Pediatric Pharmacology
Novel Method to Predict Body Weight in Children Based on Age and Morphological Facial Features
The Journal of Clinical Pharmacology XX(XX) 1–5 © 2014, The American College of Clinical Pharmacology DOI: 10.1002/jcph.422
Ziyin Huang1, Jeffrey S. Barrett, PhD, FCP1,2, Kyle Barrett1, Ryan Barrett1, and Chee M. Ng, PharmD, PhD, FCP1,2
Abstract A new and novel approach of predicting the body weight of children based on age and morphological facial features using a three-layer feed-forward artificial neural network (ANN) model is reported. The model takes in four parameters, including age-based CDC-inferred median body weight and three facial feature distances measured from digital facial images. In this study, thirty-nine volunteer subjects with age ranging from 6–18 years old and BW ranging from 18.6–96.4 kg were used for model development and validation. The final model has a mean prediction error of 0.48, a mean squared error of 18.43, and a coefficient of correlation of 0.94. The model shows significant improvement in prediction accuracy over several age-based body weight prediction methods. Combining with a facial recognition algorithm that can detect, extract and measure the facial features used in this study, mobile applications that incorporate this body weight prediction method may be developed for clinical investigations where access to scales is limited.
Keywords body weight, age, facial features, artificial neural network, children
Body weight is one of the most important physiologic parameters in pediatric medicine given it is an essential factor for determining optimal drug dosages and intravenous fluid requirement, DC shock energy voltage needed for cardiorespiratory arrest, and correct equipment sizes in pediatric patients undergoing resuscitation.1 Several methods exist for predicting body weight in the absence of scales, including age-based, length-based, and habitusbased methods.1–4 In the investigation summarized herein, a novel method is proposed using age and morphological facial features from digital images to predict the body weight for children. Age is a significant and highly correlated factor in the estimation of body weight for children. It is commonly appreciated that as a child ages, he or she will have greater height and weight.5 Likewise, the majority of pediatric weight prediction methods published to date incorporate age.1 However, most of these methods were developed using a sample population with very limited age range and employed a simple linear mathematical equation to predict a single “reference” weight for each age.3,6–8 As a result, gross inaccuracies in prediction can occur for children who reside outside the sampled age range, and/or have different background and nutritional status from the population used to develop the method.1,9 The Centers for Disease Control and Prevention (CDC) growth charts are a set of percentile curves of body measurement distributions in children aged from 2 to 20 years old compiled from national surveys and clinical records. From the CDC growth charts, the nonlinear relationship between age and weight of boys and girls
can be formulated to track the growth of children, and therefore provide a reasonable weight estimation based on the age for children.10 These charts are often used for the generation of virtual pediatric populations based on agesize covariate relationships.10 Visual perception of people’s size and decomposition of facial images can provide qualitative cues for predicting body weight.11 These relationships have been behind the carnival game of predicting body weight for many years. In more quantitative terms, it has been shown that there is high correlation between facial feature metrics and body fat, and body mass index (BMI) and body fat proportion.12 Facial features have also been used to determine if a person is overweight.13 Therefore, it would seem possible that body weight can be determined by measuring various facial feature metrics and applying the age information derived from CDC growth charts. The goal of this project is to
1
Division of Clinical Pharmacology and Therapeutics, The Children’s Hospital of Philadelphia, Philadelphia, PA, USA 2 Department of Pediatrics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA Submitted for publication 15 August 2014; accepted 1 November 2014. Corresponding Author: Chee M. Ng, PharmD, PhD, FCP, Room 4010, CTRB Building, The Children’s Hospital of Philadelphia, 3501 Civic Center Blvd, Philadelphia, PA 19104 Email: [email protected]
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develop a novel method that can efficiently measure and calculate human body weight based on simple age information and facial feature metrics derived from digital images.
