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Original Research Articles: Original Clinical Research Report

Validation of the Lusaka Formula: A Novel Formula for Weight Estimation in Children Presenting for Surgery in Zambia

Phiri, Hope MBChB, MMed*; Foy, Katie E. MBBS, MRes, FRCA; Bowen, Lowri MBBCh, MRCS, FRCA; Bould, M. Dylan MBChB, MEd, MRCP, FRCA§

Author Information
doi: 10.1213/ANE.0000000000005797
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Abstract

KEY POINTS

  • Question: Is the novel Lusaka formula accurate at predicting pediatric weight in Zambia, and does it perform better then currently used age-based formulas and the Broselow tape?
  • Findings: The Lusaka formula has comparable accuracy to the Broselow tape and out performs all other age-based formulas tested in this cohort.
  • Meaning: The Lusaka formula could improve pediatric weight estimations in Zambia, thus leading to improved patient safety.

Pediatric drug dosing is routinely weight based. Dosing errors in pediatric anesthesia are common; a recent study of 1400 pediatric anesthetics found that there was at least 1 drug error per 38 anesthetics.1 Having an accurate weight on which to base drug calculations is imperative to reduce harm associated with dosing errors.

In an emergency, weighing a child may not be practical and weight can be estimated, but this often correlates poorly with actual weight.2–5 A recent meta-analysis highlighted that the many formulas developed in high-income countries (HICs) overestimated the weight of children in low- and middle-income countries (LMICs).6 This is likely due to the higher incidence of malnutrition and chronic disease in children in LMICs. Zambia is a country in sub-Saharan Africa, which is classified as an LMIC.7 United Nations International Children’s Emergency Fund (UNICEF) reports that 40% of children in Zambia <5 years of age have chronic malnutrition (low height-for-age, or stunting) and 15% are considered as underweight.8 In 2016, Bowen et al9 investigated the accuracy of both common age-based weight estimation formulas in Zambia, and the length-based Broselow Paediatric Emergency Tape.10 The study confirmed that these formulas were inaccurate in the Zambian population. This dataset was used to develop a new weight estimation formula, which was named the “Lusaka formula.”

The primary aim of our study was to validate the “Lusaka formula” in an independent cohort of children undergoing surgery at the same institution, the University Teaching Hospital (UTH) in Lusaka, Zambia. Our secondary aim was to compare the Lusaka formula’s performance to other commonly used weight prediction formulas and the Broselow Paediatric Emergency Tape.10 As an additional exploratory aim, we planned to investigate the relationship between parental education level (as a social determinant of health amenable to policy interventions) and indicators of acute and chronic malnutrition (low weight-for-height, and low height-for-age, respectively).

METHODS

The study was approved by the Research Ethics and Science Converge (ERES) Committee. Written informed consent was obtained from a parent or guardian for all children enrolled in the study. The article has been prepared in accordance with the STrengthening the Reporting of OBservational studies in Epidemiology (STROBE) reporting guidelines.12

Development of the Lusaka Formula

From a previously published data set,9 we used linear regression to develop formulas for predicting Zambian children’s weight in kilograms. For children age 1 year or older, a linear regression using age (in years) as the independent variable and weight as the dependent variable resulted in a slope of 1.98 and an intercept of 6.98, which through close approximation can result in a simplified formula of weight = 7 + (age in years × 2) (linear r2 = 0.78; P < .001). For children age <1 year, a further linear regression using age (in months) as the independent variable and weight as the dependent variable resulted in a slope of 0.44 and an intercept of 3.55, which through close approximation can result in a simplified formula of weight = 3.5 + (age in months/2) (linear r2 = 0.55; P < .001). We note that this r2 is only moderate for children <1 year, the formula only explaining 55% of the variance of weight, so it may be expected that it would be less accurate than the formula for children older than 1 year. We have named this pair of formulas together, the “Lusaka formula.”

