Paediatric weight estimation by age in the digital era:

optimising a necessary evil

Nicholas Appelbaum (1), Jonathan Clarke (1), Ian Maconochie (2) and

Ara Darzi (1)

Author Affiliations :

1 – Department of Surgery and Cancer, Division of Surgery, Imperial College

London

2 – Department of Emergency Medicine, Division of Medicine, Imperial

College London

Word counts:Abstract: 236 words

Manuscript: 2986 words (excluding acknowledgements)

Full contact information for corresponding author:

Nicholas Appelbaum

Department of Surgery and Cancer

Division of Surgery

Imperial College London

10th Floor, QEQM Building

St Mary’s Hospital

Praed Street, London, W2 1NY

Tel: +44 (0) 20 3312 1310

Fax: +44 (0)20 3312 6950

Mob: +44 7470 2588885

Email

n.appelbaum@imperial.ac.uk

Web: www.imperial.ac.uk/ighi

www.helixcentre.com

Abstract

Background: Age-based weight estimation methods are regularly used in

paediatric emergency medicine despite their well-established inaccuracy.

Aim: Determine the potential improvement in accuracy achievable by the use

of a new mobile application, based on CDC/WHO weight-for-age centile data,

which incorporates a gender assignment, a body habitus assessment, and

which is capable of an age-in-months based calculation.

Methods: A theoretical, simulated validation study, comparing the

performance of the widely used APLS / EPALS formulae against two

contemporary habitus-adjusted methods, and the Helix Weight Estimation

Tool. 1,070,743 children from the 2015/2016 UK National Child Measurement

Program dataset, aged between 4 and 5 and 11 and 12 years, had age-based

weight estimates made by all five methods.

Results: Primary outcomes were the percentage of weight estimations within

10%, 20%, and those greater than 20% discrepant from actual weight for

each method. Our theoretical, gender-dependent, habitus-adjusted method

performed better than all other methods across all error thresholds. The

overall number of estimations within 10% was 70.4%, and within 20% was

95.45%. The mean percentage error was -1% compared to actual weight.

Conclusion: The use of a digital tool incorporating a subjective assessment

of body habitus, gender assignment, and the ability to estimate weight based

on age-in-months might be able optimise the process of paediatric weight

estimation by age, making this practice as safe and accurate as possible for

the occasions when weight estimation by age is chosen over length-based

methods.

Manuscript Text

Introduction

Background

Why do we estimate bodyweight?

Drugs for children are generally prescribed on the basis of age and on body

weight. However, frequently a critically ill child arrives in the Emergency

Department resuscitation room with his/her weight unknown to the care team,

under conditions where it is not possible to weigh the patient before

commencing emergency care. Examples of conditions which make weighing

the child unfeasible include spinal immobilisation, ongoing cardiopulmonary

resuscitation, emergency airway management, or severe pain that inhibits

movement of the child (1-3).

The accurate estimation of weight is important in paediatrics, e.g. for the

calculation of drug doses, the determination of equipment size for each child,

and the energy levels required for defibrillation. Inaccurate and imprecise

weight estimation techniques contribute to the high incidence of drug errors in

paediatric emergency medicine (4, 5).

Current methods of weight estimation

Estimation of weight by age

In spite of the fact that age-based formulae have consistently demonstrated

poor predictive accuracy, particularly in older children (6-8), there has been a

constant appetite to improve these methods, and from the 1950’s onwards, at

least 22 age-based formulae have been derived to estimate the bodyweight of

children. Some of these calculations require complex workings which, in a

stressful clinical environment, provide additional opportunities for erroneous

arithmetic to contribute to drug error (9).

What methods offer acceptable accuracy?

There is some consensus in the literature that an ‘accurate’ method would

demonstrate accuracy as 60-70% of weight estimations within 10% of actual

weight (PW10) and a moderate critical error rate as having 90-95% of

estimations within 20% of actual weight (PW20) (10, 11).