Methods Data were collected from 39 volunteer subjects and included their height, weight, age, sex and race/ethnicity, as well as facial digital images. Digital images were obtained using various smartphones (eg, Android, iPhone, etc) and digital cameras. The mean age of the subjects was 14.6 (range: 6–18) years, and the mean weight was 53.2 (range: 18.6–96.4) kg. Demographic partitions for sex (25 male, 14 female) and race (28 Caucasian, 1 African American, and 9 Asian) were not based on a priori defined stratification. Study subjects have provided consent/assent to have their image data included in the analysis dataset. Approval for the research is based on the IRB approval granted to our pediatric knowledgebase initiative at the Children’s Hospital of Philadelphia.14 The median curves of the CDC weight-for-age growth charts for male and female with ages between 2 and 20 years were formulated with a fourth-order polynomial regression using the growth charts’ percentile data file.15 The formula was used to calculate the CDC-inferred body weight prediction for each subject based on the age and sex. Facial features of the each subject were labeled and measured manually for this preliminary study. ImageJ (National Institutes of Health, Bethesda, Maryland, http:// imagej.nih.gov/ij/) was used to measure the facial feature distances for each facial image. Eleven major facial landmark points were selected, and 10 facial feature distances were measured (Figure 1). The measurements were scaled and normalized 2-dimensionally: horizontal distances were scaled relative to the eye-to-eye distance AB and vertical distances were relative to the length of the face EM which was calculated from: EM ¼ ED þ DC þ CM ffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 AB ¼ ED þ DC þ AC2 2 After normalization, 7 facial feature distances: CD, DE, HI, FG, JK, as well as the average of AC and BC, and the average of AD and BD, were used for the model searching. Along with the age-based body weight prediction from the median CDC formula, the 8 parameters were used as inputs to create the body weight prediction model using 3layers feed-forward artificial neural network (ANN) using MATLAB and Neural Network Toolbox Release 2014a (The MathWorks, Inc., Natick, Massachusetts, http:// www.mathworks.com/).
A
M
B
C
F H
G I
D J
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Figure 1. Facial feature measurements for the weight prediction model. Solid lines indicate the measurements used in the final model; the dotted lines are the reference measurements for calibration; dashed lines are the measurements used during training and were eliminated in the final model.
ANN is a machine learning method that can be used for nonlinear regression.16–18 The ANN training in this study applied tan-sigmoid transfer functions that used the input parameters to calculate a series of intermediate values (hidden neurons), and a linear transfer function that used linear combinations of the hidden neurons to calculate the output.16,17 The dataset was randomly divided into a training set (70%), a validation set (15%), and a test set (15%). The training process uses the training set data to continuously adjust weights and biases to improve the training performance of the regression model generated in each repetition (epoch), and the performance of the validation set is calculated for the model at each epoch to verify that no overfitting occurs. During the training process, if the validation mean squared error (MSE) increases for 6 consecutive epochs, training is aborted. The last validated model is returned, and then MSE of test set is calculated and recorded. As the training process randomly assigns initial weights and biases that influence the training results, the process was repeated (retrained) with 1,000 iterations, and the model with smallest test set MSE is adopted. An expanded view of ANN can be found in the review article by Cheng and Titterington.19 During the model selection process, the ANN models were built with combination of 1–6 hidden neurons and 1–8 input parameters. The entire 8 by 6 combination space of hidden neuron and input parameters was
3
Huang et al
n P
AIC ¼
n log
j¼1
^yj ðkÞÞ2
ðyj n
þ 2ðp þ 1Þ
where n is the number of samples and p is the overall number of parameters of the ANN.20,21 Among the overall models with different number of parameters, the model with smallest AIC was selected as the final optimal model. The bias and precision of the model prediction were assessed using mean prediction error (MPE) and MSE, respectively. In addition, proportion of studied population with percent absolute prediction error larger than 5%, 10%, and 20% was used to determine the model performance.