Validation of the Lusaka Formula

The study was a prospective cross-sectional study. To validate the Lusaka formula, we collected an independent data set at the same institution. Data were collected for 5 months between September 2016 and January 2017. The study was based at the UTH, Lusaka, Zambia, which is a large tertiary referral center for pediatric surgery.

All children presenting for surgery at UTH were eligible for recruitment into the study. The inclusion criteria were as follows:

  • Age 0 to 14 years
  • Presenting for surgery requiring anesthesia (general, regional, or local)
  • Date of birth was known
  • Parental informed consent

The exclusion criteria were as follows:

  • Children with external orthopedic fixation devices (due to the contribution to measured weight)
  • Children that we were unable to weigh using scales

Patients were recruited on day of proposed surgery and data collected that day. Following entry into the study, the following data were collected: age (for children <1 year the age was rounded down and recorded as the nearest month and for children over the age of 1 year age at last birthday was recorded in years), gender, weight (kg), length/height (taken from heel to crown of the head and rounded to the nearest centimeter), and mid upper arm circumference (MUAC [cm]). The World Health Organization (WHO) global database on child health parameters13 was used to provide information on expected height for age, and weight for height, to assess nutritional status. The body mass index (BMI) of each child was also calculated.13 In addition, level of parental education and operative procedure was also recorded (whether each of the mother and the father had completed primary school, secondary school, tertiary education, or none of these).

Data were collected by trained local research assistants. Weight was measured using Medical Grade III scales (as per Organisation International Meterologie Legale: OIML). The stand on scale HCS-200-RT (Sainty International Group) was used to measure weight and length. The infant ACS-20B-YE scale (Lencen Medical Co) was used for infants. The scales were calibrated on a weekly basis by research assistants. The MUAC was measured by a measuring tape/MUAC Tape (MOYO Chart, TALC UK) on the left upper arm at the midpoint of the tip of the shoulder and the tip of the elbow. Captured data were entered in a database (Excel, Microsoft), and double-checked by 2 research assistants to ensure accuracy.

Table 1. - Commonly Used Weight-Based Formulas for Calculating Weight in Children
Name of formula Formula Age range
Old APLS14 (age + 4) × 2 1–10 y
New APLS15 0.5(age [mo]) + 4
(2 × age) +8
(3 × age) +7
0–12 mo
1–5 y
6–12 y
Nelson25 (age [mo] +9)/2
(2 × age) +8
[(7 × age) −5]/2
3–11 mo
1–6 y
7–12 y
Argall17 (age ×3) + 6 1–10 y
Luscombe23 (3 × age) +7 1–10 y
ARC formula16 (2 × age) +8
3.3 × age
1–9 y
>10 y
Best Guess18 (2 × age +10)
4 × age
1–5 y
6–14 y
Michigan25 (3 × age) +10 2–12 y
Leffler21 [age (mo)/2] +4
2 × age (y)] +10
0–12 mo
1–5 y
Theron28 e(2.197099 + 0.175571 × age) 1–10 y
Shann27 (2 × age) +9
3 × age
1–9 y
>10 y
Garwood-McEwen20 (age [mo]/4) +6 1–14 y
Park formula25 (age [mo] +9)/2
(2 × age) +9
4 × age −1
1–11 mo
1–4 y
5–14 y
Tintinalli28 (2 × age) +10 1–12 y
Chinese Age Weight Rule19 (3 × age) +5 1–10 y
Age refers to age in years unless otherwise noted to be months.
Abbreviations: APLS, Advanced Paediatric Life Support; ARC, Australian Resuscitation Council.

