ \

variables sum F G I+0

_._._ /+O --- G

10000 -F

669

I ;. . : ; ; I. I . * I * . . . -

!970 71 72 73 71 75 76 77 78 79 80 81 82 83 84 85 years

Fig. 1. The sum of injured and dead elderly people, compound process variables G and Fin the 1970- 1985 period in Croatia.

g4.:I+D::G-G’+y + 0.00351F’ (-AT).

where :: denotes the operation of rank correlation, G’ the absolute value of the first derivative of variable G, and F’ ( - AT) the first derivative of variable F for the previous time interval. The results and explanations of the procedure are given in Table 2 and diagrams in Fig. 3. This is essentially a trial and error procedure, whereas different influences have to be taken into account and evaluated (Vorko-Jovic 1989).

RANKS

I

15..

14..

13.’

12 ”

11 ..

10.’

9 ‘-

8..

7 ‘a

6-m

5.

I .’

\7 ‘.

2 .’

1 . .

‘F,G.I+D -G ___ F

1 . 4 1971 72 73 71 75 76 77 78 79 80 81 k 83 84 bS y~orr

Fig. 2. Ranks of two compound process variables G and F compared to the ranks of sum of injured and dead elderly people in road traffic accidents in 1971-1985 period in Croatia.

MC 2416-W

670 Brief Communications and Research Notes

Table 2. The steps in model synthesis and their explanation

Steo Rank correlation coefficient Advantage Disadvantaee

Sl 0.5893

s2 0.5500

s3 0.8339

s4 0.9643

Simple relation Low ranks for 71-76 High ranks for 81-85

The same maxima of I/O func- Low ranks for 71-76 tions High ranks for 83-85

Rough covering of the whole Main difference in oil-crisis I/O relation years 73 and 79 not the same

maxima of I/O function Fine covering of the 71-72 and Rough covering of 73-76 pe-

77-85 period riod

The compound variable G was taken as the first step, Sl, because of its much higher rank correlation than F. G’ was added in step S2 primarily to correct for the maximum of the modelled curve. Principally, after step S2, the ranks of model after the maximum in the year 1980 were advanced, and the ranks of model from 1971 to 1979 were pushed back. Therefore, the F curve was used in its inverse form (see Fig. 1) to correct for this systematic discrepancy. The S3 curve obtained shows roughness for the years: 1972, 1975,1979,1982,1983, 1984, and 1985. Therefore, atIer longer analysis the most suitable correction was found in the delayed first derivative of the F variable and modelled in step S4. The changes in model constants, particularly in G’ term were done through all the steps in order to preserve the local rank correlation optimum.

MODEL EVALUATION

As shown in Table 2, the relation S4 from equation (6) gives the highest rank correlation between the compound input variables F and G and the output variable Z + D in the observed 1970-1985 period. Thus, the relation S4 was used for the prediction of the number of traumatized and dead elderly people in road traffic accidents for the year 1986. The following data were used as already published in the collected statistics sources (Bilten o sigumosti u cestovnom prometu, 1970-1986; Internal data of the Sta-

RANKS

15 .’

1.4 ..

13 *.

12 . .

11 *.

10 .’

9 .-

8 . .

7 *.

6 .’

5 a.

I . .

3 .’

2 . .

1 . .

-. - . - IhVURED . . . . . . . G or S1

_____ S2

- S3 - SL

I : : ; : . : : : *. : * : : :

197172 73 74 75 76 77 78 a 80 81 d2 83 84 85 years

+DEAD

Fig. 3. The sum of injured and dead elderly people in ranks, compound variable G, steps Sl-S4.

Brief Communications and Research Notes 671

tistical Department of the INA Trade “Marketing” Sector, Zagreb, 1987): fuel con- sumption of road motor vehicles (in tons), total length of roads (in km), number of registered motor vehicles, number of citizens.

Using the relation (6) and the statistical data, the result was:

50.51 + E + 0.0035 - 1287 - 1.87 = 61.80, ,

i.e. the sixth rank among the results between 1971 and 1986. For previous 15 ranks from the 1971-1985 period for output variable Z + D there were 602 injured and dead elderly people. Between the fifth and seventh rank for the 1971-1986 period there were 574 and 603 such cases, respectively. According to the subsequently obtained official statis- tical data (Statist&i bilten “ 13. maj”. 1978-l 986) there were 590 injured and dead elderly people in 1986. Thus, the result obtained is within the expected limits with the errors + 2.2% and -2.7%. The result of the prediction is given in Fig. 4 where the rank correlation equals p = 0.96765 for the 197 1 - 1986 period and is slightly higher than that for the 197 l- 1985 period.