a
70 60
we ight (kg )
sampled. For each number of hidden neurons, the starting model has all 8 input parameters, and then the input parameters were removed one by one based on the MSE of the same model complexity. For each model, the Akaike information criterion (AIC) was calculated using the formula:
Ma le
50 40
Fe ma le 30 20 10 2
4
6
8
10
12
14
18
b
Results
output la ye r
input la ye r
c
hidde n la ye r
100 90
me a s ure d we ight (kg )
The CDC median weight-for-age curves were well described by fourth-order polynomial regression, and the R2 of the two curves were both close to 1 (Figure 2a). The CDC-inferred weight of each subject was calculated based on sex and age, and was used as control references to compare the results obtained from the developed model. The body weights were roughly estimated with fourthorder polynomial regression equation developed using the CDC median weight-for-age curve (R2 ¼ 0.50, MPE ¼ 1.52, MSE ¼ 142.50), but the accuracy for the weight prediction was poor with only 25.6%, 43.6%, and 74.4% of the population with relative prediction error within 5%, 10%, and 20%, respectively. The CDC-inferred weight and the 7 measured facial feature parameters were used to develop the ANN model. The final model consisted of 4 parameters inputs (CDC median curve and 3 facial feature distances: CD, DE, and FG) and 4 hidden neurons (Figure 2b). The percent coefficient of variation calculated from the normalized manual measurements by 3 observers is 5.29%. The schematic of the ANN calculation process and the mathematical representations of the current model are shown in Figure 3. The selected model has an MPE of 0.48 and MSE of 18.43. Among the predicted values, 64.1% of the predictions fall within 5% error, 84.6% fall within 10% error, and 94.9% fall within 20% error. The coefficient of correlation (R2) value of the prediction of the overall data is 0.94, which is much higher than the value of 0.50 for CDC-inferred body weight (Figure 2c). With this model, only a total of 3 normalized facial feature distances (CD, DE, and FG in Figure 1) derived from 7 facial points
16
a ge (yrs .)
80 70 60 50 40 30
CDC Me dia n CDC+ Fa ce
20 10 10
20
30
40
50
60
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80
90
100
pre dicte d we ight (kg) Figure 2. (a) CDC weight-for-age median curves reproduced from CDC data15 (solid) and the fourth-order polynomial curve-fitting of each curve (dashed); (b) schematic of the components of the final neural network model; (c) measured weight of the subjects vs. weight predicted from CDC weight-for-age median value (cross) and from the final neural network model (circle).
4
The Journal of Clinical Pharmacology / Vol XX No XX (2014) Input La ye r Input P a ra me te rs (normali ze d input)
Hidden La ye r
Output La ye r
(Hidde n Ne urons )
(input we ight)
(la yer we ight) Output
+
+
(normal ize d output)
(bia s )
In p u t/o u tp u t:
(bia s )
Mo d e l coef ficient s :
A1 : CDC-infe rre d body we ight A2 : dis ta nce“CD” A3 : dis ta nce“FG” A4 : dis ta nce “DE” BW: ANN predicted body we ight
P re -p ro c e s s in g : : normal ize the input para me te rs to a rage be twe e n -1 a nd 1
x = (A − xoffset ) º xgain + xmin
Ne u ra l n e two rk: : ta n-s igmoid tra ns fe r function
h i = tanh(IW i • x + b 1, i) : line a r trans fe r function
y = LW • h + b2 P o s t-p ro c e s s in g : : re ve rs e d to scal e the output from [-1, 1] to the de s ire d ra nge
BW = (y − ymin)/ygain + yoffset
Figure 3. The schematic of the artificial neural network calculation process and the mathematical representations of the final model.
(Points A–G in Figure 1) were needed from the facial digital image to perform weight predictions.
Discussion In this preliminary study, we developed a novel weight prediction method based on age-based CDC-inferred median weight and 3 unique facial features from digital images. Although age-based CDC median weight alone was a weak predictor of the individual weight in our studied pediatric population, it was the most significant parameter during the ANN model development process. Removing age-based CDC median weight prediction from the input in any ANN model would cause a significant decrease in R2 and an increase in prediction error. The MPE and MSE for the best ANN model without age-based CDC median weight were 0.49 and 52.3, respectively. This finding suggests that some age information is needed in order to improve weight prediction closer to the observed weight allowing facial features obtained from digital images to further refine the prediction. After replacing the age-based CDC median weight with age itself, the MPE and MSE for the best ANN model of the same model complexity were 0.048 and 94.4, respectively, which is greater than those observed in the ANN model using the age-based CDC median weight, so the age-based CDC median weight prediction is necessary for the accuracy of the prediction. The MPE and MSE for the male subjects are 0.41 and 6.40, respectively, and for female subjects are 0.59 and 39.93, respectively. Although the errors for both sexes are
