Prediction of fetal weight at varying gestational age in the absence of ultrasound examination using ensemble learning

Journal Pre-proof Prediction of fetal weight at varying gestational age in the absence of ultrasound examination using ensemble learning Yu Lu, Xianghua Fu, Fangxiong Chen, Kelvin K.L. Wong

PII:

S0933-3657(19)30570-6

DOI:

https://doi.org/10.1016/j.artmed.2019.101748

Reference:

ARTMED 101748

To appear in:

Artificial Intelligence In Medicine

Received Date:

11 July 2019

Revised Date:

6 October 2019

Accepted Date:

27 October 2019

Please cite this article as: Yu Lu, Xianghua Fu, Fangxiong Chen, Kelvin K.L. Wong, Prediction of fetal weight at varying gestational age in the absence of ultrasound examination using ensemble learning, (2019), doi: https://doi.org/

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Prediction of fetal weight at varying gestational age in the absence of ultrasound examination using ensemble learning Yu Lua , Xianghua Fua , Fangxiong Chenb , Kelvin K. L. Wongc,d,∗ a College

of Big Data and Internet, Shenzhen Technology University, Shenzhen, China of Automaton, Guangdong University of Technology, Guangzhou, China c Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China d School of Electrical and Electronic Engineering, University of Adelaide, Adelaide, Australia b School

ro of

Abstract

lP

re

-p

Obstetric ultrasound examination of physiological parameters has been mainly used to estimate the fetal weight during pregnancy and baby weight before labour to monitor fetal growth and reduce prenatal morbidity and mortality. However, the problem is that ultrasound estimation of fetal weight is subject to populations’ difference, strict operating requirements for sonographers, and poor access to ultrasound in low-resource areas. Inaccurate estimations may lead to negative perinatal outcomes. This study aims to predict fetal weight at varying gestational age in the absence of ultrasound examination within a certain accuracy. We consider that machine learning can provide an accurate estimation for obstetricians alongside traditional clinical practices, as well as an efficient and effective support tool for pregnant women for self-monitoring. We present a robust methodology using a data set comprising 4,212 intrapartum recordings. The cubic spline function is used to fit the curves of several key characteristics that are extracted from ultrasound reports. A number of simple and powerful machine learning algorithms are trained, and their performance is evaluated with real test data. We also propose a novel evaluation performance index called the intersection-over-union (loU) for our study. The results are encouraging using an ensemble model consisting of Random Forest, XGBoost, and LightGBM algorithms. The experimental results show the loU between predicted range of fetal weight at any gestational age from the ensemble model and that from ultrasound. The machine learning based approach applied in our study is able to predict, with a high accuracy, fetal weight at varying gestational age in the absence of ultrasound examination.

1. Introduction

na

Keywords: ensemble learning, fetal weight estimation, genetic algorithm, intersection-over-union, machine learning

Jo

ur

In obstetrics, several physiological parameters are regularly monitored for a pregnant women and the fetus in her womb such as fetal heart rate, uterine contractions, and fetal weight [1, 2, 3, 4]. Among them, the fetal weight is a regular indicator for fetal development. Thus, it is very important to obtain the estimated fetal weight (EFW). Screening for abnormal growth and fetus development is one of the main purposes of prenatal testing. However, no biomarkers have been found to accurately predict the fetal intrauterine growth restriction ∗ Corresponding author. E-mail address: [email protected] (Y. Lu), [email protected] (X. Fu), [email protected] (F. Chen), [email protected] (K. K. L. Wong)

(FGR) [5]. If the FGR and correct adverse conditions such as intrauterine hypoxia can be detected in time, then it would be greatly beneficial to further diagnose and reduce the mortality rate of children [6]. The prediction of the birth weight of a fetus in the third trimester can effectively guide obstetricians to choose a more reasonable delivery model for pregnant women, which can result in a better delivery outcome and reduce complications for the mothers and infants [7, 8]. Traditionally, the estimation of fetal weight in China is generally based on existing regression models that use multiple parameters established by foreign scholars. As a result, due to the individual differences in different populations, the use of these methods to estimate the weight of a fetus in China will result in large errors, especially for large or low-weight children. Strict require-

2. Methods

ments exist for operators and equipment during ultrasonic estimations, if the fetal head is deformed, oligohydramnios and abdominal fat exist, or the image quality is poor. These characteristics cause surface measurements that are not standard; therefore, the standardisation and proficiency of the operation of the sonographer directly affects the accuracy of the fetal body weight estimation.

2.1. Background Before the 1980s, in clinical practice, the estimation of fetal weight mainly relied on the abdomen palpation via measuring the uterus height and abdominal circumference of pregnant women. The results were affected by human factors and were easily affected by factors such as uterine tension, amniotic fluid volume, fetal position and abdominal wall thickness. Although the clinical measurement method is simple, the prediction error is large and did not satisfy the clinical requirements [14, 15]. During the past several years, for improving the accuracy of the EFW, there have been a number of studies using both single and multiple physiological parameter measurements, based on two-dimensional and threedimensional ultrasonic examinations, such as shown is Table 1. Although a single parameter measurement can reflect the growth and development of fetus, it is difficult to correctly obtain the fetal weight due to the differences between fetal individuals; thus, the EFW results are not accurate. Due to the lack of measurements based on single parameters, an estimation using two parameters was used to improve the accuracy. The BPD and AC were used to estimate the fetal weight for the first time [16], but its major limitation is that the prediction error is large such that the body weight is often underestimated. The BPD, HC and AC of 160 large-headed fetuses were measured, and two different formulas were used in [17]; one formula used the BPD and AC, and the other employed the HC and AC. The results of both formulas underestimated the fetal weight. Three formulas were used for 141 suspected macrosomia fetuses [18], namely, the Hadlock, Shepard and Tamura formulas. The results show that the accuracy of the formula using the AC and FL is the highest. Hadlock et al. proposed the combined formula of HC+AC+FL and BPD+AC+FC in 1985 [19], in comparison to the two-parameter measurement method. This multi-parameter measurement method more accurately estimated the fetal weight of 2500-4000g, and the estimation error of fetal weight, which was greater than 4000g, was smaller. In [20], Siemer et al. compared the accuracy of 11 EFW formulas that are more commonly used. The estimated weight of Hadlock formulas is better, and the multi-parameter estimation method can improve the accuracy of the EFW. However, there is no formula that can accurately estimate all the fetal weights. The final results of the regression equations for these 11 widely used fetal weight estimations remain unsatisfactory.