It is well established that the most accurate methods of paediatric weight

estimation are length-based methods rather than age-based methods (6, 8,

12-14), and only length-based methods have ever achieved this level of

accuracy.

Five age-based formulae have been validated in the UK in at least sixteen

studies we are aware of. The best performing formulae have been the

Luscombe-Owens Formula (2) (derived in Sheffield), with PW10=43%, and

the Tinnings Formula (15), PW10=43.7% - both in a 2011 validation by

Marlow et al. (6). The Luscombe-Owens formula has been incorporated in

part into the new Advanced Paediatric Life Support (APLS) formula.

Paediatric weight estimation and the childhood obesity pandemic

The increasing incidence of childhood obesity (16) has recently led to the

reinvigorated interest in methods that can adjust for the variability in body

habitus in children which was first introduced with the Derived Weight

Estimating Method (DWEM) (17) in 1986. This has until recently been

predominantly applied to length-based methods, and examples of this include

the Paediatric Advanced Weight Prediction in the Emergency Room

(PAWPER) tape (13), Mercy method (18, 19) (using mid upper arm

circumference and humeral length), Yamamoto Obesity Icon system (20), and

the waist-circumference modified Broselow system (21).

Two studies have evaluated how the addition of an assessment of body

habitus could improve the accuracy of age-based weight estimation methods.

These are (where Z = age in years):

The Erker formula (22)

Wt=(2×Z)+6 For ‘tall ‘n thin’ children

Wt=(3×Z)+6 For ‘normal’ children

Wt=(4×Z)+6 For ‘tiny ‘n thick’ children

The Wells ‘derived formula’ (7)

HS1 : Wt = (1.9×Z)+5.8

HS2 : Wt = (2.3×Z)+5.8

HS3 : Wt = (2.4×Z)+7.5

HS4 : Wt = (2.9×Z)+8.3

HS5 : Wt = (3.7×Z)+8.1

In the PAWPER system, Wells et al (13) have added to the area of subjective

assessment of habitus (improving upon the Yamamoto method) by developing

a 5-point (later 7-point) (10) visual scale of body habitus scores (HS), and

these scores have been used in the multipart formula above.

Both of these methods have only been the subject of investigation in one

validation study (in a South African population, n=963 for Erker, n=635 for

Wells) where neither demonstrated ‘acceptable accuracy’, or 60% of

estimations within 10% of actual bodyweight. Additionally, without the use of a

digital tool, these increasingly complex equations pose the risk of

miscalculation error.

To our knowledge, no habitus-adjusted age-based methods have ever been

validated in the United Kingdom.

Why do age-based methods continue to be used?

Despite the availability of more accurate methods, weight based formulae are

used throughout the world, and taught on all paediatric life support courses.

Principally, however, it is because age-based methods do not require any

specific equipment that their use endures.

There is therefore a need to examine the performance of the newest age-

based weight estimation methods in English children, and to see if the

development of a simple digital tool might be able to add accuracy and safety

to weight estimation by age where this method is chosen over length-based

methods.

Objectives

1. Determine the accuracy of the APLS / European Paediatric Advanced

Life Support (EPALS) formulae and two age-based, habitus-adjusted

body weight estimation methods in a large, 2 age-banded cohort of

English children.

2. Determine the potential improvement in accuracy achievable by the

use of a new mobile application, based on CDC/WHO weight-for-age

centile data, which incorporates a gender assignment, a body habitus

assessment, and which is capable of an age-in-months based

estimation.

It was our hypothesis that this experimental method would demonstrate

improved accuracy of body weight estimation over currently taught and used

methods.

Methods

Study Design

This was a theoretical, simulated validation study, comparing the performance

of the widely used APLS / EPALS formulae with the Wells and Erker formulae,

and a new mobile application based method using WHO/CDC centile data, a

correction for body habitus, and a gender assignment. All estimates and

comparisons were made based upon and compared with English data from

the 2015/2016 UK National Child Measurement Program (NCMP) dataset

(23).