smaller than the error produced by the CDC-inferred weight, the prediction errors for female subjects are higher than the errors for male subjects. A larger sample size is needed for future study on the prediction bias from sex difference. Using the CDC curve as the base of the model has the advantage of being able to extrapolate the weight prediction to a population with wider age range. Two other commonly used age-based weight prediction methods, advanced pediatric life support (APLS) formula “weight ¼ 2 (age þ 4)” and the Nottingham pediatric weight study (NPWS) formula “weight ¼ 3 (age) þ 7,” were used as the external references for comparison purposes.6,8 As expected, these models poorly predicted the body weight (R2 ¼ 0.51 and 0.43; MSE ¼ 432.8 and 162.6, respectively) in our studied population which mainly consisted of older children (6–18 years old). Future study with younger children (under 6 years old) population is necessary to confirm the applicability of our model in a broader age group. Ethnicity is also correlated with facial features and dimensions as well as weight.22 However, the final ANN method does not show prediction bias related to ethnicity suggesting that the dependency of the weight and face on ethnicity was accounted for after the weight and selected facial features were included in the model. Further investigation is needed in order to confirm this finding with a larger, more diverse sample population. ANN approach was adopted because it is an efficient way to train nonlinear regression models using machine learning. Other linear regression methods including bidirectional stepwise regression were used. However,
Huang et al
the best linear model trial has an MSE value of 66.01 and 14 parameter terms (including product terms) which has significantly higher error and AIC value than the selected ANN model. Although an ANN model is more complicated than linear regression model, the selected ANN model can be easily saved into and used as a computational function in MATLAB or in other languages. The methodology for body weight prediction based on this approach can be automated with the development of a facial feature extraction algorithm, as selected features are major facial landmarks and there are many different existing robust methods of facial detection and feature extraction that may be useful for this application.23–25 Studies are ongoing to further validate the findings of this study with a larger pediatric population with wider age range and to develop an automatic detection algorithm that recognizes the important facial features for the ANN method. These enhancements should allow the development of an accurate weight prediction mobile application for both the pediatric caregiver and research community.
Conclusion Knowledge of a child’s body weight is essential for pediatric medicine, and using age alone for body weight prediction is not very reliable especially if the children are older. This report describes a new and novel approach to more accurately calculate the body weight of children based on age and facial features from digital images using an artificial neural network. This method can be further implemented as mobile applications so the clinicians can easily obtain accurate body weight information for optimal patient care and serve as a tool for clinical investigation where access to scales is limited. Declaration of Conflicting Interests The authors declare no conflicts of interest.
References 01. Abdel-Rahman SM, Ridge A, Kearns GL. Estimation of body weight in children in the absence of scales: a necessary measurement to insure accurate drug dosing. Arch Dis Childhood. 2014;99(6):570– 574. 02. Luscombe MD, Owens BD, Burke D. Weight estimation in paediatrics: a comparison of the APLS formula and the formula ‘Weight ¼ 3(age) þ 7’. Emerg Med J. 2011;28(7):590–593. 03. Argall JAW, Wright N, Mackway-Jones K, Jackson R. A comparison of two commonly used methods of weight estimation. Arch Dis Childhood. 2003;88(9):789–790.
