Biomedical Engineering, VoL 34, No. 2, 2000, pp. 82-86. Translated from Meditsinskaya Te]chni,~'a, Vol. 34, No. 2, 2000, pp. 21-25. Original article submitted Apri! 21, t999.
Prognosis of Postoperative Complications Using Neural Networks V. G. Shchetinin, A. A. Solomakha, and A. V. Kostyunin
Urgent Problems of Medical Prognosis. Prediction of postoperative complications is an urgent problem. Its solution allows the probability of severe complications resulting in a patient's disability to be decreased [1-3, 7-10]. In addition, correct medical prognosis is necessary for determining optimum antibiotic therapy in each individual case. Finally, prognosis of a patient's state allows the duration of patient treatment in hospital (resuscitation unit) to be decreased, which provides significant savings in the treatment cost [3, 7, 8, 10]. Prognosis of postoperative compilations can be used for optimizing the operating schedule of hospitals with high surgical activity. Besides, the results of prognosis can be of interest to medical insurance companies, because this allows the quality of surgery in general and preoperative treatment in each individual case to be assessed. Knowledge of mechanisms of postoperative complications is very useful for studying their causes and finding approaches for decreasing the probability of complications. Review of Prognostic Methods. Several approaches to the problem of predicting postoperative complications have been suggested. The most well known approach to the problem is based on the assessment of significance of various risk factors by experts [1, 7]. First, all possible risk factors are determined. Then, the significance of each risk factor is assessed quantitatively. The resulting total value of risk is then compared to several threshold values (usually, low, medium, and high risk) determined by experts. According to the second approach, statistical methods (in particular, discriminant analysis) are used for decreasing the effect of subjective factors on the results of assessment of the risk factor significances and threshold values [1, 8-10]. For this purpose, a representative sample of independent and uniform observations of
Penza
State
University.
Burdenko
Hospital,
similar clinical cases should be obtained. The number of observations should be large enough (at least, N > 60). The probability of erroneous prognosis decreases with increasing number of observations. A positive discriminator is indicative of high complication probability; a negative discriminator, of low probability. If the discriminator is zero, a decision cannot be made. The structure of the discriminator, including the independent variables (factors), should be preliminarily specified. Then, the coefficients (parameters) of the discriminator are determined using the least-squares method. The resulting values of coefficients for independent variables allow the significance of each risk factor to be assessed. The third approach is based on the use o f neural networks [4, 13, 16]. This approach significantly decreases the effect of subjective factors and statistical method limitations on the results of prognosis. Neural networks usually consist of several neuronal layers connected to each other with synaptic links. According to the concept of connectionism, the output axons of each neuron in one layer are connected to all input dendrites of neurons of the other layer. The process of training of a neural network composed of a given number of layers and neurons consists in introduction of synaptic scales providing minimization of the empirical loss function (i.e., minimization of the number of identification errors). The neural networks trained by this method are able to solve prognostic problems. However, the enormous number of interneuronal synaptic contacts makes it difficult to interpret the results of such prognosis in conventional terms. In addition, successful training requires a large number of reference examples. The self-organization methods suggested by A. G. Ivakhnenko can be used to solve these problems [5, 14, 15]. Within the context of prognosis of early postoperative complications in abdominal surgery, the selforganization methods have been considered in [6, 12, 17, 181.
Penza.