The prediction was based on already available data. To provide real predictions one should use prediction for input data employing yearly plans, statistical trends, and correct statistical interpretations.

DISCUSSION

The presented macro model exhibits several “critical years” where the differences between heuristic and model data are visible even for the function S4 with the highest correlation feature. By changing the constants in a stepwise manner and including more refinement in the mathematical description from step Sl to step S4, these rank differences are practically eliminated for the majority of years in the 1971-1985 interval.

Nevertheless, the critical 1973-74 and 1979-80 years have remained. These years (1973,1979) are the so-called “oil-crisis” years with the consequences in traffic and social tensions having been prolonged into the subsequent years (1974 and 1980). Moreover, the model has very neatly followed the Yugoslav (and Eastern Europe) social crisis from 1981 on.

R4NKS ,

16 . .

15 .’

1c .

13 .

12 .

If ‘.

10 .

9 ,*

8 ..

7 *.

6.

5 -

4 ,’

3 ”

L:::::::::f:.:::.

1971 72 73 74 7Ei 76 77 78 79 80 81 82 8.3 M 85 86 Ywrs

Fig. 4. Verification of model prediction for 1986.

I+D 4 FVRMULA

612 Brief Communications and Research Notes

To make it possible for the model data to be ranked as closely as possible to the heuristic data on injured and dead elderly people, the model data should be observed as groups of ranks (Fig. 3):

(a) group 1 of leading ranks from 1977-1980, (b) group 2 of group 1 following ranks from 1981-1982, (c) group 3 of middle ranks from 1971-1976, and (d) group 4 of “outsider” ranks from 1983-1985.

Changing the constants and structural form of expressions Sl to S4, the change of the model ranks is obtained. During this principally trial-and-error procedure, the steps described were evaluated as promising when the ranks for 1975, which is the medium rank year, were not changed.

The relative number of elderly people was practically constant for the 1980-1986 period and equal to 9.6% -+ 1% for the territory of Croatia. Thus, there was no special need to involve this variable in the modelling procedure. In case of larger variations, this should be done in order to match finer changes of the model under observation.

The model and procedure could be applied to similar traumatization and death modelling for other similar age groups.

CONCLUSION

The injury and death process of elderly people was modelled using normalized compound variables. These variables showed a very small correlation, practically exhib- iting orthogonality. This feature was used for a stepwise additive procedure controlled by the rank correlation coefficient. In this way a trial-and-error synthesis of the macro model was obtained.

The macro model includes all officially accessible data that seem to cover the main factors involved in the injury and death process occurring among elderly people in road traffic accidents over a larger territory and for longer periods of time. The model accuracy is gradually increasing as the observed time series becomes longer, without a change of other generative model factors.

The model can be used in realistic prevention of the injury and death process of elderly people because it points to the specific traffic density G as to the main cause of accidents. The best preventive method seems to be the intensive investment in new road construction.

REFERENCES

Bilten o sigumosti u cestovnom prometu 1970-1986. (Bulletin on road traffic safety 1970-1976). RepubliEki sekretarijat za unutraSnje poslove (Secretariat of Internal Affairs of Croatia Zagreb, 1971-1987.

Durakovic, Z. i sur. Medicina starije dobi. (Medicine for the elderly). Naprijed, Zagreb: 413-416; 1990. Internal data of the Statistical Department of the INA Trade “Marketing” Sector, Zagreb, 1987. Norman, L. G. Road traffic accidents. Epidemiology, control and prevention. Geneva: World Health Or-

ganization; 1962. Saobracajne nezgode na putevima 1974-1978. (Road traffic accidents 1974-1978). StatistiEki bilten, Beograd

(1131):27,30; 1979. Statisticki bilten “13. maj”. (Statistical Bulletin “13. may”), Sekretarijat unutragnjih poslova Jugoslavije

(Secretariat of Internal Affairs of Yugoslavia) Beograd, 1978-1986. Vorko-JoviC A., Stari Ijudi u cestovnom prometu (Elderly people in road traffic) Doctoral thesis. Zagreb:

Medicinski fakultet SveuEiliSta u Zagrebu; 1989. World Health Statistics Annual 1987. Geneva: World Health Organization; 1987: 110-306.