Each child had their predicted weight in kilograms calculated from the Lusaka formula and the following previously described formulas (Table 1): old Advanced Paediatric Life Support (APLS)/Pediatric Advanced Life Support (PALS),15 current APLS/PALS,16 Australian Resuscitation Council (ARC),17 Argall,18 Best Guess,19 Chinese Age Weight Rule (CAWR),20 Garwood and McEwen,21 Leffler,22 Luscombe & Owens,23 Michigan,24 Nelson,25 Park et al,26 Shann,27 Theron et al,28 and Tintinalli.29 Additionally, weight was predicted from the Broselow Paediatric Emergency Tape.10

Statistical Analysis

The precision of different formulas was then examined by calculating median percentage error [100 × (estimated weight − actual weight)/actual weight] and the percentage of actual weights that fall within 10% and 20% of the estimated weight. Bias was defined as estimated weight-actual weight. The Bland Altman method was used to examine the mean bias, 95% confidence intervals, and 95% limits of agreement in keeping with previous literature on this subject.11

The Wilcoxon signed rank test was used to compare the bias of the predictions from the Lusaka formula with the predictions from all of the other predictive formulas. With the assumption that positive and negative bias are of equal clinical significance, all values for bias were first transformed to be positive values. McNemar’s test for paired proportions was used to compare the proportion of children within 20% of estimated weight for the Lusaka formula with the proportion of children within 20% of estimated weight for all the age-based formulas. As these analyses involved 30 pairwise comparisons, we decided a priori to control the significance level at 0.05 using a Bonferroni adjustment, thus requiring P < .001 as the significance criterion for each comparison.

A multivariable linear regression analysis was performed to look at the association of both age and maternal education on a child’s body weight. All analyses were performed using SPSS version 23 (IBM).

The sample size was based on analysis of the 95% limits of agreement. According to Bland and Altman, the standard error of the 95% limit of agreement is approximately √(3s2/n), where s is the standard deviation of the differences between measurements by the 2 methods and n is the sample size.11 The 95% confidence interval is the estimate of the limit ±1.96 standard errors or ±1.96√(3s2/n). A sample size of 300 gives 95% confidence intervals of approximately 0.2 standard deviations. We aimed to recruit 330 children as a conservative estimate to allow for up to 10% data loss.

RESULTS

Three hundred and thirty children were enrolled into the study and complete data sets were available for all children. Two hundred and twenty (66.7%) were male and 110 (33.3%) were female. Table 2 describes the number of children in each age group and their respective weights.

Table 2. - Age Range of Children Recruited, With Height and Weight Distribution
Age n Height (cm) Weight (kg)
Months
 0 7 43.5 (5.5) 2.6 (0.5)
 1 4 49.5 (6.9) 3.8 (0.7)
 2 5 53.2 (3.6) 4.3 (0.9)
 3 6 59.3 (3.4) 5.7 (0.7)
 4 4 53.0 (4.2) 6.0 (1.1)
 5 8 61.9 (5.4) 6.8 (1.5)
 6 5 67.8 (17.2) 8.3 (3.1)
 7 8 68.0 (2.1) 7.5 (1.3)
 8 4 67.3 (2.8) 8.1 (1.3)
 9 6 67.2 (5.8) 8.1 (0.8)
 10 5 75.0 (6.9) 8.7 (1.6)
 11 9 71.6 (7.2) 8.4 (1.3)
Years
 1 47 75.9 (6.8) 9.8 (2.3)
 2 31 84.9 (6.4) 11.3 (1.5)
 3 38 94.1 (6.8) 13.5 (1.7)
 4 19 102.5 (7.9) 15.7 (2.5)
 5 22 106.3 (10.8) 16.8 (2.4)
 6 27 112.7 (7.3) 18.5 (3.1)
 7 17 120.3 (5.7) 21.1 (2.4)
 8 15 125.3 (8.9) 24.1 (5.4)
 9 6 132.3 (11.4) 26.5 (2.5)
 10 15 132.3 (10.7) 27.3 (7.1)
 11 6 126.5 (11.4) 24.7 (3.9)
 12 4 147.3 (8.4) 37.0 (6.8)
 13 6 143.8 (9.5) 34.9 (15.6)
 14 6 149.8 (18.6) 35.5 (7.9)

The age range was between 0 months and 14 years. Seventy-one (21.5%) were <1 year of age, and 262 (78.5%) were aged between 1 and 14 years. Most children (233; 70.6%) presented for a general surgical procedure, 33 (10%) for a neurosurgical procedure, 29 (8.8%) for an ear nose and throat procedure, 25 (7.6%) for bronchoscopy, 9 (2.7%) for a plastic surgery procedure, and 1 (0.3%) for a central venous access device insertion.

