Background: Prescribing medication appropriate to a child’s bodily dimensions is fundamental to paediatric emergency medicine. Mathematical formulae are frequently used in clinical practice to estimate children’s weights. In 1995 the UK’s paediatric reference data, describing age-related changes in bodily proportions (both weight and height), were updated and published. This study assesses the validity of using mathematical estimates, age-based estimates or length-based estimates of weight (the latter both compiled from this reference data) by comparison with actual physical measurements recorded in a paediatric clinic setting.
Methods: A prospective study was carried out in a paediatric outpatient setting recording age, weight and height for statistical comparison with these three possible methods.
Results: 544 children aged 0–11 years were recruited, with mean (SD) age, weight and height of 5.3 (2.9) years, 21.4 (10) kg and 108 (22) cm, respectively.
Conclusions: Both length-based and age-based estimates of weight outperformed the currently accepted “gold standard” mathematical estimate when applied to children up to 11 years of age (∼35 kg). Length-based estimates were statistically superior, but the physical limitations and technical constraints posed when attempting to accurately measure a child’s length in emergency environments may favour the simplicity of using the child’s age against tables of growth chart reference data to provide an estimate of their weight.
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Making calculations to prescribe medication and select equipment according to a child’s bodily dimensions is fundamental to the practice of paediatric medicine. However, mathematical errors can occur, especially when faced with a clinical emergency where delays may be critical and where errors in calculations have the potential for serious harm. In the prehospital setting, the potential for error is greatest, with personnel working autonomously in conditions of poor lighting and adverse weather, far removed from the safeguards and checks of the emergency room. Various systems and guidelines have been devised in an attempt to minimise these errors, all of which are dependent on knowledge of the child’s weight.
In an ideal situation, a child’s physical weight would be known by their rescuer. Krieser et al1 have recently advocated using parental weight estimates, with 89% of parents attending an emergency department volunteering an estimated weight. In a prehospital setting this figure is likely to be smaller, forcing the rescuer to rely on estimations of the child’s weight to facilitate their interventions and treatments. Their chosen method clearly needs to be accurate, should be dependent on factors that are readily available clinically (eg, age or length) and should ideally be easily calculable.
Methods of estimation (currently used or deserving exploration/development) include: (1) age-based estimates of weight, estimated by either mathematical formulae or referenced from growth chart data, and (2) length-based estimates of weight (again referenced from growth chart data).
Age-based estimates of weight
A child’s age is frequently the only variable known to a rescuer at the scene of an incident. If further information is not forthcoming, this limited information can be used to estimate the child’s weight using mathematical formula such as the formula described in the Advanced Paediatric Life Support (APLS) manual2 which provides an approximate weight for children aged 1–10 years. This method has become somewhat of a “gold standard” and is used worldwide: Weight (kg) = 2 (age in years + 4). This method does tend to underestimate a child’s true weight and its limitations are well recognised.1 3 4
In 1995, updated UK reference data reflecting paediatric age-related changes in bodily proportions were published by the Child Growth Foundation (their “Girls and Boys Four-in-One Growth Charts”).5 These charts are now widely used and have the support of the Royal College of Paediatrics and Child Health who recommended that these charts “should now be kept unchanged for the foreseeable future (10–20 years) … to avoid confusion and to allow a base for comparison for weight and BMI trends”.6 Using these data, a chart was constructed of estimated child weights for any given age (table 1). Table 1 was constructed as follows: for each given age from “newborn” to 11 years, the 50th centile weight for a girl and the 50th centile weight for a boy was obtained and averaged to give an estimated girl-boy weight for that age. Figure 1 illustrates these data (and also compares them with the APLS estimates described above).
This study compares the reliability of both of these age-based estimates with the length-based estimates described in table 2. Over 11 years of age the unpredictability of pubertal growth velocities and the differences between the sexes renders similar age estimations unreliable and therefore unsafe, graphically highlighted by the divergence shown in fig 2A.
Length-based estimates of weight
A child’s measured supine length can also be used to estimate their weight by using a tape device and applying knowledge of length-related increases in children’s bodily weights derived from growth chart data. This approach has both advantages and disadvantages. Clearly, if a child is found unsupervised and unconscious then a length-based estimate is the only method available. However, clinical limitations can restrict the usefulness of such length-based systems owing to problems encountered in obtaining accurate measurements. In the prehospital setting it is not uncommon for an injured child either to be trapped or rendered immobile by their injuries, making movement hazardous and making attempts to accurately measure the child’s length physically impossible—for example, the child with spinal injuries or the child victim of entrapment. Similarly, injured children are frequently shocked, agitated, uncooperative and in pain, which again can physically limit the reliability of a length-based approach.
For study purposes, 1995 UK growth chart data were used to compile a chart of approximate child weight estimates for a given length (table 2). Note that weight-for-length charts such as table 2 are not recommended for routine use in clinical practice, due to a discontinuous pattern of change seen throughout infancy and early childhood.7 Table 2 was constructed purely to allow statistical comparison of the proposed methods.