-p

ro of

Machine learning techniques have been applied in many fields [9, 10, 11, 12, 13], such as speech recognition, image processing, face recognition and automatic diagnosis. Machine learning algorithms have obtained information from experience and mine complex concepts implicit in experience and have established the mapping relationship between low-level features and high-level semantics. They can analyse the historical data of maternal check-ups and explore the relationship between conceptual entities through their own training, generalisation, self-organization and learning ability; thus, they are able to make more efficient and reasonable decisions.

ur

na

lP

re

In this paper, a dataset is established based on the electronic health record of pregnant women from the beginning of pregnancy to the prenatal delivery. The cubic spline function method was used to fit the relationships between characteristics such as the biparietal diameter (BPD), abdominal circumference (AC), head circumference (HC), and femur length (FL) (see Figure 1) and the gestational age. In addition to the characteristics obtained from ultrasound data, we also consider the physiological characteristics of the pregnant women, such as the pre-pregnancy body mass index (BMI), uterine height and AC. Then, a genetic algorithm is used to optimize the parameters of the three machine learning algorithms in parallel to construct the ensemble model. For the analysis, a total of 4212 clinical records from a hospital in Shenzhen, China, are used. The experimental results show that the intersection-over-union (loU) between the ensemble model that predicts the interval of fetal weight at any gestation and the interval of fetal weight from the ultrasound examination.

Jo

The main contributions of this paper are threefold: (1) The establishment of a temporal relationship between the gestational age and the main characteristics of fetal growth in accord with Chinese populations; (2) A proposed ensemble learning model based on a genetic algorithm with multi-parameter parallel optimisation, which can obtain better prediction results than any single model; (3) In the absence of ultrasound detection, this model has a certain degree of confidence in the fetal weight estimation at any gestation. 2

Colour Doppler ultrasound examination report Name: From:

********** in-hospital

Gender: female Clinical department: in-hospital

Age: 35 Exam ID: 180130861 Admission ID: 243601 Bed No: 02

Type of instrument: GEE6201404A Clinical diagnosis: 1: pregnancy 2 Checkpoint: second and third trimester Class I: parturition 1 pregnancy 39+2week monotocous over 18 weeks (incl. 18th week) live birth LOA in labour 9.31cm 7.24cm 22.00cm 3.40cm 0.52

HC:

33.08cm

EFW: FHR: UMBA Vmax: UMBA S/D:

3449.00±504.00 137.00bpm 62.04cm/s 2.10

AC: Amniotic fluid maximcon depth: Hear rate: UMBA Vmin:

35.10cm 6.20cm regular 29.56cm/s

-p

ro of

BPD: FL: AFI: PT: UMBA RI:

lP

re

Figure 1: A colour Doppler ultrasound examination report reproduced from its Chinese version, which includes biparietal diameter (BPD), abdominal circumference (AC), head circumference (HC) and femur length (FL), which are used in the study. AFI is an abbreviation of Amniotic Fluid Index. PT is an abbreviation of Placebtak Thickness. UMBA is an abbreviation of umbilical artery.

Table 1: The principle of calculating of EFW lies is the common use of a class of well-established regression models with multiple parameters standards for fetuses. Name Regression models

na

log10 EFW = 1.3596 − 0.00386 × AC × FL + 0.0064 × HC + 0.00061 × BPD × AC + 0.0424 × AC + 0.174 × FL log10 EFW = 1.304 + 0.05281 × AC + 0.1938 × FL − 0.004 × AC × FL log10 EFW = 1.335 − 0.0034 × AC × FL + 0.0316 × BPD + 0.0457 × AC + 0.1623 × FL log10 EFW = 1.326 − 0.00326 × AC × FL + 0.0107 × HC + 0.0438 × AC + 0.158 × FL log10 EFW = 1.5662 − 0.0108 × HC + 0.0468 × AC + 0.171 × FL + 0.00034 × HC2 − 0.003685 × AC × FL log10 EFW = [−1.7492 + 0.166 × BPD + 0.046 × AC − 2.646 × (AC × BPD)] − 3 EFW = 3200.40479 + 157.07186 × AC + 15.90391 × BPD2 log10 EFW = [−1.599 + 0.144 × BPD + 0.032 × AC − 0.111 × (BPD2 × AC)] − 3 lnEFW = −4.564 + 0.282 × AC − 0.00331 × AC2 EFW = 0.04355 × HC + 0.05394 × AC − 0.0008582 × AC + 1.2594 × (FL/AC) − 2.0661 − 3 EFW = 1.25647 × BPD3 + 3.50665 × FAA × FL + 6.3 EFW = 0.23718 × AC2 × FL + 0.03312 × HC3

Jo

ur

Hadlock I Hadlock II Hadlock III Hadlock IV Hadlock V Shepard Merz Warsof Cambell Otto20 Log Aoki Combs

The common indexes of estimating fetal weight by three-dimensional ultrasound include limb circumference, upper arm volume, thigh volume, and abdominal volume [21]. Hasenoehrl et al. [22] compared the accuracy of two-dimensional ultrasound and threedimensional ultrasound, and results show that threedimensional ultrasound has a higher accuracy. However, the current three-dimensional ultrasound operation

is complicated and time-consuming, and its method of estimating fetal weight is still being explored. A neural network for fetal weight prediction was proposed in [23] to improve ultrasound estimation of fetal weight over estimation with the other commonly used formulas generated from regression analysis. The approach using neural network that is used to train the samples to obtain a nonlinear relationship between the data can re3

long observation period of the pregnant women. To ensure sufficient sample distributions, the examination data must be after the 16th week of pregnancy. Effective preprocessing of the data is a key step to improve the accuracy of the prediction model. The specific data screening process is illustrated in Figure 2.

