Many therapeutic interventions in children depend on 3 related variables: age, measures of organ function, and body weight.^{1} The most commonly used of these 3 variables in children undergoing anesthesia and surgery is the child’s weight. Indeed, many medications in children are administered on a milligram per kilogram basis.^{2}

For most children presenting for surgery and anesthesia, direct weight measurement is possible. However, in acute medical, trauma, and surgical cases, this is often not possible or appropriate, and so an estimation of the child’s weight is necessary. Studies about pediatric weight estimation have traditionally come from emergency department (ED) data.^{3–8} Initial resuscitation is clearly of vital significance; however, the importance of pediatric weight estimation extends beyond the ED. In many acutely unwell patients and almost all critically ill patients, an actual weight cannot be determined until they have essentially recovered. The weight that is estimated for resuscitation purposes is also used during the patient’s passage through other hospital departments, including radiology, operating room, intensive care unit, and regular ward.^{5},^{8},^{9}

Several pediatric weight estimation methods are currently used.^{3–8},^{10}–12 They fundamentally depend on either the child’s age,^{4–6} height/length,^{6},^{12} or some other morphologic features of the child, for example, foot length,^{13} mid-arm circumference,^{14} or parent or clinician-based estimate.^{3} The most widely used weight estimation methods in children are the length-based Broselow tape method^{15} and the age-based Advanced Pediatric Life Support (APLS) formula.^{16}

The current epidemic of childhood obesity in the general population means that a large proportion of the millions of children who undergo surgery and anesthesia in the United States are either overweight or obese. Recent population estimates indicate that whereas the weights of children and adolescents have increased by 10 to 15 lb in the last 50 years, there was only a slight increase (0.7–0.9 in) in height. This upward shift in weight and height has led to a significant increase in the body mass index (BMI) of children.^{17} The disproportionate increase in weight relative to height in children is likely to result in gross underestimation of weight when using a length or height-based weight estimation method or if any of the age-based weight estimation methods that predated the childhood obesity epidemic is used. Indeed, several investigators have shown that the popular Broselow tape consistently underestimated the weight of children,^{4},^{8},^{10} and some have suggested that children in North America have outgrown it.^{18}

Many of the studies on pediatric weight estimation have been on children presenting to the ED. Although many of these formulae are used to estimate weight of children undergoing anesthesia and are commonly cited in pediatric anesthesia textbooks,^{19} very few investigators^{11} have attempted to validate them in children undergoing anesthesia. Given the rising prevalence of overweight and obesity in children and the importance of weight-based therapy in pediatric perioperative care, it is imperative to determine the comparative accuracies of some commonly used age-based weight estimation formulae in children undergoing anesthesia. Therefore, the primary objective of the present study was to assess the performance of 3 commonly used age-based weight estimation formulae (Table 1) at predicting directly measured weight in children undergoing elective, noncardiac operations. The hypothesis tested was that these formulae would underestimate the measured weights of children undergoing elective surgeries. A new age-based weight estimation formula was derived and its performance compared with existing formulae. Secondary objectives were to assess the performance of each weight estimation methods across BMI categories.

#### METHODS

This retrospective, cohort study compared the accuracy and applicability across age and weight categories of commonly used weight estimation methods with directly measured weight of children aged 2 to 12 years who underwent elective, noncardiac surgery at our institution. We specifically chose to evaluate 3 of several available age-based formulae for the following reasons: the APLS and Luscombe formulae because they are the most widely recommended for pediatric weight estimation, and the Theron formula because it was purposely developed for a population with high childhood obesity rates.^{20} The present investigation covered a slightly wider age range than that covered by many of the current age-based weight estimation formulas.

IRB approval with waiver of consent (use of de-identified data) was obtained before data extraction. Basic clinical, demographic (age and sex), and anthropometric (height and weight) data were abstracted from the records of all ASA physical status I to II children who underwent elective operations between 2005 and 2011. Measurement and documentation of height and weight are part of routine preoperative evaluation at our institution. Height was measured to the nearest 0.1 cm by using a wall-mounted stadiometer with the patients shoeless and head held in the horizontal plane. Body weight was measured, to the nearest 0.1 kg, by using a calibrated electronic weighing scale with patients lightly clothed in hospital gowns. In some cases, weights were obtained indirectly by measuring the weight of the child and the parent and then subtracting the parent weight to determine the child’s weight. These values were then recorded in an electronic perioperative medical information system (Centricity®; General Electric Healthcare, Waukesha, WI). Study subjects were stratified into 2 groups; thus, 75% of children (derivation cohort) were randomly selected for the primary objective of this study, and the remaining 25% of patients (internal validation cohort) were used to compare the weights estimated by the derived formula with the 3 existing age-based weight estimation formulae.

