THEME OF ARTICLE (PREDICTION OF POSTOPERATIVE COMPLICATION DEVELOPMENT IN CHILDREN’S HEALTH WITH CONGENITAL HEART DISEASES OPERATED WITH ARTIFICIAL CIRCULATION WITH THE USE OF BINARY LOGISTIC REGRESSION METHODS AND DISCRIMINANT ANALYSIS) Текст научной статьи по специальности «Клиническая медицина»

Борисова Г.В.

Студентка, Национальный технический университет Украины «Киевский политехнический институт им. Игоря Сикорского», город Киев

ТЕМА СТАТЬИ (ПРОГНОЗИРОВАНИЕ РАЗВИТИЯ ПОСЛЕОПЕРАЦИОННЫХ ОСЛОЖНЕНИЙ У ДЕТЕЙ С ВРОЖДЕННЫМИ ПОРОКАМИ СЕРДЦА, ОПЕРИРОВАННЫХ С ИСКУССТВЕННЫМ КРОВООБРАЩЕНИЕМ С ИСПОЛЬЗОВАНИЕМ МЕТОДОВ БИНАРНОЙ ЛОГИСТИЧЕСКОЙ РЕГРЕССИИ И ДИСКРИМИНАНТНОГО АНАЛИЗА)

THEME OF ARTICLE (PREDICTION OF POSTOPERATIVE COMPLICATION DEVELOPMENT IN CHILDREN'S HEALTH WITH CONGENITAL HEART DISEASES OPERATED WITH ARTIFICIAL CIRCULATION WITH THE USE OF BINARY LOGISTIC REGRESSION METHODS AND

DISCRIMINANT ANALYSIS)

Borysova G.

Student, The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

АННОТАЦИЯ

В работе представлены разработанные математические модели прогнозирования послеоперационных легочных осложнений у детей возрастом до 3 лет с врожденными пороками сердца. Определены основные факторы риска.

ABSTRACT

The paper presents a developed mathematical model for prediction of postoperative pulmonary complications of children up to 3 years old with congenital heart defects. The main risk factors are identified.

Ключевые слова: легочные осложнения, прогнозирование, математические модели, врожденный порок сердца, логистическая бинарная регрессия.

Keywords: pulmonary complications, prediction, mathematical models, congenital heart disease, logistic binary regression.

Introduction

Congenital cardio-diseases remain an important problem to this day. Just in Ukraine every year for every 1000 newborns - 80 get diagnosed with congenital heart disease. Diseases of this kind require surgical treatment, in particular operations using artificial circulation (AC). However, it is known that violations of lung function of children after such surgical intervention reach 18.4%. Such complications frequently lead to an increase in postoperative morbidity or a death of the patient.

Therefore, it is urgent to create systems for predicting such complications to support decision making by the attending physician and further correction of patient management tactics.

Work's objective

Mathematical models building for predicting the development of pulmonary complications in the early

postoperative period of children with congenital heart defects operated with the use of artificial circulation.

Materials and methods

Data for work was provided by the Amosov National Institute of Cardiovascular Surgery. The data arrays contained 333 consecutive patient observations that were accumulated during the planned treatment for 2013-2015, including 172 girls and 161 boys from birth to the age of 3 years. The data also contained the condition of patients before and after the operation, as well as the presence of pulmonary postoperative complications.

Initial data was normalized and brought to the ordinal scale, which allowed the use of appropriate statistical methods to build models. To test the built models, the data were divided into two samples: training (80%) and test (20%).

Table 1

General clinical characteristic of patients

Training data set N=258 Test data set N=75

m (n=122) f (n=136) m(n=39) f(n=36)

Age 0,033 to 36 (12 ± 1 ) 0,033 to 37 (12±1) 0,06 to 33 (13±1) 0,1 to 32 (11±1)

Chromosomal and genetic pathologies 12 9,8% 13 9,5 % 2 5,1 % 5 13,9 %

Cardio complications during surgery 8 20,6 % 6 16,7 % 9 18 % 7 12,96 %

Pulmonary complications 9 23,1 % 8 22,2 % 13 26 % 14 25,93 %

Judging by general clinical characteristics, it can The distribution of patients by the number of post-

be noted that the greatest threat is in fact - pulmonary operative complications is presented in Table 2. complications.

Table 2

Comparative analysis of complication development frequency

Training data set N=258 Test data set N=75

m (n=122) g (n=i36) m (n=39) g (n=36)

Pneumonia 10 8,2% 6 4,3% - - 3 8,4%

Atelectasis 2 1,6% 2 1,4% 1 2,6% 4 11,1%

Respiratory failure 18 14,8% 11 8,1% 8 20.5% 1 2,8%

Postoperative pulmonary complications 30 24,6 % 19 13,8 % 9 23,1 % 8 22,3 %

Without complications 92 75,4% 117 86% 30 76,9% 28 77,8%

Logical analysis and relationships analysis with the use of correlation analysis allowed to identify 6 risk factors from 33 variables including gender, age, body mass index, cardiac complications during surgery, duration of artificial ventilation of lungs and hematocrit (end of surgery).

The coefficients of the regression equation ax.. n were determined, as well as the statistical significance

Table 3

The risk factors that entered the model of predicting the development of pulmonary complications in patients after surgery in the early postoperative period determined by the method of BLR

and the odds ratio and their effect on complications - in relation to the training data set.

Using the method of binary logistic regression (BLR), mathematical models for predicting the development of postoperative pulmonary complications were created based on significant factors.

Groups by risk factors Number of patients n Odds ratio OR (95%CI) Coefficient of the regression equation ai...n * P

Var. code names Risk factors

Without pulmonary compl. With pulmonary compl.