5000 pregnant women

425 with medical histroy, etc.

89 nutrition health is not up to standard

2.2.1. Predictive model attribute parameters A hospital identification number for the pregnant women is used as the main index to extract the health records from the beginning of the pregnancy to the delivery for obtaining the birth weight. Y is defined as the EFW from ultrasound examination, and X is defined as the set of input parameters for the model. The final dataset X consists of 14 parameters, consisting of xh , x pw , x p , xn , xa , xg , xgg , x f w , x pb , xcb , xBPD , xAC , xHC , and xFL , and the meaning of each parameter is shown in Table 2.

4328 pregnancy and childbirth data which are relatively complete

42 abortion 54 early childbirth 20 congenital malformations

Parameters

ro of

34 less than 153cm in height 124 not meet the BMI requirement

xh x pw xp xn xa xg xgg xfw x pb xcb xBPD xAC xHC xFL

Height of a pregnant woman (cm) Weight of a pregnant woman (kg) Gestational week Number of pregnancy Age of a pregnant woman Weight gain of a pregnant woman (kg) Fundal height of a pregnant woman Abdominal circumference of a pregnant woman BMI of pre-pregnancy BMI of current pregnancy Fetal biparietal diameter (cm) Fetal abdominal circumference (cm) Fetal head circumference (cm) Fetal femur length (cm)

4212 pregnant women’s historical physical examination data meet requirements

-p

Table 2: Meaning of the different parameters.

re

Figure 2: Data screening process.

na

2.2. Preprocessing

lP

duce the error of predicting the fetal weight, but the accuracy of fetal weight estimation at the extremes of the weight range is not satisfactory. There are also some other machine learning based approaches [24, 25, 26] to estimating fetal growth prediction or preterm infants survival.

ur

The experimental data are obtained from Shenzhen Bao’an Maternity & Child Healthcare Hospital, which is the largest maternity and child healthcare hospital in Shenzhen City, China. A total number of 5,000 samples from 2017 are randomly selected, and no general obstetrics, gynaecology and other general medical histories regarding prenatal care are screened out. It was started from 16 weeks before parturition, as measured by the menstrual date and nutritional health, including the maternal height (≥153 cm), BMI (18.5 ≤ BMI < 30kg/m2 ), erythroprotein concentration (≥110 g/L), and whether the pregnant women receive anaemia treatments, or have any special diet recipes. It can effectively reduce the risk factors in the FGR and preterm birth. At the same time, the distribution of pregnancy tests is not equal, and their types are different during the

Meaning

Jo

2.2.2. Feature standardisation After data preprocessing, 4212 samples meet the conditions. However, the different physiological parameters have different units and orders of magnitude. To reduce these influences on the prediction results, the data need to be normalized before the model is trained to ensure that each feature is at the same order of magnitude. The normalization is shown as equation (1): y=

2(x − xmin ) −1 xmax − xmin

(1)

where x represents the current feature value, xmin and xmax represent the minimum and maximum values of 4

the current feature, respectively, and y is the normalised feature value. The data range is [−1, 1].

2.3.1. Random forest regression model Random forest is a supervised learning algorithm [29]. The random forest regression algorithm is a combined model, which incorporates a regression decision subtree. According to the principle of ensemble learning, the mean of each decision subtree is taken as the regression prediction result. The steps of the random forest regression algorithm are roughly as follows:

2.2.3. The construction of the fitted function Despite the widespread use of ultrasound technology worldwide, people are concerned about the low rate of detection of fetal developmental abnormalities in routine clinical practice [27]. However, there is a lack of appropriate international standards similar to those used to monitor infant growth [28]. In addition, there are some differences in fetal growth characteristics in different regions. Therefore, this study uses the cubic spline function method to fit four characteristics of ultrasound detection. Specifically, at the interval [a, b], a = t0 < t1 < ... < tn < t(n+1) = b, f (x) is defined as a function of [tn , b]. If f (x) meets the following two conditions: (1) f (x) is a cubic polynomial on each interval of [a, t1 ], [t1 , t2 ],..., [tn , b] and (2) f (x) and its second derivative are continuous at ti (i = 1, 2, ..., n), then the piecewise polynomial function is called the cubic spline function. The point ti is called the node of the spline function. The cubic spline function can be shown in equation (2):

ro of

-p

(2)

re

f (x) = di (x − ti )3 + ci (x − ti )2 + bi (x − ti ) + ai

1. Use the bootstrap resampling method to, randomly generate k training sets θ1 , θ2 , ..., θk . Each training set can generate a decision tree, where k is the number of random forests of the tree {T (x, θ1 )}, {T (x, θ2 )}, ..., {T (x, θk )}. 2. In the process of node splitting, m features are randomly extracted from the M-dimensional feature samples as the split feature set of this node, and m is set according to the sample size. 3. No pruning is done for each decision tree to maximize its growth. 4. When there is a new data X = x, the prediction of a the single decision tree T (θ) can be obtained by averaging the values of the leaf nodes l(x, θ). If Xi belongs to the leaf node l(x, θ) and is not 0, then the weight vectorωi (x, θ) is shown in equation (4):

a

lP

where ti ≤ x ≤ ti+1 , i = 0, 1, ..., n. The sum of squared P residuals for ti is (yi − g(ti ))2 , and the penalised sum of the squares of the above selection functions is shown in equation (3): Z b X S(f) = (yi − f (xi )) + γ ( f 00 (x))2 dx (3)

na

For a given smoothing parameter γ(γ > 0), the estimation function f (x) minimises the values of S ( f ), which is referred to as a penalty least squares estimate. The smoothing parameter γ can be given by γ = CQ3 /1000, C is a given constant, and Q is the interquartile range of the explanatory variable.