Table 3 outlines the performance of all predictive tools in terms of bias (mean, 95% confidence intervals, and 95% limits of agreement of bias) and precision (proportion of children with weight estimates within ±10% and ±20%). There was no difference found between the bias of the Lusaka formula and that of the Broselow tape,10 old APLS,14 ARC,17 or Nelson25 formulas, but all other formulas had significantly more bias between than the Lusaka (P < .0001). There was no difference found between the proportion of children within ±20% of the calculated weight between the Lusaka formula and the Broselow tape, old APLS, ARC or Nelson formulas, but all other formulas had significantly fewer children within ±20% of the calculated weight (P < .0001). The Lusaka formula was the only formula that could be applied to all of the children included in the study.

Table 3. - Precision and Bias of Methods Used to Calculate Weight
Median % error (IQR) Within ±10% of estimated weight (%) Within ±20% of estimated weight (%) Pairwise comparison of within 20% error to Lusaka formula
P valuea
Unable to estimate weight from formula (% of sample) Bias kg
Mean (SD)
95% CI
Pairwise comparison of bias with Lusaka formula
P valueb
95% limits of agreement
Broselow10 4.8 (−3.5 to 15.4) 158 (51.6) 245 (79.5) .223 23 (7) 0.9 (2.5)
0.6–1.1
.426 −4.0, 5.7
Lusaka Formula −1.4 (−10.9 to 11.3) 160 (48.5) 241 (73.0) 0 (0) −0.5 (3.7)
−0.9 to −0.1
−7.7, 6.8
Old APLS15 4.5 (−4.0 to 17.6) 121 (47.3) 192 (74.1) .390 71 (21.5) 0.6 (4.0)
0.1–1.1
.338 −7.4, 8.5
ARC16 7.4 (−2.4 to 20) 112 (43.8) 184 (71.0) .106 71 (21.5) 1.6 (4.7)
1.0–2.2
.004 −7.7, 10.9
Nelson24 7.7 (−2.9 to 19.9) 127 (42.5) 218 (72.2) .275 28 (8.5) 1.2 (3.4)
0.8–1.6
.002 −5.5, 7.9
Shann26 11.9 (3.8–25.7) 89 (34.5) 164 (63.3) .001 71 (21.5) 1.9 (4.1)
1.4–2.5
<.0001 −6.4, 10.1
CAWR19 8.3 (−6.3 to 25) 78 (32.9) 137 (57.8) <.0001 93 (28.2) 1.9 (4.2)
1.3–2.4
<.0001 −6.4, 10.1
Leffler22 15.7 (4.6–30.2) 87 (28.8) 166 (54.8) <.0001 22 (6.7) 2.1 (2.9)
(1.7–2.4)
<.0001 −3.7, 7.9
New APLS14 10.4 (−1.1 to 31.2) 112 (36.4) 117 (56.9) <.0001 19 (5.8) 2.6 (4.6)
2.0–3.1
<.0001 −6.5, 11.6
Argall17 15.9 (0.3–31.3) 61 (26.1) 125 (52.7) <.0001 93 (28.2) 2.9 (4.2)
2.3–3.4
<.0001 −5.4, 11.1
Tintinalli28 19.4 (8.3–31.9) 64 (26.0) 127 (51.4) <.0001 83 (25.2) 2.6 (3.3) 2.2–3.0 <.0001 −3.9, 9.1
Garwood20 17.4
(1.7–34.6)
63 (24.6) 129 (49.8) <.0001 71 (21.5) 3.6 (5.4)
2.9–4.2
<.0001 −7.0, 14.1
Park25 17.9 (5.8–36.1) 78 (24.1) 169 (52.3) <.0001 7 (2.1) 3.7 (5.7)
3.1–4.3
<.0001 −7.6, 15.0
Theron27 25.5 (9.3–51.2) 54 (22.8) 103 (43.5) <.0001 93 (28.2) 5.6 (7.1)
4.7–6.5
<.0001 −8.4, 19.6
Luscombe and Owens22 23.1 (8.7–38.9) 51 (21.5) 96 (40.5) <.0001 93 (28.2) 3.9 (4.2)
3.3–4.4
<.0001 −4.4, 12.1
Best Guess18 27.3 (14.6–43.7) 37 (14.3) 93 (35.9) <.0001 71 (21.5) 5.5 (6.1)
4.7–6.2
<.0001 −6.6, 17.5
Michigan23 45.1 (34.8–60.2) 5 (2.5) 21 (10.5) <.0001 130 (39.4) 8.1 (4.4)
7.5–8.8
<.0001 −0.6, 16.9
The number (proportion) of children in the study sample in whom actual weight fell within 10% and 20% from the estimated weight. Negative numbers represent a measured weight that is lower than estimated, and positive numbers a measured weight higher than estimated.
Abbreviations: APLS, Advanced Paediatric Life Support; ARC, Australian Research Council; CAWR, Chinese Age Weight Rule; CI, confidence interval; IQR, interquartile range; SD, standard deviation.
aUsed McNemar’s test.
bUsed Wilcoxon signed-rank test.