5 04. Hauda WE. Chapter 15. Resuscitation of Children. In: Tintinalli JE, Stapczynski JS, Ma OJ, et al., eds. Tintinalli’s Emergency Medicine: A Comprehensive Study Guide. 7th ed. New York, NY: McGrawHill; 2011. 05. Eveleth PB, Tanner JM. Worldwide Variation in Human Growth. Cambridge: Cambridge University Press; 1976. 06. Mackway-Jones K, Molyneux E, Phillips B, Wieteska S. Advanced Paediatric Life Support. London: BMJ Books; 2001. 07. Thompson MT, Reading MJ, Acworth JP. Best Guess method for age-based weight estimation in paediatric emergencies: validation and comparison with current methods. Emerg Med Australasia. 2007;19(6):535–542. 08. Luscombe M, Owens B. Weight estimation in resuscitation: is the current formula still valid? Arch Dis Childhood. 2007;92(5):412–415. 09. Greig A, Ryan J, Glucksman E. How good are doctors at estimating children’s weight. J Accid Emerg Med. 1997;14(2): 101–103. 10. Kuczmarski RJ, Ogden CL, Guo SS, et al. 2000 CDC Growth Charts for the United States: methods and development. Vital Health Stat 11. 2002;(246):1–190. 11. Coetzee V, Chen J, Perrett DI, Stephen ID. Deciphering faces: quantifiable visual cues to weight. Perception. 2010;39(1):51. 12. Windhager S, Patocka K, Schaefer K. Body fat and facial shape are correlated in female adolescents. Am J Hum Biol. 2013;25(6):847– 850. 13. Lee BJ, Jang J-S, Kim JY. Prediction of body mass index from facial features of females and males. Int J Bio-Sci Bio-Technol. 2012;4(3). 14. Barrett J, Mondick J, Narayan M, Vijayakumar K, Vijayakumar S. Integration of modeling and simulation into hospital-based decision support systems guiding pediatric pharmacotherapy. BMC Med Inform Dec Making. 2008;8(1):6. 15. Centers for Disease Control and Prevention, National Center for Health Statistics. Percentile Data Files with LMS Values. CDC Growth Charts 2000. 16. Neural Network ToolboxTM User’s Guide Revised for Version 8.2 (Release 2014a). Natick, MA: The MathWorks, Inc. 2014. 17. Bhadeshia HKDH. Neural networks in materials science. ISIJ Int. 1999;39(10):966–979. 18. Benitez JM, Castro JL, Requena I. Are artificial neural networks black boxes? IEEE Trans Neur Netw. 1997;8(5):1156–1164. 19. Cheng B, Titterington DM. Neural networks: a review from a statistical perspective. Statist Sci. 1994;9(1):2–30. 20. Akaike H. A new look at the statistical model identification. IEEE Trans Automat Control. 1974;19(6):716–723. 21. May R, Dandy G, Maier H. Review of input variable selection methods for artificial neural networks. In: Suzuki K ed. Artificial Neural Networks—Methodological Advances and Biomedical Applications. InTech; 2011. 22. Schneider TM, Hecht H, Stevanov J. Carbon C-C. Cross-ethnic assessment of body weight and height on the basis of faces. Pers Individ Dif. 2013;55(4):356–360. 23. Viola P, Jones M. Robust real-time object detection. Int J Comput Vis. 2002. 24. Hjelmås E, Low BK. Face detection: a survey. Comput Vis Image Underst. 2001;83(3):236–274. 25. Yuille AL, Hallinan PW, Cohen DS. Feature extraction from faces using deformable templates. Int J Comput Vis. 1992;8(2):99–111.
Novel Method to Predict Body Weight in Children Based on Age and Morphological Facial Features
The Journal of Clinical Pharmacology XX(XX) 1–5 © 2014, The American College of Clinical Pharmacology DOI: 10.1002/jcph.422
Ziyin Huang1, Jeffrey S. Barrett, PhD, FCP1,2, Kyle Barrett1, Ryan Barrett1, and Chee M. Ng, PharmD, PhD, FCP1,2
Abstract A new and novel approach of predicting the body weight of children based on age and morphological facial features using a three-layer feed-forward artificial neural network (ANN) model is reported. The model takes in four parameters, including age-based CDC-inferred median body weight and three facial feature distances measured from digital facial images. In this study, thirty-nine volunteer subjects with age ranging from 6–18 years old and BW ranging from 18.6–96.4 kg were used for model development and validation. The final model has a mean prediction error of 0.48, a mean squared error of 18.43, and a coefficient of correlation of 0.94. The model shows significant improvement in prediction accuracy over several age-based body weight prediction methods. Combining with a facial recognition algorithm that can detect, extract and measure the facial features used in this study, mobile applications that incorporate this body weight prediction method may be developed for clinical investigations where access to scales is limited.
