Performance of the Weight Estimation Formulae
The primary outcome of this study was the relationship between measured and estimated weights by the 3 formulae. Formula-derived and measured weights were highly correlated (r = 0.81–0.83, P < 0.001) with the Theron formula producing the highest correlation coefficient (Table 3). When compared with the others, the Luscombe formula was better at predicting the weights of children in our sample, with a bias (mean percentage error [MPE]) of 3.4 kg (95% confidence interval [CI], 3.2–3.5 kg) and 89.7% of estimates within 10% of measured weight. The APLS formula was the least accurate with a negative MPE, which indicates overall underestimation of weights in the study sample (Table 3).
Fig 2, A–C is the Bland-Altman plots of the difference between formula-derived and measured weights in the derivation cohort (N = 10,488) and summarizes the bias and limits of agreement obtained from Bland-Altman analysis for each weight estimation method.
Effect of High BMI
When the children were stratified into normal versus high BMI categories (Table 4), all the formulae demonstrated reduced accuracy in children with high BMI. The Theron formula was the most accurate in the high BMI cohort (76.8%). The APLS formula does not appear to be a valid weight estimation tool in overweight/obese children, showing a negative MPE of −23.21 kg (95% CI, −23.9 to −22.5 kg) and accuracy to within 10% of measured weight of only 26%.
The Michigan Formula
A linear regression equation indicated that the best line of fit to our data was represented by y = 3.36*x +9.62, r2 = 0.786 (Fig. 3). This equation was further simplified to yield the “Michigan formula”: Weight (kg) = 3 × age (in years) +10.
The derived equation was then applied to the validation cohort (N = 3912) to confirm and compare its accuracy with existing formulae. As detailed in Table 5, the derived formula was the most accurate with a MPE 3.6 kg (95% CI, 3.3–3.8 kg) and accuracy to within 10% of measured weight of 92%.
Many clinical interventions in children require manipulation of drug dosages, a step that is intricately linked with knowing the child’s weight. This makes an accurate measurement or estimate of a child’s weight a critical first step in the delivery of care to the pediatric patient. In general, the performance of a weight estimation equation will depend on the prevailing rates of high BMI in a population. Therefore, given the widespread childhood obesity rates among contemporary U.S. children, the overarching objective of this retrospective cohort study was to assess the performance of 3 commonly used pediatric age-based weight estimation formulae at predicting directly measured weight in children who underwent elective, noncardiac operations.
Consistent with several recent reports,10,12,16 we observed that many of the available formulae had modest to high accuracy as weight estimation tools. However, all the formulae had only low-to-modest accuracy when used to predict the weight of children in the high BMI category. We also derived an alternate equation, the Michigan formula, that is easy to calculate, is more accurate than existing formulae at estimating the weight of U.S. children, and has low bias and moderate-to-high accuracy even in overweight/obese children.
In contemporary pediatric anesthesia practice, almost every therapy (drugs, fluids boluses, defibrillation energy, initial ventilation setting, radiation dosage, etc.) is based on the patient’s weight. Furthermore, assessment of response to therapy or the adequacy of resuscitation, for example, urine output, need to initiate or escalate inotropic support; total parenteral nutrition requirements and antibiotic therapy are all based on the child’s weight.2–4 In most children undergoing anesthesia, it is possible to directly measure the child’s weight during the preoperative assessment. However, in children presenting with trauma or critical illness, it is often impractical or impossible to get an accurate directly measured weight. In many cases before these children present to the anesthesia care provider or to the intensive care unit, a weight has been assigned to the patient from the ED. The assigned weight is often based on one of several weight estimation methods commonly used in the ED.3–8 These formulae were however derived before the widespread increased prevalence of childhood overweight/obesity.
Although it is often possible to weigh most children undergoing anesthesia, occasionally this is impossible or the practitioner has to rely on estimated weight from the ED (where the formulae we assessed are routinely used). It is therefore important to assess the accuracy of these formulae. Desirable features of any weight estimation method apart from ease of use (requiring simple mental arithmetic) are accuracy and precision. Precision is a less desirable method of assessing performance. Accuracy is often described as the best performance measure for clinical test comparisons.5,22 Our derived equation (the Michigan formula) demonstrated superior accuracy to the APLS and Luscombe formulae and comparable accuracy with the Theron formula.
Although the APLS formula is widely used and is recommended for weight estimation in the Pediatric Advanced Life Support (PALS) manual,24 we found that despite having high correlation coefficients, it had the least accuracy and precision of all the formulae. This is in agreement with several reports, which indicate that the APLS formula consistently underestimates the weight of children.20,25,26 The high correlation and poor precision and accuracy could be explained by the fact that correlation measures relative rather than absolute agreement between 2 tests and ignores bias and precision of the tests.27 Underestimating the weight of a child undergoing anesthesia could lead to suboptimal anesthetic drug dosing, poor perioperative pain control, and under resuscitation. Conversely, overestimating a child’s weight could lead to drug overexposure when a weight-based medication dosing is used.
