Article Text

## Abstract

**Objective** To develop an age-based weight estimation rule in a Chinese population and to compare its performance with existing formulae.

**Design** Population-based observational study.

**Setting** Schools and kindergartens in Hong Kong.

**Subjects** Healthy Chinese children aged 1–10 years old on their last birthday.

**Interventions** Weight was measured to the nearest 0.2 kg.

**Main outcome measures** Linear regression was used to derive a simple formula relating weight to the child's age on his or her last birthday. The accuracy and precision of different age-based weight formulae was compared using coefficient of variation, Bland Altman plots, and by determining the proportion of children with estimates >30% outside the actual weight.

**Results** The Chinese Age Weight Rule is a simple linear formula that is more accurate than and at least as precise as any other age-based weight estimation rule: weight in kg=(3×age last birthday)+5. It is accurate and precise in children <7 years old, but all age-based weight estimates are imprecise in older children.

**Conclusions** The Chinese Age Weight Rule should be used in a Chinese population in preference to any other age-based weight estimation rule. Caution should be taken when using it in older children in whom other weight-estimation tools may be more appropriate.

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In paediatric resuscitation, knowledge of children's weight is necessary in order to provide appropriate drug and fluid doses, equipment selection, and ventilator settings. However, there is often no one accompanying the child who knows the child's weight, and the nature and urgency of the child's condition precludes the actual weighing of the child. Rapid and accurate methods of weight estimation are therefore necessary, and the most commonly used methods are age based or height based.

The Broselow Tape has been shown to be an accurate method of estimating children's weight, especially in children <25 kg,1 2 but the tape itself is expensive, and the estimation can only take place once the child is present in the department. Furthermore, because the tape should be measured against a supine child, it is difficult to use in situations where it would be clinically inappropriate for the child to lie flat, such as epiglottitis or severe asthma.

Age-based formulae however can be used prior to the arrival of the child in the department, for example, when notice has been given by prehospital care providers. This allows the receiving team to prepare appropriate fluids, drugs, and equipment in advance. Age-based formulae do not require the child to lie flat, nor is there any need to purchase equipment, which could be a particularly important consideration in developing world situations.

Numerous age-based weight formulae have been described (table 1). One of the most widely used is that taught on the Advanced Paediatric Life Support (APLS) course3: weight in kg=2×(age in years+4). Several studies have shown that this underestimates weight in Western children and have derived different formulae more appropriate for the study population.6 9–11 A New Zealand study found the APLS formula to underestimate weight in Maori, Pacific Island, and European children but to overestimate the weight of Asian and Indian children. However, there were only 79 children in this latter group.6 An Indian study of 500 children found a similar degree of overestimation.12 The Broselow Tape has been assessed in several Asian populations,13–15 but there has been no large study of age-based weight estimation formulae specifically in Chinese or other East Asian children.

The aim of this study, therefore, was firstly to derive an age-based weight estimation rule in a Chinese population and secondly to compare its accuracy and precision with existing age-based formulae.

## Methods

This was a population-based observational study, part of the Healthy Childrens' Vital Signs and USCOM Study, which also included physiological and ultrasound cardiac output monitor measurements. It was conducted between October 2008 and January 2009, in primary schools and kindergartens in Hong Kong, and recruited healthy Chinese children aged 1–10 years on their last birthday.

Head teachers of all relevant institutions in the Shatin area of Hong Kong were asked for permission to conduct the study, and parents of children in selected classes from participating schools were sent an information pack and consent form. Classes were selected by the schools to provide a representative distribution of age. Children with any chronic or current illness, or taking any medications, were excluded. Weight was measured to the nearest 0.2 kg using electronic scales (Compact precision scale C200H, Conair Far East Ltd, Kowloon, Hong Kong). Children were measured without shoes, wearing the lightest school uniform including socks. School uniforms were weighed separately and subsequent adjustment made to the measured weight of the child.

### Statistical analysis

LMS Chartmaker Pro v2.3 software (Cole and Pan, Medical Research Council UK, 2006) was used to model the relationship between age and weight.16 Briefly, the relationship is described by three age-specific cubic spline curves known as L, M, and S. M represents the median, S is the coefficient of variation, and L is the Box–Cox transformation that renders the data to follow a normal distribution, conditional on age. Combination of these three functions generates centile curves for weight.