Keywords body weight, age, facial features, artificial neural network, children
Body weight is one of the most important physiologic parameters in pediatric medicine given it is an essential factor for determining optimal drug dosages and intravenous fluid requirement, DC shock energy voltage needed for cardiorespiratory arrest, and correct equipment sizes in pediatric patients undergoing resuscitation.1 Several methods exist for predicting body weight in the absence of scales, including age-based, length-based, and habitusbased methods.1–4 In the investigation summarized herein, a novel method is proposed using age and morphological facial features from digital images to predict the body weight for children. Age is a significant and highly correlated factor in the estimation of body weight for children. It is commonly appreciated that as a child ages, he or she will have greater height and weight.5 Likewise, the majority of pediatric weight prediction methods published to date incorporate age.1 However, most of these methods were developed using a sample population with very limited age range and employed a simple linear mathematical equation to predict a single “reference” weight for each age.3,6–8 As a result, gross inaccuracies in prediction can occur for children who reside outside the sampled age range, and/or have different background and nutritional status from the population used to develop the method.1,9 The Centers for Disease Control and Prevention (CDC) growth charts are a set of percentile curves of body measurement distributions in children aged from 2 to 20 years old compiled from national surveys and clinical records. From the CDC growth charts, the nonlinear relationship between age and weight of boys and girls
can be formulated to track the growth of children, and therefore provide a reasonable weight estimation based on the age for children.10 These charts are often used for the generation of virtual pediatric populations based on agesize covariate relationships.10 Visual perception of people’s size and decomposition of facial images can provide qualitative cues for predicting body weight.11 These relationships have been behind the carnival game of predicting body weight for many years. In more quantitative terms, it has been shown that there is high correlation between facial feature metrics and body fat, and body mass index (BMI) and body fat proportion.12 Facial features have also been used to determine if a person is overweight.13 Therefore, it would seem possible that body weight can be determined by measuring various facial feature metrics and applying the age information derived from CDC growth charts. The goal of this project is to
1
Division of Clinical Pharmacology and Therapeutics, The Children’s Hospital of Philadelphia, Philadelphia, PA, USA 2 Department of Pediatrics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA Submitted for publication 15 August 2014; accepted 1 November 2014. Corresponding Author: Chee M. Ng, PharmD, PhD, FCP, Room 4010, CTRB Building, The Children’s Hospital of Philadelphia, 3501 Civic Center Blvd, Philadelphia, PA 19104 Email: [email protected]
2
The Journal of Clinical Pharmacology / Vol XX No XX (2014)
develop a novel method that can efficiently measure and calculate human body weight based on simple age information and facial feature metrics derived from digital images.
Methods Data were collected from 39 volunteer subjects and included their height, weight, age, sex and race/ethnicity, as well as facial digital images. Digital images were obtained using various smartphones (eg, Android, iPhone, etc) and digital cameras. The mean age of the subjects was 14.6 (range: 6–18) years, and the mean weight was 53.2 (range: 18.6–96.4) kg. Demographic partitions for sex (25 male, 14 female) and race (28 Caucasian, 1 African American, and 9 Asian) were not based on a priori defined stratification. Study subjects have provided consent/assent to have their image data included in the analysis dataset. Approval for the research is based on the IRB approval granted to our pediatric knowledgebase initiative at the Children’s Hospital of Philadelphia.14 The median curves of the CDC weight-for-age growth charts for male and female with ages between 2 and 20 years were formulated with a fourth-order polynomial regression using the growth charts’ percentile data file.15 The formula was used to calculate the CDC-inferred body weight prediction for each subject based on the age and sex. Facial features of the each subject were labeled and measured manually for this preliminary study. ImageJ (National Institutes of Health, Bethesda, Maryland, http:// imagej.nih.gov/ij/) was used to measure the facial feature distances for each facial image. Eleven major facial landmark points were selected, and 10 facial feature distances were measured (Figure 1). The measurements were scaled and normalized 2-dimensionally: horizontal distances were scaled relative to the eye-to-eye distance AB and vertical distances were relative to the length of the face EM which was calculated from: EM ¼ ED þ DC þ CM ffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 AB ¼ ED þ DC þ AC2 2 After normalization, 7 facial feature distances: CD, DE, HI, FG, JK, as well as the average of AC and BC, and the average of AD and BD, were used for the model searching. Along with the age-based body weight prediction from the median CDC formula, the 8 parameters were used as inputs to create the body weight prediction model using 3layers feed-forward artificial neural network (ANN) using MATLAB and Neural Network Toolbox Release 2014a (The MathWorks, Inc., Natick, Massachusetts, http:// www.mathworks.com/).
A
M
B
C
F H
G I
D J
K E
Figure 1. Facial feature measurements for the weight prediction model. Solid lines indicate the measurements used in the final model; the dotted lines are the reference measurements for calibration; dashed lines are the measurements used during training and were eliminated in the final model.