Weight estimation in overweight/obese children presents exceptional challenges. This is especially problematic in children with extreme obesity. Many of the pediatric weight estimation formulae were derived by using the weight of European children before the widespread prevalence of childhood obesity. They are therefore likely to demonstrate poor precision and accuracy when applied to a population with higher average weight or obesity prevalence rates. The Theron formula is the only pediatric equation that was specifically developed for children who are large for age.20 Although the authors did not specify the obesity prevalence in their cohort, we could speculate that their childhood obesity rates are probably as high, if not higher than ours. One major drawback of the Theron formula, however, is that it is complex (requires exponential calculation) and therefore does not lend itself to easy arithmetic computation. Our derived equation is simple and easy to use and can be rapidly computed to give a quick estimate of a child’s weight.
Whichever age-based weight estimation formula a practitioner chooses to use, it is essential to recognize the inherent limitations of all of them.28 In general, they tend to be imprecise, especially in older children. Furthermore, a formula with narrow bias (highly accurate) but very wide precision (limits of agreement) will be less useful in clinical practice because it will result in more children being given medication dosages that are outside the recommended dosage range.
This study has several strengths including use of data from a large cohort of children with directly measured weight. It is also the first study specific to a large population of children undergoing elective surgery. However, there are some limitations to the study. The single institution, retrospective, cross-sectional nature of the study design did not allow for direct verification of the measured weights that were the basis of analysis for this study. Therefore, it was impossible to independently verify the weights recorded in the electronic database. Another limitation of this study is the relatively frequent prevalence of children with high BMI in our study subjects. Since many of the formulae were not originally developed to estimate the weight of obese children and indeed many were introduced before the epidemic of childhood overweight/obesity, our findings may not be applicable to populations with different childhood obesity prevalence. Furthermore, we could only speculate and determine whether a more accurate weight estimation formula will affect clinical outcome. Although the present investigation did not examine cause and effect relationships, previous reports based on retrospective data29 have described patients given subtherapeutic dosages of anticonvulsants based on estimated weights who continued to convulse and a child with hypoglycemic seizure who received a subtherapeutic dosage of 50% dextrose. This child continued to seize and eventually required more 50% dextrose and anticonvulsants on admission to the hospital.29 Clearly, direct cause and effect of weight estimation and harm will be more difficult to establish in the perioperative period (since most anesthetic medications are usually “titrated to effect”), one could speculate that drugs with narrow therapeutic indices could potentially cause harm when given in supratherapeutic dosages based on estimated weight.
Finally, the present report could be criticized for not assessing the validity of weight prediction by using the Broselow tape (Armstrong Medical Industries, Lincolnshire, IL). However, the Broselow tape estimation is a height-based method, and we chose to focus on age-based methods because sometimes height estimation may not be practical in an emergency situation, whereas a child’s age is invariably available. In addition, several investigators have shown that the Broselow tape method consistently underestimates the weight of children and have suggested that children in developed countries have outgrown it.18 Finally, the Broselow tape is more commonly used in ED units and is rarely used by anesthesia caregivers.
In summary, the performance of 3 age-based weight estimation formulae at predicting the actual weights of children undergoing anesthesia were evaluated, and we found that all the formulae demonstrated low-to-moderate accuracy in our cohort of children. A new age-based equation (the Michigan formula) was developed and validated. It matched or surpassed in accuracy currently available age-based weight estimation formulae. The Michigan formula is easy to use and may be more appropriate at estimating the weights of children, given the prevailing childhood obesity rates. Nonetheless, given the imprecision inherent in all age-based weight estimation formulae particularly with increasing age,22 care should be taken when using the Michigan formula in children older than 9 years. Further work is required to validate the Michigan formula in other populations with similar childhood obesity pattern.
Name: Ray Ackwerh, MD, FRCA.
Contribution: This author helped design and conduct of the study, data analysis, and manuscript preparation.
Attestation: Ray Ackwerh approved the final manuscript and attests to the integrity of the original data and the analysis reported in this manuscript.
Name: Laura Lehrian, DO.
Contribution: This author helped design and conduct of the study and manuscript preparation.
Attestation: Laura Lehrian approved the final manuscript and attests to the integrity of the data and the analysis reported in this manuscript.
Name: Olubukola O. Nafiu, MD, FRCA.
Contribution: This author helped with design and conduct of the study, data analysis, and interpretation and manuscript preparation. Olubukola O Nafiu is the corresponding author.
Attestation: Olubukola O. Nafiu approved the final manuscript and attests to the integrity of the original data and the analysis reported in this manuscript.
This manuscript was handled by: Peter J. Davis, MD.