82 1~006-3398100/3402-0082525.00© 2000 Kluwcr Acadcmic/Plenuln Publishers
Prognosis of Postoperative Complications
Formulation of the Problem Consider a sample of n cases of surgery outcomes unambiguously identified by one or several experts. The sample contains both cases of early postoperative complications (for example, suppurative inflammations) and normal outcomes (the patient convalescences on term). It is assumed that each case is represented by the results xl ..... x M of clinical and laboratory examinations performed during the preparation time. According to an expert (experts), this set of symptoms is sufficient for assessing the surgery outcome with considerable accuracy. A prognostic rule sufficient to predict the surgery outcome should be compiled based on this sample. This rule should be convenient for use and interpretation by the general practitioner. Method of Solution. The solution of this problem is reduced to neural network self-organization and its presentation as a compact system of logical (characteristic) equations providing adequate description of its behavior. The use of Boolean characters allows easy interpretation of prognostic rules. This form of knowledge representation is convenient for communicating to a surgeon what should be done during the preparation time to minimize the risk of postoperative complications. Additional Requirements and Limitations. Self-organization of the neural network in question should be possible under the following conditions. First, the training reference sample is not necessarily representative (n does not exceed several dozens). Identification performed by an expert or several experts can be erroneous because of the lack of exact clinical criteria. The information value of each diagnostic character (x~..... XM) is a priori unknown, and these characters are sometimes heterogeneous: quantitative, Boolean, or nominal. Second, neither the number of cell layers nor the number of neurons per layer should be specified to set the training procedure. The trained neural network should be composed of the minimal number of neurons and cell layers. The number of synaptic connections and the number M of symptoms should also be reduced to the minimum. Nevertheless, the trained neural netw o r k should commit as few errors as possible. Third, the trained neural network should be adequately represented as a compact set of simultaneous logical equations or productions widely used in medical expert systems. The set of simultaneous logical equations can be presented in tabular form, if necessary. The resulting tables can be used in medical diagnosis even without a computer. In both cases, the confidence level of the decision should be determined.
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The time o f neural network self-organization and compiling o f prognostic rules should be minimum (no more than 2-3 sec).
Self-Organization Algorithm The m e t h o d developed in our laboratory meets the requirements listed above. The method is designed to synthesize neural networks of optimum complexity. As a result of its implementations, trained neural networks are represented as a minimal set of simultaneous logical functions gi(u~, u=) of two variables tq and u=. Tabular values o f the functions go, g6, and gs are given in Table 1. Coding of Quantitative Symptoms. Coding of the quantitative symptoms is the first stage of the training process. O u r studies revealed that in most cases it is sufficient to divide the area o f definition of variable xi into two intervals by introducing a threshold ui and a coding f u n c t i o n h(ui). The values of u; and h(ui) should be chosen to reduce to a minimum level the number of identification errors e~. If the variable x~ goes above the threshold ui o f the coding function h(u;), codes 0 or 1 are used. T h e results of coding of quantitative symptoms are given in Table 2. Neural Network Self-Organization. Further in this work, each element or formal neuron of the first layer gi(a), xl~),j :~ k = 1..... m is characterized by the number e~ of identification errors. This number is compared with the n u m b e r s ej and e~. of identification of each individual s y m p t o m xj and x k. This element is discarded if either of the following conditions is met: es > ej or ei > % Otherwise, the value yj of this neuron is used in the next (second) layer giving rise to a combined neuron g~0,), xl,0. The selection procedure is repeated, and if at least one formal neuron meets the criterion of selection, a new layer is formed. As a result, a network of formal neurons is synthesized. The resulting network can be represented as a Steinbuch trainable matrix [1 I] (Fig. 1).
TABLE 1. Tabular Vakles of Logical Functions Values o f fimction g~(u~, u~) ll I
U~
0
0
0
0
I
0
I
0
1
0
t
0
0
1
0
I
1
1
1
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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Shehetinin et ai.
T A B L E 2. Initial Set o f D i a g n o s t i c C h a r a c t e r s for D i a g n o s i n g Postoperative Complications Parameter
Notation
u~
h(u)
1. Duration o f surgical operation (planned)
xo
4.3
0
2. Hemoglobin, jliter
x~
90.9
1
3. Erythrocyte count, ×10 ~2
x2
3.3
1
4. ESR, mm/h
x~
18.0
0
5. Residtml nitrogen, Mmol/Iiter
x4
21.4
0
6. Sugar. n~nogliter
xs
4.6
0
7. Total bilirubin, btmol/liter
x~
15.4
0
8. Urea, mmol/liter
x7
6.5
0
9. Total protein, g/liter
xs
63.7
1
10. Fibrinogen, g/liter
x,
1.3
l
ll. Prothrombin index, %
x~t~
70.6
1
Note: ESR, erythrocyte sedimentation rate.