Data sources

NHS Digital publishes publicly available data from the annual NCMP survey

on every child across the UK, as each has their height and weight measured

in Reception Year (age 4-5), and again in Year 6 (age 10-11). In addition to

multiple anthropometric parameters derived from comparison to the UK 1990

Growth Standard (24), each entry contains the school local authority code.

WHO and CDC centile datasets are freely available from the US National

Center for Health Statistics (25). For this study, only CDC centile data were

required as the CDC recommendation is to use WHO centiles for children

under the age of two, and all children in the dataset used for this two age-

banded validation were older than two.

Data management

The NCMP dataset is made available after suppression in line with the NHS

Anonymisation Standard. Extreme outliers of age-for-weight above the

99.995th percentile (3192 records) and below the 0.005th percentile (631

records) were removed from the dataset. In addition to this, 89260 records

were suppressed where the local authority code and a locally small population

might have allowed for identification of an individual.

Overall, 1,076,908 records were available for analysis.

The data were processed using the Python programming language (Python

Software Foundation. Python Language Reference, version 3.6), and the

pandas library (version 0.20.2, http://pandas.pydata.org), in the Jupyter

Notebook computational environment (https://jupyter.org).

To map the NCMP data onto the CDC data, child age-in-months was rounded

to the nearest half-month. Limited secondary data cleaning, removing extreme

outliers for age was performed: in reception year, age in months 48.5, 49.5,

and 70.5, and for Year 6 children, 120.5, 141.5, and 142.5 months. Table 1

shows the overall study population characteristics.

The total sample size analysed was 1,070,743 children.

Analysis of the APLS, EPALS and habitus-adjusted formulae

For each child in the dataset, their predicted weight was calculated using the

current APLS formula, the current EPALS formula, the Erker formula, an

estimate based on the CDC 50th centile weight for age, and the Wells formula.

For the Erker formula, we considered ‘tall ‘n thin’ children as those with a

height-for-age above the 90th percentile, and a weight-for-height below the 10th

percentile. We considered “short ‘n thick” children as those below the 10 th

percentile of height-for-age, and above the 90 th percentile for weight-for-

height. All other children were considered “normal”.

For the Wells formula, habitus scores between HS1 and HS5 were allocated

to the median BMI Z-scores from the original paper (7). All subjects in the

dataset were then allocated to the nearest HS according to their actual BMI.

The Helix weight estimation method

We chose to use 7 habitus scores, each mapping closely onto the habitus

scores used by Wells et al in the PAWPER-XL system (10). We assigned

CDC weight-for-age and BMI-for-age centiles to each habitus score as

follows: HS1=10th, HS2=25th, HS3=50th, HS4=75th, HS5=90th, HS6=95th, and

HS=97th centiles.

Each child in the dataset was allocated to the CDC BMI-for-age centile (10 th,

25th, 50th, 75th, 90th, 95th, 97th) closest to their actual BMI from the NCMP

dataset, and the corresponding CDC weight-for-age centile was used to

determine an estimated weight.

Determination of accuracy and precision

Each of these estimates was compared to the child’s actual weight from the

NCMP dataset. For each weight estimate, the percentage error (PE) and

absolute percentage error (APE) were calculated. W e is estimated weight, and

W t is actual patient weight.

PE=(W e−W t

W t)×100

APE=|(W e−W t

W t )|×100

The percentage of weight estimations within a threshold range (0% - 100% of

estimations) was calculated. Estimates within 10% (PW10), 20% (PW20) and

those being greater than 20% from actual weight (PW>20) were calculated

from these results.

The overall accuracy of the models was tested by calculating the mean

percentage error (as a measure of estimation bias) and the root mean square

percentage error (a measure of the standard deviation around the true value)

(11).

