J. Dehasse*, A-C. Cornet

Introduction

The aim of this project is to evaluate the dangerousness of dogs that have already bitten human beings. The usual way to do this is by means of an expertise such as a behavioural consultation. We combined the important (quantitative) variables on which this evaluation is based to build up an additive formula. Based on this formula we developed a scale of dangerousness.. The formula had been improved by multiple linear regressions. It is easy to use by people not qualified in behaviour.  

Models, Materials and Methods

There are two steps in the development of a dangerousness scale and in its evaluation: 
(1)   the development of a formula of dangerousness
(2)   the validation of the formula

Development of a dangerousness scale

The scale was developed by insight on the basis of theoretical modelling. The variables were selected and eliminated according to what seemed to be heuristically and clinically operant, objective, quantifiable, and easy to determine even for a person non qualified in behaviour.

The selected variables are: mass of the dog and mass of the (bitten) victim, categories of persons at risk (bitten victims), offensive-proactive vs. defensive-reactive aggression, predictable vs. unpredictable aggression, bite control, simple vs. multiple bite(s) and held vs. non-held bite(s). At the beginning, each variable received a value from 1 to 7, depending on the number of items in each variable. This value was modified (weighted) after statistical analysis of the variance of each variable.

Description and initial values of the variables

Mass. The mass of the dog in relation to the mass of the victim is an important variable to consider to evaluate the danger for the victim. The variable is valued as follows: [4 x mass of the dog / mass of the victim].

Victims. The same kind of bite will have different consequences for the victim depending on whether the victim is a man or women, a child or an elderly or handicapped person. . Epidemiological studies show that children are in greater danger than adults (bites in the face, etc.). The items are classified as follows:

1. Adult men
2. Adult women, people with a minor handicap, fearful people
3. Child between 6 and 10 years of age, elderly people, people with a medium handicap.
4. Child between 3 and 6 years of age, people with a significant handicap.
5. Child less than 3 years of age, people with a major handicap. 

Offensive (proactive) vs. defensive (reactive) aggression. This variable describes the movement of the dog relative to that of the victim. If the dog moves forward to attack the person who is at some distance from it, the aggression is called offensive-proactive. If the dog reacts aggressively to a person moving toward it, the aggression is called defensive-reactive. The person can avoid the bite easier if the attack is reactive; the attack is often more severe if the dog is offensive-proactive than if it is defensive-reactive. The respective values of these items are:

1. defensive-reactive aggression
2. offensive-proactive aggression

Predictable vs. unpredictable aggression. A predictable attack is preceded by a well-organised and understandable threat. A direct attack without any preceding threat is unpredictable. The predictability has to be evaluated by the victim. An attack is always unpredictable for children under 3 years of age. It is evident that a predictable attack can be avoided more easily than an unpredictable one. In the first case, it is probable that the person can defend himself and thereby reduce the danger of the bite. The respective values of these items are:

1. Predictable attack
2. Partially predictable attack
3. Unpredictable attack

 Control and intensity of the bite. The less controlled the bite, the more intense the wounds and the greater the danger for the victim. The respective values of these items are:

1. Mouthing: no trace
2. Pinch: blue spot, haematoma
3. Controlled bite: haematoma
4. Controlled and held bite: epidermal wound
5. Hard bite: muscular wound
6. Hard and held bite: muscular lacerations
7. Predatory bites: muscular wrecking

 Simple vs. multiple bites. A dog that bites repetitively is more dangerous then a dog that bites once. A dog that holds the bite is more dangerous then a dog that pinches and lets go of the person immediately. The respective values of these items are:

1. Simple bite
2. Simple held bite
3. Multiple bites
4. Multiple held bites

The mathematical formula

Two mathematical formulas have been established that link all these variables. One formula is based on an addition, the other on the multiplication of the selected variables. The multiplication model may increase the risk of multiplication errors. A model based on an addition is easier to apply for everybody, including non-professionals. However, the best formula is the one that gives the best correlation results with the expert considered as the standard.

The items [mass, victim, offensive/defensive, predictable/unpredictable, control, simple/multiple] are x₁, x₂, x₃, x₄, x₅, x_{6, ,} respectively. All the variables (x) are independent.

Multiplication model: y = x_{1 *} x_{2 *} x_{3 *} x_{4 *} (x_{5 +} x₆₎

Addition model: y = x₁ + x₂ + x₃ + x₄ + x₅ + x₆. The addition formula is based on a linear multiple regression model. The b_i parameters are estimated by the least square method, a method assuming that the best-fit curve is the one that has the minimal sum of the deviations squared (least square error) from a given set of data (Efunda, 2003). Each variable is analysed by a ‘t’ of Student test to determine if the variable contributes to the explanation of ‘y’. All of the variables should be statistically significant with an accepted probability of 95%.

A ‘F’ of Fisher test is applied on the regression mean square:  F = CM_model / CM_error .

Each variable then receives a calculated weight (b_i) coefficient, and a constant (b₀) may be added: y = b₀ + b₁x₁ + b₂x₂ + b₃x₃ + b₄x₄ + b₅x₅ + b₆x₆. 

If significant, the new addition formula (with new coefficients) will then be applied to the cases examined by the 5 veterinarians.

Validation of the formula

The dogs were included if they had bitten people. Age or sex was no criteria for selection.