Nutritional status of the children was assessed using the WHO global database14 on child health parameters. Chronic malnutrition was assessed using height-for-weight (stunting): 256 children (78.0%) had either mild or no evidence of chronic malnutrition, 27 children (8.2%) had moderate chronic malnutrition, and 45 children (13.7%) had severe chronic malnutrition. Acute malnutrition (wasting) was assessed using weight-for-height for children ≤5 years, and BMI14 for children over 5. Three hundred and seven children (95.3%) had either mild or no evidence of acute malnutrition, 12 children (3.7%) had moderate acute malnutrition, and 3 children (0.9%) had severe acute malnutrition. Of the 194 children age 6 months to 5 years, only 1 child had an MUAC of <115 cm, which also supports a diagnosis of severe acute malnutrition (wasting).

Paternal educational level could only be attained for 110 (33%) fathers: of these, 26 (23.6%) had completed only primary education, 80 (72.7%) had completed only secondary education, and 1 (0.9%) had completed tertiary education. Maternal educational level was available for 221 mothers (66%): 78 (35.3%) had completed primary education, 142 (64.2%) had completed secondary school, and 1 (0.45%) attained tertiary education. In children <1 year of age, maternal educational level had no impact on the child’s weight. In children >1 year of age, there was a significant correlation between the child’s weight and maternal educational level. If the mother had only completed primary school education, there was a B value of −2.3, t = −3.9 (95% CI, −3.4 to −1.1; P < .001). This is comparable to the effect on weight of a year’s age, which had a B value of 2.0.

DISCUSSION

The Lusaka formula was not different in either bias or precision to either the Broselow tape or the old APLS, ARC or Nelson formulas, and outperformed all other formulas. The Lusaka formula was used for all children presenting for surgery, while all other formulas excluded some children, which were not included in the relevant age or weight ranges.

Twenty two percent of children had moderate or severe chronic malnutrition (stunting) and 4.7% of children had moderate or severe acute malnutrition (wasting). In children >1 year old, having a mother who had only completed primary school predicted weight with an effect size equal to 1 less year of life. We were not able to draw conclusions on the effect of paternal educational level due to a lack of data. Children mostly attended with their mother, but it is not entirely clear to us why data collection failed to identify the fathers confirmed educational level. Our malnutrition data are lower than the WHO figures of 40% of children under 5 suffering from stunting.8 This may be encouraging, however, a 2018 joint report by the Zambian government and UNICEF highlighted that Lusaka has the lowest percentage of child poverty in the country (18%) and 84% of Zambia’s poor population live in rural areas.30 It also concluded that children living in rural areas had significantly increased deprivation scores compared to children in urban areas.30 As children attending UTH were likely to be from the urban Lusaka area, this could account for these differences and may affect the generalizability of this formula to rural areas of LMICs. Further study could focus on validating the Lusaka formula in varied areas of Zambia, particularly rural areas.