Three age-based rules were derived. Firstly, linear regression was used to derive a simple age-based formula for the whole sample, relating weight with the child's age on his or her last birthday. The equation was approximated to produce a formula using integers only. Secondly, having split the sample into two age-groups according to the inflection in the LMS curve, a two-part rule using a different linear regression formula for each age group was derived. Thirdly, the median values obtained from the LMS curve were determined, without creating a formula.

For these three, and the nine previously published rules (table 1), the accuracy of weight estimation was assessed in three ways. Firstly, Bland Altman plots17 determined the mean bias and the 95% limits of agreement. The bias indicates the mean percentage difference between estimated and actual weight, and the limits of agreement indicate in what range 95% of the differences between estimated and actual weights will fall. Secondly, coefficient of variation was calculated as the standard deviation of the differences between estimated and actual weights, divided by the overall mean of estimated and actual weights.18 Thirdly, we determined the proportion of estimates that were within 10%, 20% and 30%, or >30%, different from the actual weights.

The sample was split into two age groups for subgroup analysis. Some studies have analysed their data by weight groups,1 2 12 14 15 so we also split our sample into the following subgroups: <20 kg, 20–30 kg, >30 kg. Each rule was compared with each other rule. Two-tailed t tests were used to compare the Bland Altman bias, and χ^{2} tests to compare the proportions of subjects with weight estimates >30% different from actual weight. p<0.05 was considered to be statistically significant.

MedCalc 10.4.0.0 for Windows (Frank Schoonjans; MedCalc, Mariakerke, Belgium) and Statview 5.0 for Windows (SAS Institute Inc, Cary, North Carolina, USA) were used for analysis.

### Ethics

Ethics approval was obtained from the Clinical Research Ethics Committee of the Chinese University of Hong Kong. Written parental consent was obtained for all subjects more than a week prior to the school visit. Children who were unwilling to participate on the day of the study were excluded.

## Results

One thousand two hundred and forty-eight Chinese children aged between 1 and 10 years old on their last birthday were included (median age 7.1 years, 45% girls). The distribution of weight for age, together with the centile curves derived from the LMS analysis, is shown in figure 1. The inflection in the median curve at 7 years old was used to define age groups for further analysis. There were 639 children aged 7–10 years on their last birthday and 609 aged 1–6 years.

From simplified approximation of the linear regression equations, we derived two Chinese Age Weight Rules (CAWR), for weight (w, kg) according to age (a, years last birthday). For the whole sample, CAWR: w=3a+5. For the two-part rule, CAWR-2: for children aged 1–6 years on their last birthday, w=(7a+25)/3, and for children aged 7–10 years on their last birthday, w=4a–4.

Figure 2A is the Bland Altman plot for CAWR. Figure 2B–D summarises the bias and limits of agreement obtained from Bland Altman analysis for each rule; for all children, children aged 1–6 years on their last birthday and children aged 7–10 years on their last birthday. The LMS-derived median rule is titled Curve, and other rules are named as in table 1. A positive bias means an overestimation; and a negative bias, an underestimation of actual weight.

Overall, CAWR had the least bias (+0.8%). The difference in bias between this rule and all the others, and between each of the others, was highly statistically significant (p<0.0001 for all comparisons except for that between Tintinalli and Curve, p=0.0007). The limits of agreement encompassed a range of 90.5% for Theron and for all other rules from 76.3% to 82.1%.

For children aged 7–10 years on their last birthday, CAWR-2 and Curve had the least bias (±1.2%). The differences between these rules and the others, and between each of the others, were highly statistically significant (p<0.0001) except between Tintinalli and Nelson (no significant difference). The limits of agreement ranged from 86.1% to 90.0%.

For children aged 1–6 years on their last birthday, Curve (−1.4%), Shann (−1.5%), CAWR (−2.0%), and CAWR-2 (+2.1%) had the least bias. The differences between these rules and the others, and between each of the others, were highly statistically significant (p<0.0001) except between APLS, ARC, and Nelson (which are identical) and between Tintinalli and Argall (no significant difference). The limits of agreement ranged from 64.4% to 70.3%.

Coefficients of variation were similar for all rules: approximately 25% for 7–10 year olds and 19% for 1–6 year olds.