The values of symptoms are applied to the first and second input dendrites of neurons of the first layer (horizontal buses in Fig. 1). The output axons o f these neurons are connected t h r o u g h vertical buses to the first input dendrites of neurons of the second layer. The junctions of the vertical and horizontal buses are marked with open circles. First input dendrites of neurons of the first layer are m a r k e d with filled circles. It should be noted that horizontal buses corresponding to non-informative symptoms have no junctions with
w
,go
I
~go w
•
#/&
I
1
~zt
Fig. i. T r a i n e d logical n e t w o r k w i t h inputs xo . . . . . x~o a n d o n t p u t s 3'0. . . . . Y2~. I n p u t d e n d r i t e s u~ of formal n e u r o n s g(u~, u21, g e {go, &,, g,~} are m a r k e d with solid circles.
vertical buses. The larger is the number of junctions between horizontal bus and vertical buses, the greater is the distinguishing capacity of the symptom. Interpretation of the Trained Network. The synthesized network can be easily represented as a set of simultaneous logical equations or syndromes sl . . . . . sx composing a symbolic rule
y = M-
of-
N ( s I. . . . .
si = g(Xk, Xi), i = 1 . . . . .
s,O, N,
where M is the number of syndromes sufficient to make the diagnostic decision, and N is the total number of neurons in the last layer or the number of syndromes. In this context, M is the decisive condition, and its value ranges from N1 to N, where NI = N / 2 + 1 for even-numbered N and Nj = (N + 1)/2 for odd-numbered N. Obviously, the reliability of the diagnostic conclusion increases with increasing number M, and it attains the maximum level at M = N. This set of simultaneous logical equations can be easily presented in tabular form (e.g., as diagnostic tables, which can be used even without a computer).
Prognosis of the Risk of Complications The developed algorithm was used for synthesizing and training a neural network for prognosis of the risk of early postoperative complications in abdominal surgery. The neural network was trained using a sample of five patients with abdominal surgery complications and eight patients with normal outcome of abdominal surgery. These cases were encoded as y = 0 and y = 1, respectively. The initial set of-symptoms was represented by the results of 19 laboratory and clinical examinations routinely performed after abdominal surgery. The trained neural network contained n = 2 layers. The first layer was composed of 11 fbrmal neurons; the second layer, of 21 formal neurons (Fig. 1). Seven variables (x3-xl 0) were the o u t p u t characters of the network (Table 2). It can be seen from Fig. 1 that these outputs have 1, 12, 1, 9, 7, 5, and 8 connections with vertical buses, respectively. The characters x 3 and x 5 can be excluded without decreasing significantly the accuracy of solution. Syndrome Complex and Diagnostic Table. The trained network can be represented as a syndrome complex:
Prognosis of Postoperative Complications
y = M - qf
.... N ( s
I .....
s19),
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T A B L E 3. Prognosis o f Complicated (C) and Normal (N) Outcomes of Abdominal Surgery x4
x,
where s~, ..., s~9 are syndromes:
sl ~- go(Y)o, Y9), sa = go(Y9, XI0)' S7 = g0(Y7, Xa), slo = gs(Ys, x4), s13 = go(Y3, x4), s16 = gs(Y> xs), sl9 = gs(Yl, xs);
x~
Xio
Outcome
M/N
0
0
0
0
C
17/19
0
0
0
l
C
15/19 17/19
0
0
1
0
C
S2 =
0
0
1
1
C
16/19
$5 S8 s)~ si4 Sly
0
1
0
0
C
15/19
0
l
0
1
C
17/19
0
1
1
0
C
16/19 19/19
gs(_Vlo, Xg), s3 = go(Ylo, &o), = g8(Y9, Xl0), S6 = go(Ys, X4), = go(Y6, X(,), S9 = go(Ys, X4)' = go(Y4, x4), s12 = gs(Y4, x4), = go(Y2, x6), sis = goO'>.xs), = go(Y1, x6), sis = go(Yl, xs),
YJ. . . . . 3qo are additional variables:
Yl = Y4 : 3:7 = 3qo =
xs
g0(Xl0, X4), Y2 = gS(Xlo, X4), )'3 = go(xJo, Xc,), g0(Xl0, Xs), Y5 = gS(xl0, X8), Y6 = ga(xv, X4), g0(X9, X6), Y8 = ga(x9, X(,), Y9 = gs(Xs, X4), g d x 6 , x4).