1. Erstad BL. Which weight for weight-based dosage regimens in obese patients? Am J Health Syst Pharm. 2002;59:2105–10
2. Cella M, Knibbe C, Danhof M, Della Pasqua O. What is the right dose for children? Br J Clin Pharmacol. 2010;70:597–603
3. Krieser D, Nguyen K, Kerr D, Jolley D, Clooney M, Kelly AM. Parental weight estimation of their child’s weight is more accurate than other weight estimation methods for determining children’s weight in an emergency department? Emerg Med J. 2007;24:756–9
4. Luscombe M, Owens B. Weight estimation in resuscitation: is the current formula still valid? Arch Dis Child. 2007;92:412–5
5. DuBois D, Baldwin S, King WD. Accuracy of weight estimation methods for children. Pediatr Emerg Care. 2007;23:227–30
6. Geduld H, Hodkinson PW, Wallis LA. Validation of weight estimation by age and length based methods in the Western Cape, South Africa population. Emerg Med J. 2011;28:856–60
7. Sandell JM, Charman SC. Can age-based estimates of weight be safely used when resuscitating children? Emerg Med J. 2009;26:43–7
8. Black K, Barnett P, Wolfe R, Young S. Are methods used to estimate weight in children accurate? Emerg Med (Fremantle). 2002;14:160–5
9. Frush DP, Soden B, Frush KS, Lowry C. Improved pediatric multidetector body CT using a size-based color-coded format. AJR Am J Roentgenol. 2002;178:721–6
10. Argall JA, Wright N, Mackway-Jones K, Jackson R. A comparison of two commonly used methods of weight estimation. Arch Dis Child. 2003;88:789–90
11. Hofer CK, Ganter M, Tucci M, Klaghofer R, Zollinger A. How reliable is length-based determination of body weight and tracheal tube size in the paediatric age group? The Broselow tape reconsidered. Br J Anaesth. 2002;88:283–5
12. Leffler S, Hayes M. Analysis of parental estimates of children’s weights in the ED. Ann Emerg Med. 1997;30:167–70
13. Grivas TB, Mihas C, Arapaki A, Vasiliadis E. Correlation of foot length with height and weight in school age children. J Forensic Leg Med. 2008;15:89–95
14. Cattermole GN, Leung PY, Mak PS, Graham CA, Rainer TH. Mid-arm circumference can be used to estimate children’s weights. Resuscitation. 2010;81:1105–10
15. Luten R. Error and time delay in pediatric trauma resuscitation: addressing the problem with color-coded resuscitation aids. Surg Clin North Am. 2002;82:303–14, vi
16. Luscombe MD, Owens BD, Burke D. Weight estimation in paediatrics: a comparison of the APLS formula and the formula ‘Weight=3(age)+7’. Emerg Med J. 2011;28:590–3
17. Ogden CL, Fryar CD, Carroll MD, Flegal KM. Mean body weight, height, and body mass index, United States 1960–2002. Adv Data. 2004;347:1–17
18. Ken Milne W, Yasin A, Knight J, Noel D, Lubell R, Filler G. Ontario children have outgrown the Broselow tape. CJEM. 2012;14:25–30
19. Brown TCK, Fisk GC Anesthesia for Children. 19922nd ed London Blackwell Scientific Publications:68–70
20. Theron L, Adams A, Jansen K, Robinson E. Emergency weight estimation in Pacific Island and Maori children who are large-for-age. Emerg Med Australas. 2005;17:238–43
21. Kuczmarski RJ, Ogden CL, Guo SS, Grummer-Strawn LM, Flegal KM, Mei Z, Wei R, Curtin LR, Roche AF, Johnson CL. 2000 CDC growth charts for the United States: methods and development. Vital Health Stat 11. 2002;246:1–190
22. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1:307–10
23. van Stralen KJ, Dekker FW, Zoccali C, Jager KJ. Measuring agreement, more complicated than it seems. Nephron Clin Pract. 2012;120:c162–7
24. Kleinman ME, de Caen AR, Chameides L, Atkins DL, Berg RA, Berg MD, Bhanji F, Biarent D, Bingham R, Coovadia AH, Hazinski MF, Hickey RW, Nadkarni VM, Reis AG, Rodriguez-Nunez A, Tibballs J, Zaritsky AL, Zideman DPediatric Basic and Advanced Life Support Chapter Collaborators. . Pediatric basic and advanced life support: 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science with Treatment Recommendations. Pediatrics. 2010;126:e1261–318
25. Krieser D, Nguyen K, Kerr D, Jolley D, Clooney M, Kelly AM. Parental weight estimation of their child’s weight is more accurate than other weight estimation methods for determining children’s weight in an emergency department? Emerg Med J. 2007;24:756–9
26. Luscombe M, Owens B. Weight estimation in resuscitation: is the current formula still valid? Arch Dis Child. 2007;92:412–5
27. Levey AS, Bosch JP, Lewis JB, Greene T, Rogers N, Roth D. A more accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Modification of Diet in Renal Disease Study Group. Ann Intern Med. 1999;130:461–70
28. Cattermole GN, Graham CA, Rainer TH. Pediatric weight estimation. Ann Emerg Med. 2013;62:101
© 2014 International Anesthesia Research Society
29. Lim CA, Kaufman BJ, O’Connor J Jr, Cunningham SJ. Accuracy of weight estimates in pediatric patients by prehospital Emergency Medical Services personnel. Am J Emerg Med. 2013;31:1108–12