ωi (x, θ) =

l{Xi ∈ Ri (x, θ)} #{ j = X j (x, θ)}

(4)

5. Given an independent variable X = x, the predicted value of a single decision tree is the weighted average of the predicted values Yi (i = 1, 2, ..., n). The predicted value of the single decision tree is shown in equation (5): µ=

N X

wi (x, θ)Yi

(5)

ur

i=1

6. By averaging the decision tree weights X = X(i ∈ {1, 2, ..., n}), the weight ωi (x) is obtained for each observation i ∈ (1, 2, ..., k), as shown in equation (6): k 1X ωi (x) = wi (x, θ)y (6) k i=1

Jo

2.3. Machine learning algorithms At present, the estimation of the fetal weight at home and abroad is generally adopted to the multi-parameter estimation method based on the results of ultrasound examination. However, because of the differences in the women physionomy from China and women from foreign countries, this study uses machine learning algorithms with the advantages of self-training, generalisation, self-organisation and learning ability to explore the relationship between the maternal physical characteristics and the fetal weight and to further improve the accuracy of the prediction.

7. For all y, the prediction of random forest can be recorded as µ µ=

N X i=1

5

wi (x)Yi

(7)

5. Solving the optimal solution of the objective function: P T 1 X ( i∈gi gi )2 (t) ˜ P C (q) = − + γT (12) 2 j=1 i∈I j hi + α

2.3.2. XGBoost model The boosting algorithm is one of the most popular algorithms for ensemble learning [30]. The weights of each weak classifier are superimposed to form a strong classifier, which reduces the error and improves the accuracy. Gradient boosting [31] is an improvement in the basis of boosting method. The idea of the algorithm is to continuously reduce the residuals and further reduce the residual of the previous model in the gradient direction to obtain a new model. XGBoost [32] is an improved version of the gradient boosting algorithm. XGBoost implements a second-order Taylor expansion for the loss function and obtains the optimal solution for the regular term in addition to the loss function. This algorithm makes full use of the parallel computing advantages of a multi-core central processing unit (CPU) to improve the accuracy and speed. The algorithm steps can be expressed as follows:

i

ro of

2.3.3. LightGBM model LightGBM [33] is a gradient learning framework based on tree learning that supports efficient parallel training. Compared with XGBoost, the training efficiency is faster, the accuracy is higher, and it has a greater advantage in processing large-scale data. This model adapts to several optimisation algorithms. For instance, the framework is used to discretize continuous floating-point eigenvalues into k integers and constructs a histogram decision tree algorithm with width k. A leaf-wise leaf growth strategy optimization algorithm with a depth limitation is proposed to ensure high efficiency while preventing over-fitting.

(8)

-p

1. Objective function: X X l(ˆyl , yi ) + ( fk ) C(φ) =

where I j = {q(Xi ) = j} is defined as the instance set of leaf j.

k

where ( fk ) = γT + 21 α||ω||2 . Specifically, l is a differentiable convex loss function that measures the difference between the prediction yˆ l and the target yi . While  penalises the complexity of the model (i.e., the regression tree function), T is the number of leaves in the tree, and K is the number of tree ensemble, γ and α are expressed as proportion fk (x) = Wq(x) corresponds to an independent tree structure q and leaf weights W. 2. Training objective function: n X

l(yi , yˆ (t−1) + ft (xi )) + ( ft )

i=1

na

Ct =

lP

re

2.3.4. Genetic algorithm The genetic algorithm [34] is based on the basic principles of biogenetics, i.e., simulating the natural laws of natural biological populations. The core idea of the algorithm encodes the parameters to be optimized into a series of chromosomes. Through the natural inheritance of these chromosomes, natural selection occurs using the already established ”natural rules”, that is, the fitness function. In this process, the highly adaptive chromosomes are more likely to survive; thus, the evolution of the entire ”population” is realised after several generations. The moderately largest chromosome may be the global optimal solution to the problem. The flowchart is shown in Figure 3.

(9)

Let yˆ (t) be the prediction of the i-th instance at the t-th iteration, adding ft to minimise the following objective. 3. The Taylor two-order expansion of the objective function is approximated by:

ur

2.4. Approach to estimating the fetal weight 2.4.1. Ensemble methods Ensemble methods in machine learning that create multiple models are powerful prediction techniques since they can increase the diversity of algorithms and reduce generalisation error to improve the accuracy of the results [35]. This method is divided into stacking, blending and voting. Ensemble methods have two basic elements: one is that the correlation between single models should be as small as possible, and the other is that the performance between single models is not too different. In practice, it is often the case that a single model with a low correlation coefficient and good performance can significantly improve the final prediction

n X 1 [l(yi , yˆ (t−1) ) + gi ft (xi ) + hi ft2 (xi )] + ( ft ) 2 i=1 (10) where gi = δyˆ(t−1) l(yi , yˆ (t−1) ), and hi = δ2yˆ(t−1) l(yi , yˆ (t−1) ) are first and second order gradient statistics on the loss function. 4. Removing the constant term:

Jo

C˜(t) 

C˜(t) 

n X 1 [gi ft (xi ) + hi ft2 (xi )] + ( ft ) 2 i=1

(11) 6

sults of the random forest model, consisting of the following: the maximum number of features is used by a single decision tree δmax f , the minimum number of leaf nodes δmin l , the maximum depth of the decision tree δmax d , and the minimum number of samples required for the internal node subdivision δmin s . For the XGBoost model, the influence factor mainly includes the learning rate θeta , the maximum depth of the tree θmax d , and the minimum leaf node sample weight θmin w . Regarding the LightGBM model, the influence factors consist of the tree model depth γmax d , the minimum number of leaf nodes γmin l , the minimum leaf node weight γmin w , and the learning rate γeta . If a traditional grid search method is used to optimise 15 parameters, then optimisation takes a very long time. The genetic algorithm, as an intelligent evolutionary algorithm, has a strong global search capability. Therefore, this study proposes an ensemble model based on the multi-parameter parallel optimisation of the genetic algorithm. The specific steps are as follows:

Population initialisation

Calculate the fitness value of each individual in the population

Termination condition

false

ro of

Survival of the fittest Choose a parent individual

true

Selection, variation, crossover operations Generation of next generation population

1. Data preprocessing: the original data is preprocessed and divided into a training set and a testing set. 2. Initialise parameters of the genetic algorithm such as the population size, crossover probability, and mutation probability. 3. Select the optimisation parameters and interval. According to the above analysis, there are a total of 15 parameters to be optimised: 4 parameters of the random forest model, 3 parameters of the XGBoost model, 4 parameters of the LightGBM model, and 4 parameters of the ensemble model. The optimal interval is determined by chromosome coding. 4. Determine the fitness function. Calculate the average relative error between the predicted value and the true value, so the fitness function is shown in equation (14):

-p

false

Maximum number of iterations

Termination

lP

Figure 3: The flowchart of the genetic algorithm.

re

true

ur

na

result. The random forest is a kind of bagging algorithm, which focuses on reducing the variance. XGBoost is a boosting algorithm, which focuses on reducing the bias. However, LightGBM is a recently proposed algorithm. Therefore, the three classes of algorithms in this paper satisfy the diversity, correlation, and performance requirements. In this study, voting is used to construct an ensemble model, which is shown in equation (13): hα ( f ) = α0 + α1 f1i + α2 f2i + α3 f3i

n

MAPE =

(13)

f i − yi 1 X hα ( f i ) − yi ( +| 1 |+ n i=1 yi yi |

Jo

where α1 , α2 , α3 are the weight parameters, α0 is a constant, i represents the number of i-th samples i = 1, 2, ..., n and f1 , f2 , f3 represent the predicted values of the random forest, XGboost, and LightGBM models, respectively.

f i − yi f2i − yi |+| 3 |) yi yi

(14)

where hα ( f i ) represents the ensemble model predictive value, and yi denotes the true value. Moreover, f1i , f2i , f3i are the output values of the random forest, XGBoost, and LightGBM models, respectively, and n is the number of training sets. 5. Parameter optimisation: First, decode the chromosomes in the population; then calculate the fitness value of each generation of the population, and

2.4.2. Multi-parameter optimisation based on the genetic algorithm According to the above basic model analysis, the parameters that have a large impact on the prediction re7

perform the survival of the fittest. Finally, determine whether the population performance satisfies the maximum number of genetics, and if so, the optimal parameter is output; otherwise, according to the genetic strategy, the selection, crossover and mutation operations are used to obtain the offspring. 6. Result judgement: if the MAPE error requirement is satisfied, then the optimisation is finished. Otherwise, repeat step (4). 7. Input the test sample to obtain the best prediction result. The detailed process is shown in Figure 4.

Original data

Training set

Parameters initialisation

Data Processing

ensemble model Random forest

XGBoost Testing set

n 1 X |yture − y pred | n i=1 ytrue

true

Trained model

(15)

Prediction result

na

1 2 f scope ∩ f scope

lP

re

where yture denotes the true label and y pred denotes the predicted fetal weight. To better reflect the coincidence between different intervals, this paper introduces a novel concept, originally used in the field of image processing, namely, loU. This method can reflect the coincidence degree of different learning algorithms for predicting the fetal weight interval, and it is shown in equation (16): IoU =

1 2 f scope ∪ f scope

false

Parameters encoding

Initialising population parameters

Calculate fitness values

Updating population

Selecting, crossing and mutating to produce the next generation population

(16)

1 where f scope represents the fetal weight prediction range 2 of the algorithm model and f scope represents the fetal weight range of the ultrasound examination.

ur

false

Whether the maximum number of iterations is reached

true

Figure 4: Fetal weight estimation process based on the genetic algorithm.

Jo

3. Results

Whether the accuracy meets requirements

-p

MRE =

ro of

lightGBM

2.4.3. Performance evaluation index This paper uses two indexes to measure the performance of the ensemble model. The first index is the mean relative error (MRE), which is a measure of the credibility. If n is the number of samples, then the MRE is shown in equation (15):

3.1. Analysis of the fitting function

The fitting results of the percentile curves are shown in Table 3. Among the percentiles, the R2 (determination coefficient) of the BPD is at least 0.953, and the MRE is at most 0.20. The minimum R2 of the AC is 0.955, and the maximum MRE is 0.22. The minimum R2 of the HC is 0.950, and the maximum MRE is 0.24. The minimum R2 of the FL is 0.951, and the maximum MRE is 0.16. The R2 of each index is above 0.95, and

Based on the screening steps in the previous sections, a total of 4212 samples were selected, of which 3370 samples are used as the training sets and 842 samples are used as the test sets. Then, a cubic spline function was used to establish a functional relationship between the four indexes of ultrasound examination and the pregnancy. The fitting results are shown in Figure 5. 8

ro of

Figure 7: Mean relative error of different models. Figure 5: Four feature fitting curves.

na

lP

re

-p

8%. The MRE of the formula method in [16] is 14.6%. The MRE of the ensemble model is approximately 6%. In the absence of ultrasound detection, the fitting function is used to fit the four eigenvalues, and then the integrated model is used to predict the fetal weight range. The loU index is used to prove the effectiveness of the algorithm (see Table 4). In Table 4, in the absence of an ultrasound examination, the ensemble model, can predict the fetal weight range. Compared with the ultrasonic examination, the loU value is greater than 0.6. To some extent, the fetal weight can be predicted at any gestation according to the maternal characteristic parameters and the fitted four ultrasonic characteristic values. The prediction results of some samples are shown in Fig. 7. The ”0”, ”1”, ”2”, ”3” and ”4” values of the graph’s abscissa represent the ultrasonic examination, this paper, the XGBoost, the LightGBM, and the random forest models, respectively, and the ordinate expresses by the predicted fetal weight range. From the graph results, after optimizing the multi-model parameters based on the genetic algorithm, the advantages of each model can be effectively utilized, so that the fetal weight prediction interval is closer to the fetal weight range of the ultrasound examination.