It should be noted that in the case under consideration the n u m b e r o f syndromes N = 19 and, therefore, the level o f decision making complexity is M = [10, 19]. This s y n d r o m e complex can be easily represented as a diagnostic table (Table 3). The sought solutions are one o f 25 = 32 intersections between lines corresponding to Boolean characters x4, x(,, x 8, Xg, and Xlo. C o n f i d e n c e o f a decision is evaluated as M / N . The closer is this value to 1, the greater is the probability o f correct prediction, tf M / N - ~ 0.5, a decision cannot be made (it is necessary to perform additional examinations).
Discussion The rule was tested in 118 clinical cases. A relatively high rate o f diagnostic errors (18%) was due to the lack o f exact clinical criteria of postoperative complications [12]. In c u r r e n t medical practice, almost all postoperative patients are treated with antibiotics. Introduction of the m e t h o d o f complication prognosis into medical practice w o u l d allow the antibiotic therapy to be prescribed only if necessary. Prognosis o f postoperative complications is especially useful in aged patients and patients with oncological diseases. The training samples in these cases
Note:
M/N
0
1
1
1
C
1
0
0
0
C
15/19
1
0
0
1
C
15/19
1
0
1
0
C
t6/19
1
0
1
l
C
16/19
l
1
0
0
C
14/t9
1
1
0
t
C
17/19
1
1
1
0
C
15/19
1
!
1
1
C
19/19
0
0
0
0
C
14/t9
0
0
0
1
C
16/19
0
0
1
0
C
16/19
0
0
1
I
C
19/19
0
1
0
0
C
I6/19
0
I
0
I
C
12/19
0
I
I
0
C
19/19
0
I
1
t
C
14/19
1
0
0
0
C
16/19
1
0
0
I
C
14/19
l
0
1
0
C
12/19
I
0
1
1
N
14/19
1
I
0
0
C
19/19
1
1
0
l
N
14/19
l
1
1
0
C
14/19
1
1
l
1
N
19/19
is the relative level of the decision confidence.
should contain corresponding reference examples o f normal and complicated o u t c o m e s . The developed algorithm can be used for constructing symbolic decision-making rules providing p r o g n o sis o f outcomes o f various surgical operations (for example, in cardiosurgery). The developed algorithm o f self-organization allows neural networks to be trained using unrepresentative training samples compiled by experienced physicians. The trained neural networks p r o v i d e d errorless identification of test examples. The n u m b e r of intervals for
86
Shchetinin et aL
c o d i n g q u a n t i t a t i v e p a r a m e t e r s was reduced to two. T h e n u m b e r of diagnostic symptoms a n d the number of neurons in t r a i n i n g n e t w o r k s was r e d u c e d to the m i n i m u m . T h e t r a i n e d neural n e t w o r k s were a d e q u a t e l y represented by a s y n d r o m e complex. T h e s y n d r o m e complex c a n be presented in t a b u l a r f o r m as a d e c i s i o n m a k i n g (prognostic) table. T h e a l g o r i t h m a l l o w s the confidence level o f the decision to be e v a l u a t e d . C l i n i c a l trials s u p p o r t e d the efficiency o f the c o m p i l e d p r o g n o s t i c rules. In m o s t cases (more t h a n 82%), the r e s u l t i n g prognosis was c o n s i s t e n t with clinical c o n c l u s i o n .
6.
7. 8. 9. 10.
11.
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12.
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