##### Statistical Analysis

Data analyses were performed with Statistical Package for the Social Sciences (IBM Corp, IBM Statistics for Windows, Version 19.0; IBM Corp, Armonk, NY) and with MedCalc for Windows, version 9.6.0.0 (Medcalc Software, Ostend, Belgium). Means and standard deviations (SDs) of demographic and anthropometric variables were compared along gender lines. Continuous variables (age, height, weight, and BMI) were examined for normal distribution with the Kolmogorov-Smirnov test. Data that were clearly incorrectly entered, missing, or corrupted were subjectively removed. BMI was calculated as weight in kilograms divided by the square of the height in meters (BMI = kg/m^{2}) for all patients. BMI was then transformed into a categorical variable for the grouping of children into 2 categories; thus, normal BMI signifies sex-specific BMI between the 5th to 84th percentile, while high BMI (overweight and obese) denotes sex-specific BMI ≥85th percentile based on reference growth charts from the National Center for Health Statistics/Centers for Disease Control and Prevention.^{21} Weight categories were described as frequencies or percentages and compared along gender lines.

Each child’s estimated weight was computed by using the equations displayed in Table 1. Several methods were used to determine the agreement between calculated and directly measured weight. First, Pearson correlation coefficient (*r*) was used to explore the strength of relation between calculated weight and measured weight. Next, the absolute bias for each weight estimation method was calculated. Bias denotes the mean difference (in kg) between the estimated weight and measured weight. We also determined the precision (percentage error [PE]) for each weight estimation method by using the formula: PE = 100 × (calculated weight-measured weight)/measured weight.

Next, the agreement between the different weight estimation methods and the measured weight was tested by using the Bland-Altman method.^{22} This is a scatterplot of bias (as defined above) plotted on the y-axis against the mean of the estimated and measured weights on the x-axis. This technique displays bias, precision (SD of bias), and limits of agreement (bias ± 1.96 SD). A positive bias indicates overestimation by the formulae, while a negative bias implies underestimation.

Subsequently, the accuracy of each weight estimation formulae was calculated. Accuracy refers to the proportion of estimated weights that is within a predetermined target, and it incorporates both bias and precision.^{23} A 10% accuracy was chosen for consistency with previous studies and because this threshold is often considered clinically significant.^{4},^{5},^{8} Subgroup analysis was conducted to determine the performance of each weight estimation formula among children classifiable as overweight/obese, by calculating the correlation, precision, bias, and accuracy across BMI categories.

Finally, exploratory analysis (on the derivation cohort) was performed by using simple linear regression to derive a new age-based weight estimation formula. Measured weight (in kg) was the dependent variable (y-axis), while age (in years) was the independent variable (x-axis). Performance of the derived formula was compared with existing equations by repeating the preceding analyses in the validation cohort (*N* = 3912). All reported *P* values were 2-sided, and a *P* value of ≤0.05 was considered to be significant.

#### RESULTS

A total of 13,933 children were studied, of whom 55.5% were boys. Most (68.7%) patients were of Caucasian ethnicity. The mean age of all the subjects was 7.4 ± 3.6 years, while the mean weight was 28.8 ± 15.6 kg (range 8–90 kg), and the mean height was 1.2 ± 0.2 m. The mean BMI was 18.2 ± 4.3 kg/m^{2} with a range of 10.28 to 39.97 kg/m^{2}. Patient distribution according to age groups was as follows: Age 2–5 years = 4505 (43.0%), age 6–9 years = 3784 (36.1%), and age 10–12 years = 2199 (21.0%). The overall prevalence of high BMI was 31.1% (overweight = 14.8%; obese = 16.4%). There was no significant difference in the distribution of high BMI by age groups (2–5 years = 30.9% vs 6–10 years = 32.0% vs 11–12 years = 34.1%; *P* = 0.061).

The total number of randomly selected children (the derivation cohort, *N* = 10488) including their mean weights stratified by sex for each age is displayed in Table 2. As expected, the weight of the children increased progressively with age. Next, the mean measured weights at each age as well as the mean of the formula-derived weights for each age were computed. As shown in Figure 1, estimated weights by the 3 formulae had close approximation to the measured weight in younger children but deviated considerably from measured weights in older children. Across all age groups, APLS formula-derived weights were lower than measured weights, while the Theron formula tended to overestimate weights especially in older children.

Table 2 Image Tools |
Figure 1 Image Tools |

##### 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, r^{2} = 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%.

#### DISCUSSION

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.

##### Study Limitations

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 data^{29} 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.

#### DISCLOSURES

**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.