Figure 6: Mean relative error of different models.

ur

the MRE is within the tolerance; thus, the fitting result is satisfactory.

Jo

3.2. Model prediction analysis

The random forest, XGboost, LightGBM models and the ensemble model will use the genetic algorithm. Multi-parameter parallel optimisation is used to predict the fetal weight, which is compared with the multiparameter formula [16] used in an ultrasonic examination. The experimental results are shown in Figure 6.

3.3. Analysis of the fetal growth change The fetal growth curve is an important index of the fetal health status, which can provide a basis for early diagnosis and the prevention of fetal abnormalities. At the same time, pregnant women can observe the trend of

As shown in Figure 6, the MRE based on the single machine learning algorithm model is approximately 9

Table 3: Fitting results of each percentile curve.

Centile P95 P75 P50 P25 P10

γ 0.3 0.2 0.1 0.2 0.3

BPD MER 0.16 0.12 0.09 0.20 0.15

R2

γ

AC MER

R2

γ

HC MER

R2

γ

FL MER

R2

0.954 0.960 0.965 0.953 0.955

0.4 0.3 0.2 0.3 0.1

0.22 0.18 0.13 0.17 0.23

0.958 0.966 0.970 0.963 0.955

0.4 0.2 0.2 0.3 0.1

0.20 0.17 0.15 0.24 0.18

0.956 0.961 0.962 0.950 0.957

0.4 0.3 0.2 0.1 0.2

0.16 0.12 0.08 0.11 0.09

0.951 0.953 0.967 0.955 0.960

Table 4: IoU of the different algorithms.

Fetal weight interval of ultrasound

Random forest XGBoost LightGBM This paper

ro of

IoU

0.607 0.623 0.610 0.650

re

-p

fetal weight changes in each gestational week, including the average fetal weight curve, the 10th percentile curve and the 90th percentile curve. Therefore, based on the characteristic parameters of pregnant women and the fitted ultrasound characteristic parameters, this study uses the ensemble model to predict the fetal weight at the current moment and to timely understand the trend of fetal growth. When comparing with the 10th and 90th percentiles of China’s fetal growth standard curve [36], if the curve is lower than the 10th percentile, the fetus is small for its gestational age (SGA), and conversely, when the curve is greater than the 90th percentile, the fetus is large for its gestational age (LGA). A sample was randomly selected from the testing set, and the fetal weight is predicted by the ensemble model proposed in this study. The experimental results are shown in Fig. 8.

Figure 8: Fetal growth prediction curve.

na

lP

Table 5: Different models that predict the fetal birth weight.

Parameters Hadlock[17] GA-BP[23] Random forest XGBoost LightGBM Ensemble model in this paper

MRE (%)

Accuracy (%)

10.2 7.5 8.3 8.2 8.4 7.0

52.3 63.1 60.0 62.1 59.4 64.3

ur

Table 5 shows that the ensemble model proposed in this paper predicts the fetal birth weight and has a certain degree of improvement in the MRE and accuracy compared with the single machine learning algorithm model and the multi-parameter method. The MRE is reduced by approximately 3%, and the accuracy is improved by approximately 12%.

3.4. Experimental analysis of fetal birth weight

Jo

To verify the superiority of the model, the ensemble model is used to predict the birth weight of the fetus. From the testing sets, 527 samples have a record of an ultrasound examination within one week prior to delivery. In addition, it is more objective to evaluate the accuracy of different algorithms, this study uses another criterion, that is, the error between the predicted and actual fetal weight is within ±250g, and the prediction is considered to be accurate [37]. Therefore, different algorithms are used to predict fetal birth weight. The experimental results are shown in Table 5.

4. Discussion In clinical practice, the growth parameters of the fetus are mainly obtained by ultrasound examination and are then compared with the fetal growth standard curve. 10

5. Conclusion

However, there are limitations in the actual operation. Obstetricians can only judge abnormal fetal development and a reasonable body weight based on the current results. However, it is impossible to observe the growth trend of the fetus in each gestational age, which results in reducing the accuracy of the diagnosis.

According to the historical data of the physical examinations of pregnant women, this study uses the cubic spline function method to fit the functional relationship between the BPD, AC, HC, and FL and the gestational age and proposes an ensemble model based on the genetic algorithm parallel optimization of multiple parameters to predict the fetal weight at any gestational age compared with ultrasound-based estimation methods. The experimental results show that the ensemble model proposed in this paper can predict the growth curve of a fetus according to the changes in the related parameters of pregnant women and can effectively reduce the estimation error in the fetal weight. Additionally, the MRE is reduced by 8%. The loU of the ensemble model is 0.64, the MRE in the birth weight of the fetus is reduced by 3%, and the accuracy is increased by 12%. In the future, a time series of the historical physical examination data of pregnant women can be used to improve the prediction model to further improve the accuracy and practicability of model’s prediction.