Five behaviourist veterinary behaviourists from 3 different European countries participated in the study. Where possible, the veterinarians, or a technician present, evaluated the dog with the dangerousness formula at the beginning of the behavioural consultation. At the end of his/her behavioural consultation, the veterinarian gave a subjective value from 0 to 10 to the dangerousness of the dog examined; the value 0 means “no dangerousness”, the value 10 “danger may be lethal”. Even though the evaluation done during this consultation is subjective and cannot be considered a golden standard, it is used as the reference value to which the formula will be compared and correlated.

The dogs were followed up for 3 months and incidents of biting were recorded. 

Results

The total number of dogs included in this study was 86.
The results of the multiplication (scaling) model have been correlated to 44 cases evaluated by the first author (J. Dehasse, 2001). The neperian logarithm of the scale result was correlated with the (subjective) evaluation of the expert. The correlation was 0,81 (0,809). 
The addition formula used in the same 44 cases showed the best correlation factor (0,85) after weighing the variables. 
Several veterinary experts in behavioural medicine then applied this new formula to correlate the results of the formula with clinical evaluations of 86 cases. Two of the veterinarians were responsible for the majority of the cases.

 The victims in the sample population were mostly female and adults.

 The attack was more often offensive-proactive (56 dogs, 65,1%) than defensive-reactive (30 dogs, 34,9%).

The attack was unpredictable in half of the cases.

The bite level was generally controlled, leading to superficial wounds.

Bites were generally simple and not held, leading to not too severe wounds.

Most of the dogs were evaluated to be of small to medium danger. This may be a factor to help treating these animals.

Four dogs were euthanized (4,6%). 58 dogs (67,4%) received medication, 15 dogs (17,4%) did not receive any medication, in 11 (15,1%) cases it was not specified. 73 dogs (84,9%) received a behavioural therapy, in 11 (15,1) cases this was not specified. 18 dogs (20,9%) had bitten again during the 3 months following evaluation and treatment.

Discussion

Discussion of variables

The breed of the dog is not taken into account in the variables. This variable was rejected,  as not enough epidemiological validated studies exist that show the influence of the breed on the degree of dangerousness of the dog.

Many other items, such as muscularity, type, diagnosis or context of aggression, were not taken into consideration either, because non-professionals might not be familiar with these items. Additionally, they are not easy to objectify or standardize and they may also not be independent of the chosen variables.

Discussion of validation

The formula was analysed on the basis of a first sample of 44 cases of dogs that have bitten humans examined by Joël Dehasse (2001). The number of liberty degrees was (44 – 6 variables – 1 constant) = 37. This is enough to validate a multiple linear regression. The core study was done on 86 cases. This number is quite small and the statistician said that, to get the best results, one should use 200 cases.

Although five veterinarians participated in this study, the sample was not distributed equally among them, two of the veterinarians evaluated more than 75% of the cases.

Each dog was examined once by a veterinarian. Even if the variables are quite easy to objectify, there could be differences of evaluation of the same dog dangerousness by different experts. The analysis of the  objectivity of the test has not been done.

Does this test have a predictive value? In order to find this out, the clinical case files were re-examined to see if the dogs had bitten in the 3 months following the clinical evaluation. Only the factor x₆ (simple vs. multiple bite) showed a significant predictive value.

A U Mann Whitney test between the dangerousness as evaluated by the scale (formula) and the recurrence of biting is not significant (U = 329,5, p= 0,362). The formula is not predictive of recurrence of biting. Only the x₆ variable may be predictive.

Discussion of experts and the clinical value

As this formula does not require any knowledge in ethology or in behavioural medicine, non-experts (in veterinary behaviour medicine, in animal behaviour therapy or in animal ethology) can use it as a first criterion to determine whether a dog should be supervised, euthanized or referred to an expert who will then decide on a diagnosis and a treatment. Also veterinary surgeons in general practice may use it to determine if the dog should best be referred to a specialist or not.

The formula may have a clinical prospective value if extrapolated from one person bitten to another belonging to another victim category. If a man has been bitten and the formula gives a value of 5, the same bite would have produced a value of 9 if applied to his 3-year-old child.

The formula, or at least the variables included in the formula, has a pedagogic importance. In the case of intense emotion, which is the case if somebody has been bitten, it may be required to rely on logical elements of dangerousness, such as the ones analysed in this scale.

Conclusion

It is possible and realistic to carry out a simple evaluation of the dangerousness of (a bite of a) dog without any specific knowledge of ethology or behavioural medicine. This evaluation could be handy for any veterinary surgeons (not specialised in veterinary behavioural medicine) anxious to get a first idea of the level of dangerousness of a dog biting within a specific environment.

References

• Cornet A-C 2003 Contribution à l'élaboration d'une formule mathématique mesurant la dangerosité chez un chien mordeur: essai de validation. Memoir to obtain the title of Veterinary Behaviourist of the Veterinary Schools (France).

• Dehasse J 2001 Evaluation of dangerousness of dogs, which have bitten. Poster. CABSTG, Birmingham, April 4.

• Dehasse J (2002) Le chien agressif, Publibook.com, Paris. 

• Efunda 2003 http://www.efunda.com/math/leastsquares/leastsquares.cfm, 6 April 2003

Dr Joël Dehasse - Behaviorist veterinarian - www.joeldehasse.com - 2008-07-17