Empirically, 50 cm was set as the minimum length for the study since attempts to accurately measure infants of smaller proportions in an emergency would certainly be unreliable. The upper length for the range (160 cm) reflects the upper limit of the available growth chart data.
A study was undertaken to compare children’s actual physical measurements recorded in an outpatient setting with: (1) age-based mathematical estimates (APLS formula); (2) age-based estimates compiled from growth chart reference data (table 1); and (3) length-based estimates, again derived from growth chart reference data (table 2), in order to establish the most accurate and reliable method for weight estimation in emergency practice.
During an 11-week period a prospective comparison study was performed which aimed to recruit all children aged 11 years and under attending our children’s outpatient clinics. On arrival, each child’s age, weight and height were routinely recorded in their case notes by a member of the paediatric nursing team. Lengths were measured using either a Castlemead Magnimetre (Welwyn Garden City, Hertfordshire, UK) wall-fixed stadiometer or a Rollameter (Raven Equipment Ltd, Great Dunmow, UK) stadiometer (depending on whether the child was able to stand up straight independently), with weights measured digitally using a Wedderburn Weighmed500 clinical scale. The recorded ages, weights and heights were statistically compared to determine the reliability of APLS estimates, age-based estimates and length-based estimates when used to estimate a child’s weight.
To allow these clinical measurements to be used for study purposes, research and ethical Committee approval was obtained as well as written consent from each individual enrolled. Issues of confidentiality and those related to the Data Protection Act were also addressed.
The Bland-Altman approach8 was chosen to compare age-matched observed weights and lengths (recorded in the outpatient setting) with the age-based and length-based estimates described in tables 1 and 2. This approach uses graphical methods to examine by how much an estimate is likely to differ from an observed clinical measurement, referred to as the bias. Along with the bias, 95% limits of agreement (LOA) were calculated. These limits provide an interval within which 95% of the differences would be expected to lie. The narrower the LOA, the greater the degree of confidence the clinician can have in using that estimate as a replacement for the child’s true weight. Where these observed differences are found not to be normally distributed or where there are departures from crucial assumptions, a transformation of the measurements and estimates is applied. Following such transformation, the bias and LOA are recalculated on the most suitable scale. The 95% confidence intervals (95% CI) for the LOA are then also determined.
Three estimates for weight were examined:
Age-based estimates as calculated by the APLS formula (APLS).
Age-based estimates from growth chart data.
Length-based estimates using growth chart data.
To enable suitable comparison between the APLS formula and the age-based estimate of weight, mid-year values for weights were used. For the length-based estimates, the number of cut-off points needed to be reduced to allow fair comparison with the other two methods (ie, table 2 describes 23 cut-off points for length-based estimates which was reduced to 12 to allow suitable comparison with the two age-based methods which each had 12 cut-off points.
A total of 846 children (49.7% girls and 50.3% boys) attended the outpatient department during the study period and consented to having their age, weight and height recorded. A further six children were not enrolled due to parental objections. The mean (SD) age was 6.4 (4.9) years. There were 544 children aged 1–11 years with a mean (SD) age of 5.3 (2.9) years. The mean (SD) weight and height for this subgroup were 21.4 (10) kg and 108 (22) cm, respectively. These measurements are shown in fig 2A and B.
The estimates of weight (APLS, age-based and length-based) were compared with the observed physical measurements for each of the 544 subjects. Figure 2 and the initial Bland-Altman plots (fig 3A–C) for the weight estimates show that the estimates vary more as weight increases. Log transformation was performed to overcome this issue, allowing further analysis. The ratio of the estimate to the observed measurement against the average was calculated and the LOA were determined for each estimate. The purpose of this transformation was to remove excess variability and this proved reasonably successful, although at higher weights some still persisted (fig 4). As the LOA on a log scale are difficult to interpret on the original scale, the final Bland-Altman plots present the ratio of the estimate to the true weight (since back transformation would give the limits as ratios of the estimate to the observed measurement). These are shown graphically in fig 5. Table 3 shows the mean ratio and LOA (with 95% CI) for each estimate. Since the sample size was sufficiently large, the 95% CIs on the LOA are very narrow and, as a result, are not shown on the plot.
All three methods of estimation underestimated the child’s true weight, with the APLS formula showing the most bias. On average, the APLS formula estimated a child’s weight to be 88% of the observed value, with 95% of estimates being between 54% and 122% of the observed weight (table 3 and figs 4 and 5). The age-based estimates were, on average, the closest of the three methods assessed, estimating a child’s weight to 98% of their observed weight. The LOA (figs 4 and 5) were, however, the widest (±36%), with estimates being between 61% and 134% of the observed weight. On average, the length-based estimates estimated a child’s weight to be 96% of their observed weight and had the narrowest LOA (±24%) (figs 4 and 5).