MPE=1n∑e=1

n

(W e−W t

W t)

RMSPE=√ 1n∑e=1n (W e−W t

W t)2

95% limits of agreement were calculated as a measure of precision.

Assessing the geographic burden of error for the APLS formula

We studied the geographical variation of the error burden across England for

the APLS method alone, as it is the most commonly used method. We pooled

children by their local authority code, and calculated the mean percentage

error, as well as PW10, PW20 and PW>20 with for each local authority. This

data was visualised using Tableau Desktop (Tableau Software, Seattle

Washington, USA).

Statistical analysis

Frequencies and proportions were reported for categorical variables, medians

and IQRs for continuous variables. The median absolute percentage error for

each estimation method was compared using the Mann-Whitney U-test. A

p<0.0001 was considered significant. Previous studies have examined the

mean percentage error as a primary outcome measure, however, this

provides little insight, as two methods with very different error distributions but

the same mean error would appear identical. By taking the absolute

percentage error and comparing errors non-parametrically it is possible to

assess the overall precision of the methods used. Statistical analysis was

performed using Stata (Stata-Corp. 2015. Stata Statistical Software: Release

14. College Station, TX: StataCorp LP)

The primary outcome was the performance of the various age-based weight

estimation methods compared to actual weight. A PW10>60% and a

PW20>90% was chosen as representing safe performance.

Results

Figure 1 shows the pooled performance (as PW10, PW20 and PW>20) for all

methods across the entire study population. Figure 2 shows the performance

of each method stratified by age and gender.

The performance of the APLS and EPALS formulae (these are the same

formula in the reception-year band) was poor in both age ranges. The pooled

PW10 for the APLS formula was 36.5% for the EPALS formula, 28.1%.

Not only were these formulae highly inaccurate, but their error distribution was

such that the percentage of estimations in excess of 20% discrepant from

actual weight was particularly high. This was more pronounced in the older

children, rising from 25.5% in Reception Year boys to 36.6% in Year 6 boys

for the APLS formula, and 59.9% for the EPALS formula in the older boys.

The performance and error distribution of the APLS formula varied

considerably by local authority. Figure 3 shows the mean percentage error for

the APLS formula as a ‘heatmap’ across England. The MPE, PW10, PW20

and PW>20 results from two different local authorities have been shown to

demonstrate the degree of the heterogeneity. There is, however, a small

contribution to this error burden made by the average time during the school

year that children are weighed. Underestimations will be exaggerated in local

authorities where schools, on average, weigh late in the school year.

The two habitus-adjusted formulae performed better than the non habitus-

adjusted formulae and performed better in the younger children. The pooled

PW10 for the Erker and Wells formulae were 53.7% and 59.4% respectively.

The performance of the Erker and Wells formulae was similar to that reported

in a recent validation (7).

The CDC median method was used for comparison only and is not used

clinically anywhere to our knowledge.

Our theoretical, gender-dependent, habitus-adjusted method performed better

than all other methods across all error thresholds. The overall PW10 was

70.4%. As with all methods, performance was better in the younger children. It

was, however, in the older children, in particular the older girls (who had a

higher median BMI), where this new method showed the most significant

improvement over the other formulae. The PW10 for Year 6 girls was 66.2%,

compared to 48% for the Erker formula, and 46.5% for the Wells formula. The

drop in PW10 between the Year 6 boys and girls was 3.1% for the

experimental method, and 12.7% for the best performing formula.

Table 2 shows the accuracy and precision measures of the model stratified by

habitus score and age. The model performed ‘accurately’ (PW10>60%) in all

categories except for Habitus Score 7 in the Year 6’s, where PW10=55.9%

MPE +5.6%.

The overall estimation bias (MPE) was -1%. The limits of agreement around

the MPE were wide, as is the case with all age-based methods.