-p

ro of

In this experiment, the examination data of pregnant women are integrated, and the eligible sample data are screened to establish the multi-dimensional data structure and form a basic database. A cubic spline function is adopted to fit the relationship between several features of ultrasound detection and the gestational age. Using this approach, combined with multi-channel data information, the powerful ability of a computer and an effective machine learning algorithm model, the fetal weight at any gestational age can be predicted. This is particularly useful for unavailability of obstetric ultrasound in most low-resource areas [38]. Pregnant women can always be aware of the fetal growth trend, which is of great significance for the auxiliary diagnosis of fetal abnormal development. This study proposes an ensemble estimation model based on the multi-parameter parallel optimization of a genetic algorithm. On one hand, this approach pays attention to the fetal growth curve and understands and predicts the development of the fetus, which will help to improve the accuracy of clinical diagnosis. On the other hand, in the absence of ultrasound testing, pregnant women can always understand the impact of their own nutrition, health and other aspects on fetal development, and reasonable advice can be provided. For example, if a pregnant woman in the 28 gestational week wants to know if her baby’s weight is standard, then a comparison can be made with the standard fetal weight at the 28 gestational week.

re

Acknowledgement

na

lP

This work is supported by the Natural Science Foundation of Top Talent of Shenzhen Technology University (Grant No. 2019010801011) and the National Natural Science Foundation of China (No. 81771927, No. 61472258). We also would to like to thank all staff at the Shenzhen Bao’an Maternity & Child Healthcare Hospital for participating in the study.

References [1] J. Villar, L. C. Ismail, C. G. Victora, E. O. Ohum, International standards for newborn weight, length, and head circumference by gestational age and sex: the Newborn Cross-Sectional Study of the INTERGROWTH-21st Project, The Lancet 384 (9946) (2014) 857–868. doi:10.1016/S0140-6736(14)60932-6. [2] A. T. Papageorghiou, E. O. Ohuma, D. G. Altman, T. Todros, International standards for fetal growth based on serial ultrasound measurements: the Fetal Growth Longitudinal Study of the INTERGROWTH-21st Project, The Lancet 384 (9946) (2014) 869–879. doi:10.1016/S0140-6736(14)61490-2. [3] Y. Lu, Y. Gao, Y. Xie, S. He, Computerised Interpretation Systems for Cardiotocography for both Home and Hospital Uses, in: Proceedings of the 31st IEEE International Symposium on Computer-Based Medical Systems (CBMS 2018), 2018, pp. 422–427. doi:10.1109/CBMS.2018.00080. [4] M. SaberIraji, Prediction of fetal state from the cardiotocogram recordings using neural network models, Artificial Intelligence in Medicine 96 (2019) 33–44. doi:10.1016/j.artmed. 2019.03.005.

Jo

ur

The weight of a fetus is closely related to the nutritional status of the pregnant woman. If the pregnant mother’s diet is unreasonable, such as with picky eaters, partial eclipse, and avoidance eaters, nutritional deficiencies may be apparent, so that the weight of fetus is lower than normal. Therefore, pregnant women should pay attention to increasing their nutrition, especially with the diversification of food, to ensure that the fetus is well developed, which is an important part of eugenics. Of course, over-nutrition cannot be an issue with pregnant women, otherwise the weight gain will be too fast, and the fetus will be too large, which will increase the burden during pregnancy and the difficulty during childbirth. 11

[22]

[23]

[24]

[25]

[26]

re

[27]

ro of

[21]

T. Goecke, R. L. Schild, Fetal weight estimation by ultrasound: Comparison of 11 different formulae and examiners with differing skill levels, Ultraschall in der Medizin 29 (2) (2008) 159– 164. doi:10.1055/s-2007-963165. J. Milner, J. Arezina, The accuracy of ultrasound estimation of fetal weight in comparison to birth weight: A systematic review, Ultrasound 26 (1) (2018) 32–41. doi:10.1177/ 1742271X17732807. G. Hasenoehrl, A. Pohlhammer, R. Gruber, A. Staudach, H. Steiner, Fetal Weight Estimation by 2D and 3D Ultrasound: Comparison of Six Formulas, Ultraschall in der Medizin 30 (6) (2009) 585–590. doi:10.1055/s-0028-1109185. H. Zhu, J. Tao, K. Yu, X. Zhu, Z. Yuan, Fetal Weight Prediction Analysis Based on GA-BP Neural Networks, Computer Systems & Applications 27 (3) (2018) 162–167. doi:10.15888/ j.cnki.csa.006252. A. Naimi, R. Platt, J. Larkin, Machine learning for fetal growth prediction, Epidemiology 29 (2) (2018) 290–298. doi:10. 1097/EDE.0000000000000788. M. Podda, D. Bacciu, A. Micheli, R. Bell`u, G. Placidi, L. Gagliardi, A machine learning approach to estimating preterm infants survival: development of the preterm infants survival assessment (pisa) predictor, Scientific Reports 8. doi: 10.1038/s41598-018-31920-6. Y. Lu, X. Zhang, X. Fu, F. Chen, K. K. L. Wong, Ensemble machine learning for estimating fetal weight at varying gestational age, in: Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019), 2019, pp. 9522– 9527. doi:10.1609/aaai.v33i01.33019522. B. G. Ewigman, J. P. Crane, F. D. Frigoletto, M. L. LeFevre, R. P. Bain, D. McNellis, Effect of Prenatal Ultrasound Screening on Perinatal Outcome, The New England Journal of Medicine 329 (12) (1993) 821–827. doi:10.1056/ NEJM199309163291201. M. de Onis, WHO Child Growth Standards based on length/height, weight and age, Acta Paediatrica 95 (S450) (2006) 76– 85. doi:10.1111/j.1651-2227.2006.tb02378.x. L. Breiman, Random Forests, Machine Learning 45 (1) (2001) 5–32. doi:10.1023/A:1010933404324. R. E. Schapire, The strength of weak learnability, Machine Learning 5 (2) (1990) 197–227. doi:10.1007/BF00116037. J. H. Friedman, Greedy Function Approximation: A Gradient Boosting Machine, The Annals of Statistics 29 (5) (2001) 1189– 1232. T. Chen, C. Guestrin, XGBoost: A Scalable Tree Boosting System, in: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2016), 2006, pp. 785–794. doi:10.1145/2939672.2939785. G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, T.-Y. Liu, LightGBM: A Highly Efficient Gradient Boosting Decision Tree, in: Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), 2017. S. K. Pal, P. P. Wang (Eds.), Genetic Algorithms for Pattern Recognition, CRC Press, 1996. T. G. Dietterich, An Experimental Comparison of Three Methods for Constructing Ensembles of Decision Trees: Bagging, Boosting, and Randomization, Machine Learning 40 (2) (2000) 139–157. H. Lei, S. W. Wen, Ultrasonographic examination of intrauterine growth for multiple fetal dimensions in a chinese population, American Journal of Obstetrics and Gynecology 178 (5) (1998) 916–921. doi:10.1016/S0002-9378(98)70523-X. A. K. Jain, R. P. W. Duin, J. Mao, Statistical pattern recognition: a review, IEEE Transactions on Pattern Analysis and Machine Intelligence 22 (1) (2000) 4–37. doi:10.1109/34.824819.