ANN is a machine learning method that can be used for nonlinear regression.16–18 The ANN training in this study applied tan-sigmoid transfer functions that used the input parameters to calculate a series of intermediate values (hidden neurons), and a linear transfer function that used linear combinations of the hidden neurons to calculate the output.16,17 The dataset was randomly divided into a training set (70%), a validation set (15%), and a test set (15%). The training process uses the training set data to continuously adjust weights and biases to improve the training performance of the regression model generated in each repetition (epoch), and the performance of the validation set is calculated for the model at each epoch to verify that no overfitting occurs. During the training process, if the validation mean squared error (MSE) increases for 6 consecutive epochs, training is aborted. The last validated model is returned, and then MSE of test set is calculated and recorded. As the training process randomly assigns initial weights and biases that influence the training results, the process was repeated (retrained) with 1,000 iterations, and the model with smallest test set MSE is adopted. An expanded view of ANN can be found in the review article by Cheng and Titterington.19 During the model selection process, the ANN models were built with combination of 1–6 hidden neurons and 1–8 input parameters. The entire 8 by 6 combination space of hidden neuron and input parameters was
3
Huang et al
n P
AIC ¼
n log
j¼1
^yj ðkÞÞ2
ðyj n
þ 2ðp þ 1Þ
where n is the number of samples and p is the overall number of parameters of the ANN.20,21 Among the overall models with different number of parameters, the model with smallest AIC was selected as the final optimal model. The bias and precision of the model prediction were assessed using mean prediction error (MPE) and MSE, respectively. In addition, proportion of studied population with percent absolute prediction error larger than 5%, 10%, and 20% was used to determine the model performance.
a
70 60
we ight (kg )
sampled. For each number of hidden neurons, the starting model has all 8 input parameters, and then the input parameters were removed one by one based on the MSE of the same model complexity. For each model, the Akaike information criterion (AIC) was calculated using the formula:
Ma le
50 40
Fe ma le 30 20 10 2
4
6
8
10
12
14
18
b
Results
output la ye r
input la ye r
c
hidde n la ye r
100 90
me a s ure d we ight (kg )
The CDC median weight-for-age curves were well described by fourth-order polynomial regression, and the R2 of the two curves were both close to 1 (Figure 2a). The CDC-inferred weight of each subject was calculated based on sex and age, and was used as control references to compare the results obtained from the developed model. The body weights were roughly estimated with fourthorder polynomial regression equation developed using the CDC median weight-for-age curve (R2 ¼ 0.50, MPE ¼ 1.52, MSE ¼ 142.50), but the accuracy for the weight prediction was poor with only 25.6%, 43.6%, and 74.4% of the population with relative prediction error within 5%, 10%, and 20%, respectively. The CDC-inferred weight and the 7 measured facial feature parameters were used to develop the ANN model. The final model consisted of 4 parameters inputs (CDC median curve and 3 facial feature distances: CD, DE, and FG) and 4 hidden neurons (Figure 2b). The percent coefficient of variation calculated from the normalized manual measurements by 3 observers is 5.29%. The schematic of the ANN calculation process and the mathematical representations of the current model are shown in Figure 3. The selected model has an MPE of 0.48 and MSE of 18.43. Among the predicted values, 64.1% of the predictions fall within 5% error, 84.6% fall within 10% error, and 94.9% fall within 20% error. The coefficient of correlation (R2) value of the prediction of the overall data is 0.94, which is much higher than the value of 0.50 for CDC-inferred body weight (Figure 2c). With this model, only a total of 3 normalized facial feature distances (CD, DE, and FG in Figure 1) derived from 7 facial points
16
a ge (yrs .)
80 70 60 50 40 30
CDC Me dia n CDC+ Fa ce
20 10 10
20
30
40
50
60
70
80
90
100
pre dicte d we ight (kg) Figure 2. (a) CDC weight-for-age median curves reproduced from CDC data15 (solid) and the fourth-order polynomial curve-fitting of each curve (dashed); (b) schematic of the components of the final neural network model; (c) measured weight of the subjects vs. weight predicted from CDC weight-for-age median value (cross) and from the final neural network model (circle).
