DEATH PROBABILITY DETERMINATION IN BURN PATIENTS AS THEY ARE ADMITTED TO HOSPITAL. MATHEMATICAL MODEL OF LOGISTIC REGRESSION

Herruzo Cabrera R., García Torres V., Fernández Arjona M., Rey Calero J.

Preventive Medicine Department, Autonomous University and Burn Unit of La Paz Medical Center, Madrid, Spain

SUMMARY. With the intention of improving death probability determination in bum patients, a sophisticated technique is proposed based on a logistic regression model. The method was used over a 3-year period, taking into account I I variables Presented by all the bum patients admitted to a Bums Unit. A Logress computer program was used to calculate the coefficient of independent variables. Tables are given for the simple calulation of death probability in these patients.

Introduction
Death probability in bum patients, as they are admitted to hospital, is extremely important because it can change the therapeutical performance. Even more, death probability in these patients varies according to the therapeutical procedures. To give an example: from 1964 to 1968, in burn patients treated with famenide acetate, the mortality rate decreased, while from 1969 to 1973 there was an increase in this rate because of the appearance of resistant micro-organisms (1).
For this reason it.is important to update different hospital death probabilities, in order to evaluate the effect of new therapies and whether or not we can still use old ones.
On the other hand, although mortality has decreased in the last years in all ages and extents Of body area burned (b.a.b.) (2), these two variables are still the main death aetiologies (3, 4, 5, 6, 7).
If we wish to calculate death probability, making use of stratification of our patients using these two variables, we may find that some of the strata have too few patients, which may produce mistakes in the probability result that we obtain (8, 9).
For this reason we'have to use more sophisticated techniques to calculate death probability, such as a logistic regression (1, 7) or a discriminatory analysis (10). With these two methods we are able to get efficient marginal values. Furthermore, we can handle many more variables for our study, which is very difficult to do just with a stratification model (8).
Finally, as we can obtain a logistic regression equation, we can obtain death probability values simply by consulting the different tables (11).

Material and methods
For three years (June 1984 to December 1987) we studied all patients admitted to the Critical Ward of the Bum Unit of La Paz Hospital. In all cases we recorded I I variables at the moment of admission:

We classified all the data dichotomically except for: age (0-19; 20-39; 40-59; 60-79 and >80), b.a.b. (< 9%; 10- 19%; 20-39%; 40-59%; 60-89%; > 90%~ and burn depth (superficial, subdermic, dermic).
We used the Logress computer program (12) to calculate the coefficient of independent variables, and we also obtained the odds ratio and the limits of 95%. With all this information we are in a better position to understand the real influence of each variable in the equation.

Results
We used an interactive method: first we calculated our equation for all variables regarding death factor and'then we used two variables (age and b.a.b.), because these two variables are decisive in death probability (see equations in Tab. 2).
Using this last equation we can calculate death probability in every stratum (Tab. 3). As can be seen, values are very similar to those in Tab. I (real data), especially in the central strata.
For marginal strata, where we have too few patients with high confidence limits and the percentages are unsteady, it is much better to use Tab. 3 than Tab. 1. This proves the advantages of multivariant methods.

( ) mortality percentage in this stratum

Bum depth: superficial

subdermic

dermic

Equation 1: Exhaustive model

25.1%

49.2%

25.7%

Death probability = 1/1 + e 4.39 + 0.79 (age) - 0.49 (sex) + 0.93 (b.a.b.) + 0. 11 (deep) - 0.28 (face bum) + 0.59 (perineum bum) - 1.48 (scald) - 0.04 (flame) + 1. 13 (chemical) + 0. 18 (electrical).

Equation 2: Simplified model: Significant variables only

Death probability = I / I + e (- 4.62 + 0.81 (age) + 0.91 (b.a.b.)

Discussion
Because of the kind of variables (dichotomic and qualitative with three or more strata), the best model is a logistic regression (13), which can show us the decisive variables in the equation, their odds ratio and limits.
We can see in Tab. 2 that bum depth is of no significance, despite the findings of other authors (7, 9, 14). This might be because in our study we -did not check the percentage of b.a.b. in every depth stratum (15). Other variables are not significant either.
The described death probability is better than in other Units (1, 3, 7, 10, 14), with a survival increase especially in older patients, because we used intensive instrumentation techniques (2) that were surgically more aggressive, achieving faster crust control.
We agree with Clark (7) when he says that death probability, when the patient is admitted to hospital, must be treated as a risk of death rather than as a control of therapies, since therapy success depends on several factors, e.g. kind of bum, inhalation injury, etc., and of course it is a problem to use the same probits in different units. We think that every Bum Unit should have its own probits.

The death percentages obtained have been rounded off in multiples of ten Finally, in Tabs. 2 and 3 we can easily obtain death probability without using a calculating machine. With these tables we only have to make an addition (11).
We can obtain the probability with the independent term of every equation plus the weights" of every variable category in the equation (these "weights" can be found in Tab. 4); we then have to extrapolate the result in Graph I or in Tab. 5, which presents the probability at intervals of 10%, each one in relation to the above addition.

RESUME. Les Auteurs, dans le but d'am6liorer la d6termination de la probabilit6 de mort chez les patients br~116s, proposent une technique sophistiquée bas6e sur un mo&le de r6gression logique. La m6thode consid&re I I variables pr6sent6es par tons les patients brfil6s hospitalis6s chez une Unit6 de Brill6s pendant une p&iode de 3 ans. Un programme d'ordinateur Logress a 6té utilis6 pour calculer les variables ind6pendantes. Les Auteurs fournissent des Tables pour la calculation rapide de la probabilit6 de mort de ces patients.

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