This paper focuses in two parallel objectives. First it aims in presenting a series of Artificial Neural Network models that are capable of performing prognosis of abdominal pain in childhood. Clinical medical data records have been gathered and used towards this direction. Its second target is the presentation and application of an innovative fuzzy algebraic model capable of evaluating Artificial Neural Networks' performance [1]. This model offers a flexible approach that uses fuzzy numbers, fuzzy sets and various fuzzy intensification and dilution techniques to perform assessment of neural models under different perspectives. It also produces partial and overall evaluation indices. The produced ANN models have proven to perform the classification with significant success in the testing phase with first time seen data.
The wide range of problems in which Artificial Neural
Networks can be used with promising results, is the reason of their
growth [
Prognosis is a medical term denoting an attempt of physician to accurately estimate how a patient's disease will progress, and whether there is chance of recovery, based on an objective set of factors that represent that situation. The inference about prognosis of a patient when presented with complex clinical and prognostic information is a common problem, in clinical medicine. The diagnosis of a disease is the outcome of combination of clinical and laboratorial examinations through medical techniques.
In this paper various ANN architectures using different learning rules, transfer functions and optimization algorithms have been tried. This research effort was motivated form the fact that reliable and seasonable detection of abdomen pain constitute attainments in effective treatment of disease and avoidance of relapses. That is why the development of such an intelligent model that can collaborate with the doctors will be very useful towards successful treatment of potential patients.
decision rules can predict which children are at risk for appendicitis (appendicitis is the most common surgical condition of the abdomen). One such numerically based system is based on a 6-part scoring system: nausea (6 point), history of local RLQ pain (2 point), migration of pain (1 point), difficulty walking (1 point), rebound tenderness / pain with percussion (2 point), and absolute neutrophil count of >6.75 x 10`3/μL (6 point). A score <5 had a sensitivity of 96.3% with a negative predictive value of 95.6% for AA.
To date, all efforts to find clinical features or laboratory tests,
either alone or in combination, that are able to diagnose
appendicitis with 100% sensitivity or specificity have proven
futile. Also, there is only one research work [
The incidence of Acute Appendicitis (AA) is 4 cases per 1000 children. However appendicitis despite pediatric surgeons’ best efforts remains the most commonly misdiagnosed surgical condition. Although diagnosis and treatment have improved, appendicitis continues to cause significant morbidity and still remains, although rarely, a cause of death. Appendicitis has a male-to-female ratio of 3:2 with a peak incidence between ages 12 and 18 years. The mean age in the pediatric population is 6-10 years. The lifetime risk is 8.6% for boys and 6.7% for girls.
The 15 factors that are used in the routine clinical practice for the assessment of AA in childhood are: Sex, Age, Religion, Demographic data, Duration of Pain, Vomitus, Diarrhea, Anorexia, Tenderness, Rebound, Leucocytosis, Neutrophilia, Urinalysis, Temperature, Constipation. The sex (males), the age (peak of appearance of A.A in children aged 9 to 13 years), and the religion (hygiene condition, feeding attitudes, genetic predisposition) were in relation with a higher frequency for AA. Anorexia, vomitus, diarrhea or constipation and a slight elevation of the temperature (370 C - 380 C) were common manifestation of AA. Additionally, abdominal tenderness principally in the RLQ of the abdomen and the existence of the rebound sign, are strongly related with AA. Leucocytosis (>10.800 K/μl) with neutrophilia (neutrophil count > 75%) is considered to be a significant clue for AA. Urinalysis is useful for detecting urinary tract disease, normal findings on urinalysis are of limited diagnostic value for appendicitis.
The role of race, ethnicity, health insurance, education, access to healthcare, and economic status on the development and treatment of appendicitis are widely debated. Cogent arguments have been made on both sides for and against the significance of each socioeconomic or racial condition. A genetic predisposition appears operative in some cases, particularly in children in whom appendicitis develops before age 6 years. Although the disorder is uncommon in infants and elderly, these groups have a disproportionate number of compilations because of delays in diagnosis and the presence of comorbid conditions.
As diagnosis, there are four stages of appendicitis, including acute focal appendicitis, acute supurative appendicitis, gangrenous appendicitis and perforated appendicitis. These distinctions are vague, and only the clinically relevant distinction of perforated (gangrenous appendicitis includes into this entity as dead intestine functionally acts as a perforation) versus non-perforated appendicitis (acute focal and supurative appendicitis) should be made.