4
The Journal of Clinical Pharmacology / Vol XX No XX (2014) Input La ye r Input P a ra me te rs (normali ze d input)
Hidden La ye r
Output La ye r
(Hidde n Ne urons )
(input we ight)
(la yer we ight) Output
+
+
(normal ize d output)
(bia s )
In p u t/o u tp u t:
(bia s )
Mo d e l coef ficient s :
A1 : CDC-infe rre d body we ight A2 : dis ta nce“CD” A3 : dis ta nce“FG” A4 : dis ta nce “DE” BW: ANN predicted body we ight
P re -p ro c e s s in g : : normal ize the input para me te rs to a rage be twe e n -1 a nd 1
x = (A − xoffset ) º xgain + xmin
Ne u ra l n e two rk: : ta n-s igmoid tra ns fe r function
h i = tanh(IW i • x + b 1, i) : line a r trans fe r function
y = LW • h + b2 P o s t-p ro c e s s in g : : re ve rs e d to scal e the output from [-1, 1] to the de s ire d ra nge
BW = (y − ymin)/ygain + yoffset
Figure 3. The schematic of the artificial neural network calculation process and the mathematical representations of the final model.
(Points A–G in Figure 1) were needed from the facial digital image to perform weight predictions.
Discussion In this preliminary study, we developed a novel weight prediction method based on age-based CDC-inferred median weight and 3 unique facial features from digital images. Although age-based CDC median weight alone was a weak predictor of the individual weight in our studied pediatric population, it was the most significant parameter during the ANN model development process. Removing age-based CDC median weight prediction from the input in any ANN model would cause a significant decrease in R2 and an increase in prediction error. The MPE and MSE for the best ANN model without age-based CDC median weight were 0.49 and 52.3, respectively. This finding suggests that some age information is needed in order to improve weight prediction closer to the observed weight allowing facial features obtained from digital images to further refine the prediction. After replacing the age-based CDC median weight with age itself, the MPE and MSE for the best ANN model of the same model complexity were 0.048 and 94.4, respectively, which is greater than those observed in the ANN model using the age-based CDC median weight, so the age-based CDC median weight prediction is necessary for the accuracy of the prediction. The MPE and MSE for the male subjects are 0.41 and 6.40, respectively, and for female subjects are 0.59 and 39.93, respectively. Although the errors for both sexes are
smaller than the error produced by the CDC-inferred weight, the prediction errors for female subjects are higher than the errors for male subjects. A larger sample size is needed for future study on the prediction bias from sex difference. Using the CDC curve as the base of the model has the advantage of being able to extrapolate the weight prediction to a population with wider age range. Two other commonly used age-based weight prediction methods, advanced pediatric life support (APLS) formula “weight ¼ 2 (age þ 4)” and the Nottingham pediatric weight study (NPWS) formula “weight ¼ 3 (age) þ 7,” were used as the external references for comparison purposes.6,8 As expected, these models poorly predicted the body weight (R2 ¼ 0.51 and 0.43; MSE ¼ 432.8 and 162.6, respectively) in our studied population which mainly consisted of older children (6–18 years old). Future study with younger children (under 6 years old) population is necessary to confirm the applicability of our model in a broader age group. Ethnicity is also correlated with facial features and dimensions as well as weight.22 However, the final ANN method does not show prediction bias related to ethnicity suggesting that the dependency of the weight and face on ethnicity was accounted for after the weight and selected facial features were included in the model. Further investigation is needed in order to confirm this finding with a larger, more diverse sample population. ANN approach was adopted because it is an efficient way to train nonlinear regression models using machine learning. Other linear regression methods including bidirectional stepwise regression were used. However,
Huang et al
the best linear model trial has an MSE value of 66.01 and 14 parameter terms (including product terms) which has significantly higher error and AIC value than the selected ANN model. Although an ANN model is more complicated than linear regression model, the selected ANN model can be easily saved into and used as a computational function in MATLAB or in other languages. The methodology for body weight prediction based on this approach can be automated with the development of a facial feature extraction algorithm, as selected features are major facial landmarks and there are many different existing robust methods of facial detection and feature extraction that may be useful for this application.23–25 Studies are ongoing to further validate the findings of this study with a larger pediatric population with wider age range and to develop an automatic detection algorithm that recognizes the important facial features for the ANN method. These enhancements should allow the development of an accurate weight prediction mobile application for both the pediatric caregiver and research community.
Conclusion Knowledge of a child’s body weight is essential for pediatric medicine, and using age alone for body weight prediction is not very reliable especially if the children are older. This report describes a new and novel approach to more accurately calculate the body weight of children based on age and facial features from digital images using an artificial neural network. This method can be further implemented as mobile applications so the clinicians can easily obtain accurate body weight information for optimal patient care and serve as a tool for clinical investigation where access to scales is limited. Declaration of Conflicting Interests The authors declare no conflicts of interest.
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