Comparing the LOA for each method, the length-based estimate was found to be reliable to within 24% of the observed weight, the APLS within 34% and the age-based estimate within 36%; this provides evidence to support the use of the length-based method.
Without unravelling the complexities of child growth, it is clear that age, length and weight are all interrelated. Intuitively, the relationship between length and weight (fig 2B) is clearly stronger than that of age and weight (fig 2A): a tall child invariably weighs more than a shorter child although an older child is not necessarily heavier than a younger child—an observation supported statistically by this study (length-based estimates had the narrowest LOA).
Length-based and age-based estimations of a child’s weight were both superior to the mathematical estimates (APLS formula) currently in use, although all three methods underestimated the child’s true weight.
Where circumstances permit a child’s length to be accurately measured, this technique was statistically found to be the most reliable. However, it should be emphasised that study lengths were accurately measured under optimal conditions in a controlled clinic setting, conditions far removed from those encountered by the roadside or in a resuscitation bay. A study to quantify the limitations of length-based techniques in emergency practice would be informative (eg, observing differences between lengths measured with a tape device under real-life emergency conditions and subsequent convalescent length measurements made in hospital under controlled circumstances). The various clinical situations that limit the usefulness of length-based measurements have already been described and, if such further study were to reveal significant differences between length measurements recorded in an emergency and “controlled” length measurements, it is possible that these technical difficulties might offset the statistical benefits of length-based estimates.
Age-based estimates (growth chart) were reasonably accurate and demonstrated much less bias than APLS estimates (98% vs 88%). They have the advantage of being simple to use and could replace APLS estimates as a future “gold standard” if they were more readily available. To this end, a chart for use by front-line ambulance personnel or for display on emergency department whiteboards of estimated weights could be compiled by simplifying table 1 (see Appendix 1). (The BNF for Children9 also offers a similar chart inside its back cover.)
While the limitations of the APLS formula are well described, in the absence of an accurate length measurement or a chart of age-based estimates, a rescuer might still reasonably use such an approximation for children aged 10 years and under.
Mathematically, it would be possible to correct for the weight underestimations (or bias) seen with each of the three methods by inflating each estimate by the reciprocal of their mean bias.8 Considering, for example, the APLS estimate, if it were to be inflated by the reciprocal of the mean ratio (eg, 1/0.88 = 1.14), near 100% agreement between the estimate and the true value could, on average, be obtained. This modified APLS formula becomes:
Weight (kg) = 25/11 (age in years + 4)
One of the strengths of the original APLS formula was its relative simplicity (although miscalculating this formula is frequently seen on APLS courses; personal observation). If this modified APLS estimate were adopted, attempting to multiply by an inflation factor of 25/11 in a clinical emergency would be cumbersome to say the least, would cause genuine confusion and would certainly increase the frequency of drug calculation errors seen—reasons enough to endorse the continued usage of the APLS formula in its current unadulterated form. In addition, applying inflation factors to each of the estimates has the undesired result of inflating/widening their LOAs by a similar factor, making them less reliable. The LOA of the modified APLS becomes ±39% (compared with ±34% in its original form), and the LOAs of the age-based and length-based estimates become 38% and 26%, respectively. As a result, it is difficult to endorse such inflations since they adversely affect the overall reliability of the chosen method.
This study also highlights the difficulties encountered when attempting to apply a “one size fits all” approach to the diverse range of individual body sizes seen in daily practice, even within a group of children of a similar age. Whichever method the clinician ultimately chooses, he/she must also independently consider the individual child’s bodily proportions before applying generalisations found to be statistically applicable to a study cohort of children. This observation becomes even more relevant beyond 11 years of age where pubertal changes render simple attempts (age, length, etc) to estimate an adolescent’s weight unreliable and, in these circumstances, adult criteria must be considered.
Length-based and age-based estimations of a child’s weight are both suitable methods of weight estimation for use in emergency practice. Both methods are more accurate than the APLS formula. Length-based estimates were statistically superior, but the physical limitations and technical constraints posed when attempting to accurately measure a child’s length in real-life emergency environments may favour the simplicity of using the child’s age against growth chart reference data.
The authors thank the nursing team and receptionists of Poole Hospital children’s outpatients department who coordinated and collected the data as well as Dr D Shortland, Clinical Director, who supervised the project. The Child Growth Foundation is acknowledged for permission to use their LMS Dataset.
APPENDIX: PROPOSED WEIGHT REFERENCE CHART FOR UK AMBULANCE PERSONNEL AND EMERGENCY ROOM WHITEBOARD USAGE
Competing interests: JMS is the author of the SandellTape, a resuscitation device incorporating both age- and length-based estimates of children’s bodily proportions.
Ethics approval: Research and ethical committee approval was obtained as well as written consent from each individual enrolled. Issues of confidentiality and those related to the Data Protection Act were also addressed.