Discussion

This is a first, theoretical validation of a weight estimation method which

employs a body habitus correction, an estimation based on age-in-months,

and which is gender dependent.

Our group is affiliated with the Helix Centre, a multidisciplinary team of

clinicians, designers and technologists at St Mary’s Hospital in London.

Although we argument above that it is precisely because of the lack of a need

for specific equipment that weight estimation by age persists, almost all

emergency clinicians have on their person a device capable of safely making

almost any calculation: their mobile telephone. This model has thus been

packaged into a simple mobile application, which will be made freely available

to interested researchers and parents as part of an invitation to participate in

an open, worldwide validation of this methodology.

Limitations

The principal limitation to this study is that the NCMP dataset only includes

children of ages 4-5 and 11-12 years, albeit with a considerable sample size.

These two age-bands sit on the weight-for-age growth curve at the point

which the growth curves begin to widen, and where habitus assessment is

more critical to model accuracy. Assumptions cannot be made about the

accuracy of this model outside of these age ranges.

The models assume perfect allocation of subjects to habitus scores and error

has not been modeled for any of the methods. There is considerable

subjectivity in visual assessment of habitus. Correlation between evaluator

assessment of patient habitus and actual BMI-for-age centile has been found

by Garcia et al, to be suboptimal in one study, although for a considerably

simpler tool (11).

Because it may be difficult to distinguish between adjacent body habitus

scores when examining patients, misclassification will almost certainly occur

for both the experimental model and the Wells formula, with a consequent

decrease in performance. Additionally, considering the fact that a short child

weighs less than a tall child of similar age and habitus, a visual best-guess

would take this into account, whereas a habitus adjusted model would

overestimate the weight of a shorter than average, moderately overweight

child. This is a fundamental shortcoming of weight-by-age methods.

It is possible that this analysis has imposed restrictions that might have

negatively affected the performance of the Erker formula compared to actual

life. By segmenting the allocations by children who were both ‘tall and thin’, or

‘short and thick’, the number of reallocations was relatively low. In clinical

practice, it is likely that an obese child would be allocated to the ‘tall and thin’

formula as it is obvious this formula will yield the greater estimated weight.

Pharmacological considerations

The addition of a body habitus correction to an age-based methodology more

accurately predicts total body weight than ideal body weight.

It has been reported that there is a bias towards hydrophilic drugs (e.g.

adrenaline, amiodarone) in paediatric CPR (26), which should ideally be

dosed against an ideal bodyweight, as this gives a better estimate of the

volume of distribution. A method returning a total bodyweight estimate in

overweight children could theoretically result in overdosing of medications that

do not distribute widely into adipose tissue.

There are many drugs, however, that are used regularly in paediatric

emergencies (e.g. benzodiazepines) that are hydrophobic, and where a total

body weight estimate is appropriate.

Computerised decision support systems will likely be developed in the future

where individualised dosing against pharmacokinetic considerations is

possible, even in the resuscitation environment. It is important to consider the

bearing weight estimation methods will have on this.

Conclusions

Weight estimation by length, and even better, habitus-adjusted length-based

models will almost always outperform age-based methods, and so these

methods should be considered the first line method of choice. However,

weight estimation by age is a persistent phenomenon despite the well

documented inaccuracy of the various methods.

By incorporating a subjective assessment of body habitus and a gender

assignment into a simple digital tool capable of an age-in-months based

calculation in the case a date of birth is known, it may be possible to optimise

weight estimation by age, making it at least as safe and accurate as possible

for the occasions when weight estimation by age is chosen over length-based

methods.

This mobile application needs to be validated in the clinical environment, and

our research team looks forward to working with interested collaborators in

order to do so.

Acknowledgements

We are grateful for the time and assistance we have received from the

following people:

Dr Philip Pratt, Dr Eduardo D’Aguilar and John Morrell for their advice and

technical assistance. Sara Vrbinc for her work on the user interface and

constant advocacy for usability in all of our work.

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