Currently in Zambia, parental or health care worker estimations and various age-based formulas are used to estimate pediatric weights. We have shown that currently published formulas are not as accurate as the Lusaka formula in this population. In particular, the current APLS/PALS formula was shown to have poor accuracy, with overestimation of weight in this cohort. This is concerning as APLS/PALS are commonly taught courses across the world and thus that formula is likely to be used in Zambia by local and international health care providers. This could lead to dangerous overdosing of children, especially malnourished children. The large variation in available formulas is also a concern, as providers could mix up the various formulas leading to errors. This may be particularly relevant in a pediatric resuscitation, as stress and time pressures can lead to increased human error.

The Lusaka formula benefits from simple mathematics, which could be done without a calculator, and does not require any additional equipment, this is in comparison to the Broselow tape, which requires the tape to be purchased. Using the Lusaka formula may result in the reduction of drug dosing errors, optimal drug dosing, and improved patient safety for pediatric patients.

It has previously been noted that age-based formulas created in HICs are not appropriate in LMICs. A 2017 systematic review and meta-analysis looked at the current literature on pediatric weight estimation on LMICs.6 Twenty-five studies were included, which captured 31,391 patients. The authors noted that multiple age-based formulas had been studied. The authors concluded that all age-based formulas performed poorly and none met their benchmark acceptability, and also commented on the poor performance of the current APLS system. They found that parental estimates and 2-dimensional length and body habitus systems (eg, the Mercy Method31 and PAWPER tape32) outperformed age-based formulas, and suggested age-based formulas be abandoned.32 However, parental estimates were dependent on the parent being a regular caregiver and the child having had a recent weight. The authors also note that the 2-dimensional body habitus systems can be subjective and requires training. To our knowledge, the accuracy of parental estimation and 2-dimensional methods has not been assessed in Zambia and is beyond the scope of this article, however it is a possible direction for future research.

A strength of our study is that this we had complete data sets available for all children, with the exception of some missing data on parental education level. The formula is simple and would be easy to introduce. A limitation of our study is that our study only included children in Lusaka, a large urban area. As previously stated, there can be differences in malnutrition levels between rural and urban areas.30 We found a significant gender difference in our data, (66.7% male vs 33.3% female), which was similar to that found in the Bowen et al.9 This likely represents the increased likelihood for males to present with particular general surgical conditions such as inguinal hernia.

In conclusion, the Lusaka formula could be a useful tool for pediatric weight estimation in Zambia; in our cohort, it performed better then all other formulas. It may be more useful than previously described formulas for other countries in the region, or other LMICs, but further research is required to assess generalizability. Further study should focus on validation of the Lusaka formula in more rural areas, to ensure it is reflective of the Zambian population. The use of this weight-based tool in Zambia could reduce harm from inaccurate weight-based calculations, for example, drugs or ventilator tidal volumes.

ACKNOWLEDGMENTS

The authors thank all the parents and children who took part in this study. The authors also thank all of the local researchers involved in data collection, and all the staff at UTH for their support in this project.

DISCLOSURES

Name: Hope Phiri, MBChB, MMed.

Contribution: This author helped design the study, collect the data, write and edit the manuscript.

Name: Katie E. Foy, MBBS, MRes, FRCA.

Contribution: This author helped write and edit the manuscript.

Name: Lowri Bowen, MBBCh, MRCS, FRCA.

Contribution: This author helped design the study and edit the manuscript.

Name: M. Dylan Bould, MBChB, MEd, MRCP, FRCA.

Contribution: This author helped design the study, analyze, and edit the manuscript.

This manuscript was handled by: Angela Enright, MB, FRCPC.

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