The present study is based on data set that is obtained from the Pediatric Surgery Clinical Information System of the University Hospital of Alexandroupolis, Greece. It consisted of 516 children’s medical records. Some of these children had different stages of appendicitis and, therefore, underwent operative treatment. This data set was divided into a set of 422 records and another set of 94 records. The former was used for training of the ANN, while the latter for testing. A small number of data records were used as a validation set during training to avoid overfitting. Table 1 represents the stages of appendicitis as well as the corresponding cases for each one. The 3rd column of Table 1 depicts the coding of possible diagnosis, as they used for ANN training and testing stages.
ev ten i tra m e ta pO tre
Data were divided into two groups, the training cases (TRAC) and the testing cases (TESC). The TRAC consisted of 417 concrete medical data records and the TESC consisted of 101. Each input record was organised in a format of fifteen fields, namely sex, age, religion, area of residence, pain time period, vomit symptoms, diarrhoea, anorexia, located sensitivity, rebound, wbc, poly, general analysis of urine, body temperature, constipation. The output record contained a single field which corresponded to the potential outcome of each case.
The determination if the TRAC and TESC data sets was
performed in a rather random manner. The training and testing
sample size which would be sufficient for a good generalization
was determined by using the Widrow’s rule of thumb for the LMS
algorithm which is a distribution free, worst case formula [
In the case examined here with 417 training examples used, the classification error that could be tolerated would be about 4%.
During experimentations, numerous ANN architectures,
learning algorithms and transfer functions were combined in an
effort to obtain the optimal network. For the Tangent Hyperbolic
(TanH) transfer function the input data were normalized (divided
properly) in order to be included in the acceptable range of [
Modular and radial basis function (RBF) ANN applying the
ExtDBD learning rule and the TanH transfer function were also
used in an effort to determine the optimal networks. RBFs have an
internal representation of hidden neurons which are radially
symmetric, and the hidden layer consists of pattern units fully
connected to a linear output layer [
Traditional ANN evaluation measures like the Root Mean Square
Error (RMS error), R2 and the confusion matrix were used to
validate the ensuing neural network models. It is well known that
the RMS error adds up the squares of the errors for each neuron in
the output layer, divides by the number of neurons in the output
layer to obtain an average, and then takes the square root of that
average. The confusion matrix is a graphical way of measuring the
network’s performance during the “training” and “testing” phases.
It also facilitates the correlation of the network output to the actual
observed values that belong to the testing set in a visual display
[
Finally, the FUSETRESYS (Fuzzy Set Transformer Evaluation
System) that constitutes an innovative ANN evaluation system has
been applied offering a more flexible approach [
Fuzzy logic enables the performance of calculations with
mathematically defined words called “Linguistics” [
x − a c − x μs(x;a,b,c)=max{min{ , },0} a<b<c (2) b − a c − b μs(x;a,b,c,d)= max{min{ x − a ,1, d − x },0}a<b<c<d b − a d − c (3) The model can produce various overall degrees of convergence (OVDECOV) for all of the training examples by applying either fuzzy T-Norm or fuzzy S-Norm conjunction operations, depending on the optimistic or pessimistic point of view of the developer. T15 15 15 15 7 9 9 7 7 0 9 0
μ ⎛ ~
⎜⎜ A∩ B~ ⎟⎟⎞
⎝ ⎠
Norms tend to produce lower aggregation indices so in the case of
ANN evaluation they can be considered as a pessimistic approach,
whereas the opposite happens with S-Norms [
= Min {μ ~ (Χ),μ ~ (Χ)} if Max {μ ~ (Χ),μ ~ (Χ)} = 1 else
A B A B μ ⎜⎜⎛⎝ A~∩ B~ ⎞⎟⎟⎠ = 0 (4)μ ⎜⎛⎜⎜⎝ Α ∩~ Β~⎞⎟⎟⎟⎠ = 2 − [μ A~{X ) μ+ μA~{B~X( X)μ)B~−( Xμ A)~{X )μ B~ ( X )] (5)
The fact that the FUSETRESYS evaluates each training/testing example separately, offers a more clear view of the ANN’s performance. In this way the developers know if the network operates extremely bad or well in specific cases.