-p

[5] A. Conde-Agudelo, A. T. Papageorghiou, S. H. Kennedy, J. Villar, Novel biomarkers for predicting intrauterine growth restriction: a systematic review and meta-analysis, BJOG An International Journal of Obstetrics and Gynaecology 120 (6) (2013) 681–694. doi:10.1111/1471-0528.12172. [6] S. L. Miller, P. S. Huppi, C. Mallard, The consequences of fetal growth restriction on brain structure and neurodevelopmental outcome, The Journal of Physiology 594 (4) (2016) 807–823. doi:10.1113/JP271402. [7] E. K. Pressman, J. L. Bienstock, K. J. Blakemore, S. A. Martin, N. A. Callan, Prediction of birth weight by ultrasound in the third trimester, Obstetrics & Gynecology 95 (4) (2000) 502– 506. doi:10.1016/S0029-7844(99)00617-1. [8] H. K. Ahmadzia, S. M. Thomas, A. M. Dude, C. A. Grotegut, B. K. Boyd, Prediction of birthweight from third-trimester ultrasound in morbidly obese women, American Journal of Obstetrics and Gynecology 211 (4) (2014) 431.e1–431.e7. doi: 10.1016/j.ajog.2014.06.041. [9] L. Chuang, J.-Y. Hwang, C.-H. Chang, C.-H. Yu, F.-M. Chang, Ultrasound estimation of fetal weight with the use of computerized artificial neural network model, Ultrasound in Medicine & Biology 28 (8) (2002) 991–996. doi:10.1016/ S0301-5629(02)00554-9. [10] Q. Zhang, J. H. L. Hansen, Language/Dialect Recognition Based on Unsupervised Deep Learning, IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (5) (2018) 873–882. doi:10.1109/TASLP.2018.2797420. [11] K. K. L. Wong, L. Wang, D. Wang, Recent developments in machine learning for medical imaging applications, Computerized Medical Imaging and Graphics 57 (2017) 1–3. doi: 10.1016/j.compmedimag.2017.04.001. [12] C. Ding, D. Tao, Trunk-Branch Ensemble Convolutional Neural Networks for Video-Based Face Recognition, IEEE Transactions on Pattern Analysis and Machine Intelligence 40 (4) (2018) 1002–1014. doi:10.1109/TPAMI.2017.2700390. [13] H. Fr¨ohlich, K. Claes, C. D. Wolf, X. V. Damme, A. Michel, A Machine Learning Approach to Automated Gait Analysis for the Noldus Catwalk System, IEEE Transactions on Biomedical Engineering 65 (5) (2018) 1133–1139. doi:10.1109/TBME. 2017.2701204. [14] N. G. Anderson, I. J. Jolley, J. E. Wells, Sonographic estimation of fetal weight: Comparison of bias, precision and consistency using 12 different formulae, Ultrasound in Obstetrics & Gynecology 30 (2) (2007) 173–179. doi:10.1002/uog.4037. [15] M. Scioscia, F. Scioscia, G. Scioscia, S. Bettocchi, Statistical limits in sonographic estimation of birth weight, Archives of Gynecology and Obstetrics 291 (1) (2015) 59–66. doi: 10.1007/s00404-014-3384-4. [16] S. L. Warsof, P. Gohari, R. L. Berkowitz, J. C. Hobbins, The estimation of fetal weight by computer-assisted analysis, American Journal of Obstetrics and Gynecology 128 (8) (1977) 881– 892. doi:10.1016/0002-9378(77)90058-8. [17] F. P. Hadlock, Sonographic estimation of fetal age and weight, Radiologic Clinics of North America 28 (1) (1990) 39–50. [18] G. I. Hirata, A. L. Medearis, J. Horenstein, M. B. Bear, L. D. Platt, Ultrasonographic estimation of fetal weight in the clinically macrosomic fetus, American Journal of Obstetrics and Gynecology 162 (1) (1990) 238–242. doi:10.1016/ 0002-9378(90)90857-4. [19] F. P. Hadlock, R. B. Harrist, R. S. Sharman, R. L. Deter, S. K. Park, Estimation of fetal weight with the use of head, body, and femur measurements—a prospective study, American Journal of Obstetrics and Gynecology 151 (3) (1985) 333–337. doi:10. 1016/0002-9378(85)90298-4. [20] J. Siemer, N. Egger, N. Hart, B. Meurer, A. M¨uller, O. Dathe,

lP

[28]

[29] [30]

na

[31]

[32]

ur

[33]

Jo

[34] [35]

[36]

[37]

12

Jo

ur

na

lP

re

-p

ro of

[38] S. Z. Wanyonyi, S. K. Mutiso, Monitoring fetal growth in settings with limited ultrasound access, Best Practice & Research Clinical Obstetrics & Gynaecology 49 (2018) 29–36. doi: 10.1016/j.bpobgyn.2018.02.001.

13