Annals of the MBC  vol. 4  n' I 
March 1991
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 3year 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 microorganisms (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:
Age 
Face Burns 
Sex 
Perineum Burns 
Body Area Burned 
Flame Burns 
Burn Depth 
Chemical Burns 
Death 
Electrical Burns 
Scald 




We classified all the data dichotomically
except for: age (019; 2039; 4059; 6079 and >80), b.a.b. (< 9%; 10 19%; 2039%;
4059%; 6089%; > 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.


AGE 


019 
2039 
4059 
6079 
>80 

0  9% 
83 
160 
100 
70 
13 


(0%) 
(0%) 

(46%) 


10  19% 
17 
36 
49 
17 
5 


(0%) 
(3%) 
(21%) 
(18%) 
(60%) 
B. 
20  39% 
21 
34 
26 
18 
4 


(0%) 
(0%) 
(23%) 
(39%) 
(75%) 
A. 
40  59% 
4 
25 
10 
5 
1 



(20%) 
(30%) 
(80%) 
(100%) 
B. 
60  89% 
5 
16 
7 
4 
4 


(20%) 
(37%) 
(28%) 
(50%) 
(75%) 

> 90% 
0 
5 
4 
5 
0 



(60%) 
(50%) 
(60%) 


Tab. I 

( ) 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.
B.A.B. 
AGE 

0  19 
20  39 
40  59 
60  79 
>80 
0  9% 
0 
0 
0 
10 
20 
10  19% 
0 
0 
lo 
20 
40 
20  39% 
10 
10 
20 
40 
60 
40  59% 
10 
20 
40 
60 
80 
60  89% 
30 
50 
60 1 
80 
90 
> 90% 
50 
70 
80 
90 ' 
100 

Tab. 3 

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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