Also when there are several neurons in the output layer, the
traditional approaches produce separate evaluation results for each
one whereas the FUSETRESYS can produce an additive
performance index (ADPERI) of the ANN. This could be done
under different perspectives and under different degrees of
optimism [
Finally the application of fuzzy set hedges offers the “dilution”
and the “intensification” options. In this way by using the dilution
approach the developer softens the membership function over the
fuzzy set and weakens the membership constraints so that a point
of the Universe of discourse is “truer” than it would be before [
In this way the ANN can be evaluated strictly by using a “very
well fit” evaluation option, or in a more relaxed way by using the
“somewhat fit” option. Of course it is in the developer’s hand to
decide the potential type of the ANN’s evaluation and the degree
of dilution or intensification. For a more detailed description of
FUSETRESYS please see [
Several experiments were performed. The following table 2
presents the structure of the four most effective Back Propagation
(BP) multilayer (ML) neural networks. In all cases of ANN
models, the classical approach for overcoming the overfitting
problem has been followed. More specifically, a set of validation
data have been provided to the algorithm in addition to the training
data. The algorithm has monitored the error with respect to this
validation set, while using the training set to drive the gradient
descent search. The number of weight tuning iterations performed
by the system, were determined in each case based on the criterion
of lowest error over the validation set. Two copies of the best
performing weights are kept: one copy for training and another one
of the best performing weights thus far.
made towards the development of modular ANN (MODANN) for
the classification problem solution. The term MODANN refers to
the “adaptive” mixtures of local experts (LOCEXP) as proposed
by [
They consist of a group of BP ANN referred to as local experts competing to learn different aspects of a problem. A “gating ANN” controls the competition and learns to assign different parts of the data space to different networks.
1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97
Code number for each evaluated record
The LOCEXP have the same architecture but they can apply
distinct learning rules or transfer functions. Also the number of the
output processing elements of the gating network is equal to the
number of LOCEXP used. The number of the neurons in the
hidden layer of the gating network should be larger than the
number of the output processing elements [
The following figure 2 depicts the gating probabilities for the optimal MODANN.. The above Table 6 presents a small sample of the 101 distinct PADECOV values produced by the FUSTRESYS.
Also the Einstein T-Norm was applied for the determination of the overall degree of convergence of the ANN. The ML#2 ANN had a very high OVEDECOV index with a value of 0.98299 whereas the other ML#3 ANN and the MODANN #REF1 had OVEDECOV indices as high as 0.97. The Drastic Product T-Norm was not applied in this research effort because it was proven unnecessary from the data in table 5 where there were no serious indications of extreme bad ANN performance in any of the testing examples.
The above research has obtained six ANNs with good level of convergence and it has proven that there exist at least four ANNs that have high performance indices, in the case of abdominal pain classification. Namely the best ANNs are two ML BP ANN, a RBF ANN and a MODANN using a referee gating network and two local experts. All of them have been described in the previous sections.
A very interesting part of the whole research effort is the
application of an innovative ANN evaluation model called
FUSETRESYS that uses fuzzy logic and fuzzy algebra proposed in
[
The new evaluation scheme has performed individual convergence indices namely PADECOV, for the output of each single data record used in the testing phase. The worst PADECOV value equals to 0.6666 which actually is the degree of membership of each data record to the FS “Actual output value equal to the desired value”. This worst case appears three times exactly in the same cases of data records, for the ML#2, ML#3, #1REF ANN and it shows that the classification capacity of the developed networks is not bad even in the worst cases. This conclusion becomes stronger by considering the fact that the second worst PADECOV index has a value of 0.833.
If an overall ANN validation is performed the traditional evaluation instruments agree with the FUSETRESYS that the most suitable ANN is the ML BP with code# 4 whereas all of the other developed ANN have almost an equally good performance. The Einstein T-Norm produces a higher “good performance index” for the MODANN than the traditional methods.
As it can be seen in table 7, the OVDECOV indices have very high values for ML#2 and for REF#1 and ML#3 networks when a “Partly fit” validation is performed. There is significant differentiation when a very strict evaluation is done under the linguistic “Very well fit”. The OVDECOV indices fall from 0.99 to 0.75 for ML#2, from 0.99 to 0.65 for #REF and from 0.99 to 0.71 for ML#3 respectively. This is a very useful approach and it shows the actual power of FUSETRESYS due to the fact that it shows the differentiation of the average convergence degree of the three ANN when more strict validation methods are applied. So ANN fed with the same data records in testing and appearing to have more or less the same performance, they are very seriously differentiated when more strict convergence validation methods are performed.
The proposed ANN architecture faces the appendicitis prediction quite satisfactory, based on both the above presented results, and the pediatric surgeon’s opinion that used these ANNs in their everyday routine clinical practice.
The innovative ANN evaluation model that was applied successfully in this research effort will be used extensively in the future, in an integrated effort to check its validity under various perspectives.
We would like to thank the pediatric surgeons of the Pediatric Surgeon Department of Medical School of Democritus University of Thrace, for their contribution in the concession of the medical records.