1 2 3 4 5 6 7

X1 Gender M 92 30 1,0 0,563 0,03

F 117 19 2,0 (1,1-3,8)

X2 Age Up to 1 year 101 37 3,3 (1,6-6,7) 0,696 0,001

More than 1 year 108 12 1,0

X3 Body mass index Normal 11 13 1,0 0,403 0,002

Lower than normal 82 32 3,0 (1,2-7,5)

Higher than normal 16 4 4,7 (1,2-18,4)

X4 Cardiac complications during surgery No 173 32 1,0 0,274 0,002

Other compl. 14 1 2,6 (0,3-20,4)

Cardiovascular system compl. 20 13 0,3 (0,1-0,6)

Pulmonary compl. 2 3 0,1 (0,02-0,8)

X5 Duration of artificial ventilation of lungs (hours) 0 2 1 1,0 0,780 0,000

1-6 131 11 5,9 (0,5-70,9)

7-12 30 3 5,0 (0,3-72,7)

13-24 17 8 1,1 (0,1-13,5)

>24 28 27 0,5 (0,04-6,1)

X6 Hematocrit (end of operation) Normal 89 31 1,0 0,585 0,008

Lower than normal 118 18 2,3 (0,02-5,7)

Higher than normal 1 1 0,3 (0,2-0,7)

a0* = -3,229

*)

a0 - constant term of BLR equation; p - significance.

The resulting mathematical model (on the training data set) looks like this:

k =—

1 1 + e"Zl

Where:

Z = 0,563-Xj + 0,696-x2 + 0,403-x3 + 0,274-x4 +0,78-x5 + 0,585-x(

ki - the probability of developing pulmonary complications (on the training data set);

e - the basis of natural logarithms (~ 2,71828); zi - variable that determines the degree of influence of risk factors on the development of pulmonary complications;

factor, that affects the development of pulmonary complications.

In addition, according to the Table 3 (column 5), it was determined that children with an artificial ventilation duration of between one and twelve hours have

Table 4

Risk factors (quantitative variables) that are included in the model of prediction of pulmonary complications development are determined using the DA method

. 0 ,8 x . 0 585 x -3 229

4 . °,/8 x5 . °,585 x6 3,229

the greatest chance of developing pulmonary complications in the early postoperative period. The high probability of development of pulmonary complications is observed among children with a body mass index higher than normal and among children under the age of one year.

Another method for selecting informative variables was discriminatory analysis (DA). Most informative risk factors are used to calculate discriminant functions.

№ Risk factors Var. code names in math. model Coefficient of linear discriminating function bi.m Level of significance, p

Absent pulmonary compl. n=209 Present pulmonary compl. n=48

1 2 3 4 5 8

1 Gender X1 5,483 4,827 0,030

2 Age X2 7,604 7,337 0,001

3 Body mass index X3 2,179 2,547 0,007

4 Cardiac complications during surgery X4 2,390 2,791 0,000

5 Duration of artificial ventilation of lungs (hours) X5 2,920 3,870 0,000

6 Hematocrit (end of operation) X6 6,053 6,290 0,008

b0= -20,135 b0 = -22,254

The resulting mathematical model (on the training data set) looks like this:

Y = 4,827x +7,337x2 +2,547x3 +2,791x4 +3,870x5 +6,290x6 - 22,254

Where:

Y - variable, which determines the degree of influence of prognostic factors on the development of postoperative complications;

xi.. n - factors, that affect the development of

postoperative complications.

Characteristics of the model quality assessment for training and test data sets built by the methods of BLR and DA are given in the Table 5.

Table 5

Characteristics of the model quality assessment for training and test data sets

BLR Observation Predicted absence of pulmonary compl. Predicted presence of pulmonary compl. Percentage of correctness % Sensitivity % Specificity %

Training data set, N = 258

Absence of pulmonary compl. 200 9 82,9 85,11 60,86

Presence of pulmonary compl. 35 14

Test data set, N = 75

Absence of pulmonary compl. 56 2 85,3 86,15 80,00

presence of pulmonary compl. 9 8

DA Training data set, N = 258

Absence of pulmonary compl. 160 49 75,97 92,49 42,35

Presence of pulmonary compl. 13 36

Test data set, N = 75

Absence of pulmonary compl. 48 10 76,0 85,7 47,37

Presence of pulmonary compl. 8 9

The obtained results confirm the adequacy of the models, since after constructing the ROC curves on the training and test data sets of the BLR and DA methods, areas under the curves had the following meanings:

S = 0,815 - training set (figure 1) and S = 0,857 - test set (figure 1) (p < 0,001) for BLR;

S = 0,813 - training set (figure 1) and S = 0,758 - test set (figure 1) (p < 0,001) for DA.

The similarity of the obtained results also confirms the correctness of the built models.

>

'ü c

Ï 0«-

0»

Training data set

ROC curves

—¿—j

J

ff

f

¡S rf

n SBLR = 0,815

SDA= 0,813

Test data set

ROC curves

I 0.4 0* 0» 10

1 • Specificity

a

Figure 1. ROC- curves, build using SPSS Statistics: a - on training data set (on the left), b - on test data set (on the right)

Conclusions

In the course of the work, mathematical models for prediction of postoperative complication development in children's health with congenital heart diseases operated with artificial circulation were built using the methods of BLP and DA. The proof of the quality of the models are the ROC curves that were built in the SPSS Statistics environment - the area under which in all cases was more than 0.7.

However, the model built on the binary logistic regression method has a better percentage of correctness and specificity compared to a model based on discriminant analysis.

These models will allow to determine the risk group relative to the patient's condition and can be used to develop decision support systems and to contribute in the correction of the patient's treatment path.

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