Overall, the proportions of estimates >30% different from actual weight were 13.9% for CAWR and 13.4% for CAWR-2. These were not significantly different from APLS, ARC, Nelson, Tintinalli, or Curve, which were all within 11.9%–14.4%. Argall (17.1) was higher than CAWR (p<0.05), and Luscombe, Tinning, and Theron were highly significantly greater (23.1%–39.6%, p<0.0001).

For 7–10 year olds, the proportions of estimates >30% different from actual weight were 20.2% for CAWR and 18.8% for CAWR-2. These were not significantly different from APLS, ARC, Nelson, Shann, Tintinalli, or Curve, which were all within 16.4%–20.8%. Argall (23.5%) was higher than CAWR-2 (p=0.047). Luscombe, Tinning, and Theron were highly significantly greater (28.3%–60.0%, p<0.0001).

For 1–6 year olds, the proportions of estimates >30% different from actual weight were 7.4% for CAWR and 7.7% for CAWR-2. These were not significantly different from APLS, ARC, Nelson, Shann, Tintinalli, Argall, or Curve, which were all within 6.9%–10.3%. Tinning (11.2%) was higher than CAWR-2 (p=0.021). Luscombe and Theron were highly significantly greater (17.1%–17.7%, p<0.0001).

The data for weight subgroups are included in the appendix. The trend was similar to the age subgroups: age-based estimation rules are more precise in smaller, younger children, and unreliable in larger, older children.

## Discussion

The relationship of weight with age is not linear, even within the limited range of 1–10 years. Some age-based rules have therefore attempted to account for this with different linear equations for different age groups4–6 9 or by using nonlinear equations.6 However, this study has shown that a simple linear formula, CAWR, can perform as well as more complex formulae. Even if there were a slight theoretical superiority of a more complex rule, the added complexity might lead to more errors in calculation. If different rules perform similarly, it would be more prudent to use the simplest.

Rather than use a formula at all, a standard growth chart of weight for age might be preferable.19 20 Firstly however, although growth charts are used in nonurgent settings, they are not always available in emergency situations. They could be provided in areas that treat children, but valuable time might be spent looking for the chart, and it would not help prehospital practitioners, unless carried as a pocket reference or as an application on a smart phone. This could be produced cheaply, but it is unlikely that all such practitioners would carry one all the time. Secondly, because integer values are required for mental calculation of fluid and drug doses, the use of a centile chart will still result in approximate values of weight for each year of age. This need for approximation means that growth charts do not necessarily provide better estimates of weight than formulae. It is notable therefore that this study has shown that the estimates derived from such a chart (Curve) are no better than those derived from a simple, linear formula.

Weight-estimation rules must be both accurate and precise. Accuracy is a measure of the average deviation from reality and is reflected by the Bland Altman bias. Precision is a measure of the scatter and is reflected by the limits of agreement, and also by the proportion of estimates that fall outside a certain acceptable limit, in this case, 30% of the true value. Bias can be improved by using locally derived average values of weight for age, whether in a formula or a chart. There will always be some inaccuracy because of the practical desirability to use integer values for both age and weight. But it is the population distribution of weight for age which determines the precision of an estimation tool, and therefore, however accurate a rule becomes, it will become dangerously imprecise in older children whose spread of weight for age is greater. Other methods of weight estimation, such as from the child's height,1 foot length or mid-arm circumference,21 might be more precise22 23 but depend on the presence of the child. The advantage of age-based rules is that they can be calculated before the clinical encounter, whether waiting in the resuscitation room or travelling to the scene of an incident. There will therefore always be value in age-based rules, but caution must be taken of the imprecision in older children, and more precise methods used as soon as is practical.

CAWR is both clinically and statistically significantly more accurate than many existing rules. This is not surprising, as it was derived in this population, and further validation is required to confirm the degree of accuracy. The bias (the mean difference between estimated and actual weight) is within 3.5% in all age groups. Some rules, including the older APLS, underestimate by >10%. Others, including the more recent Tinning and Luscombe, overestimate by about 10%. Theron, which was developed in ‘large for age’ Maori and Pacific Island children, hugely overestimates. Generally, the inaccuracies are greater still in the 7–10 year olds but reduced in the 1–6 year olds.

However, although the new rules demonstrate a high degree of accuracy, it is apparent that none of the rules is very precise. For CAWR, the proportion of estimates >30% different from the actual weight is no different from the best of the other existing rules. In younger children, about 7% would have weight estimates deviating >30% from reality, which might be considered acceptable, but this proportion rises to about 20% in older children. This is probably an unacceptably high proportion of clinically significant estimation errors. The Bland Altman limits of agreement and coefficients of variation also demonstrate the increasing scatter of weight for age in older children. The limits of agreement describe the range within which 95% of expected estimations will lie; in older children, this range implies that 95% of children will have estimates within about 45% above or below the average.

The main strength of this study is its large size. It is also the first of its kind in a Chinese population. No other study has compared the performance of all the major age-based rules, and we included examples of simple, complex and nonlinear rules. We have assessed accuracy and precision in a number of ways. Bland Altman plots and coefficient of variation are commonly used to compare two measurements of the same variable,18 in this case, the estimated weight and the actual weight. However, the proportion of subjects whose error of estimation would be greater than a certain percentage is also important to determine, as it is perhaps most readily understood in a clinical context. Previous papers have used 10% as a cutoff.8 13–15 However, most drugs have a therapeutic ratio (ratio of toxic to effective dose) of >50%.24 We have presented data for cutoffs of 10%, 20%, and 30% as representing a more pragmatic limit.

There are several limitations. Firstly, we excluded children with any illness. Although these rules are used clinically in ill and injured children, the intention in practice is to estimate a child's normal weight, not to measure their weight while ill, which may be significantly less than their ideal weight because of the disease process. However, by excluding those even with minor illness that would not affect weight, we introduced a potential selection bias. This was done for pragmatic reasons, as language barriers and different cultural perceptions of disease would have made it very difficult to specify in our invitation letter which illnesses were excluded. We do not think that the exclusion of children with minor illness is likely to have significantly skewed our results. Secondly, we have not included children from 11 years old or <1 year old. Many rules do not include infants, and those that do use a different formula from that for those >1 year old.5 7 Similarly, only a few rules are intended for children of 11 years or older.5 6 9 We felt it best to study an age group that all rules would apply to. It was also practically very difficult to recruit infants. Thirdly, the division of the sample at 7 years appears arbitrary. This cutoff was chosen for three reasons: it reflected the inflection of the weight for age curve, which was the point at which the divergence of the centile curves also increased. Pragmatically, it roughly divided our sample in to equal subgroups, and it was the cutoff used in Nelson.5

## Conclusion

This is the first study of age-based weight estimation methods in a Chinese population. New formulae (CAWR and CAWR-2) have been derived for use in this population, which perform as well as or better than previously published age-based methods. Of the two new formulae, CAWR-2 is more complex but does not significantly outperform CAWR. Curve, the method using the median values derived from centile curve construction, is also of similar accuracy and precision to CAWR. We would therefore recommend the use of the simpler formula: weight=(3×age)+5. In this derivation study, this rule is at least as precise as any other published rule, and more accurate than other commonly used formulae. The rule is most precise in younger children, but in common with all age-based rules, is imprecise in older children. If this rule is validated, we would recommend its use for Chinese children in time-critical emergency care situations when measurement of the child's weight is not possible by other means. Whatever rule is applied, caution must be used with children >7 years old.

### What is already known on this topic

Age-based formulae to estimate children's weight are widely taught for use in resuscitation.

The most commonly quoted formula, weight=(age+4)×2, underestimates the weight of Western children.

Most of the formulae were derived in Western populations, and none has been validated in a Chinese population.

### What this study adds

This study describes a new formula, the CAWR, for use in Chinese children: Weight in kg=(3×age last birthday)+5.

This formula is more accurate than, and at least as precise as, previously published age-based formulae.

Caution is advised when applying age-based rules in older children because the degree of imprecision is of potential clinical significance.

## Appendix

## References

## Footnotes

Funding We received a grant of HK$72,000 from the Chinese University of Hong Kong to conduct this study. We also received a grant of HK$100,000 from the Hong Kong College of Emergency Medicine.

Competing interests None.

Ethics approval This study was conducted with the approval of the Chinese University of Hong Kong Clinical Research Ethics Committee.

Provenance and peer review Not commissioned; externally peer reviewed.

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