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# Table 2 Summary and description of weight estimation methodologies described in the literature

Name | Formula | Restrictions/limitations/acceptable accuracy benefits | ||
---|---|---|---|---|

Age-based and length-based formulas | Ali formula |
Wt = (2.5 × Z) + 8
| Derived in a Trinidadian population of children ≤ 5 years of age in 2012. No validation studies to date. Age restriction 1 to 5 years of age. | |

Argall formula |
Wt = (3 × Z) + 6 or [Wt = 3 × (Z + 2)]
| Developed from a small UK study in 2003 (300 children). Generally found to underestimate weight, more so in older and heavier children. Age restriction 1 to 10 years of age. | ||

Advanced Paediatric Life Support formula (APLS) (new) | \( Wt=\frac{z}{2}+4 \) | For infants ≤ 12 months of age | Derived in a UK population and adopted in 2011 by the Advanced Life Support Group from a combination of the original APLS and the Luscombe formulas. It was untested and unvalidated at the time of adoption. Generally overestimates weight. Age restriction birth to 12 years of age. | |

Wt = (2 × Z) + 8 or [Wt = 2 × (Z + 4)]
| For children aged 1 to 5 years | |||

Wt = (3 × Z) + 7
| For children aged 6 to 12 years | |||

Australian Resuscitation Council formula (ARC) |
Wt = 3.5
| At birth | Adopted by the ARC in Australia in 1996. Same as New Zealand Resuscitation Council formula. Generally underestimates weight, more so in older and heavier children. Differing accuracy in different ethnic, socio-economic and international populations. No specific age restriction noted. | |

Wt = (2 × Z) + 8
| For children aged 1 to 9 years | |||

Wt = 3.3 × Z
| For children 10 years and over | |||

Best Guess formulas (BG) | \( Wt=\frac{z+9}{2} \) | For infants ≤ 12 months of age | Also known as the Tinning formulas. Derived in Australian population in 2007 from a retrospective database study of more than 70,000 children. Generally overestimates weight, especially in poorer populations. Has been evaluated in several validation studies with mixed results. | |

Wt = (2 × Z) + 10 or [Wt = 2 × (Z + 5)]
| For children aged 1 to 5 years | |||

Wt = 4 × Z
| For children aged 6 to 14 years | |||

Bicer formula |
Wt = (3 × Z) + 6 or [Wt = 3 × (Z + 2)]
| For children aged 3 to 6 years | Although these formulas are mentioned and evaluated in the Bicer study, the analysis and reporting is fatally flawed and cannot be evaluated; the origin of the first formula of the set is the same as the Argall formula. Age restriction proposed by Bicer to be 3 to 18 years. | |

Wt = (4 × Z) − 3
| For children aged 7 to 18 years | |||

Chinese age-weight rule 1 (CAWR-1) |
Wt = (3 × Z) + 5
| For children aged 1 to 10 years | Developed in Hong Kong for ethnic Chinese children in 2011 from a sample of 1248 children. Age restriction 1 to 10 years (although developers advise use with caution over 7 years). | |

Chinese age-weight rule 2 (CAWR-2) | \( Wt=\frac{\left(Z\times 7\right)+25}{3} \) | For children aged 1 to 6 years | ||

Wt = (4 × Z) − 4
| For children aged 7 to 10 years | |||

European Paediatric Life Support formula (old APLS formula) (EPLS) |
Wt = 2 × (Z + 4) or [Wt = (2 × Z) + 8]
| Original population and date of derivation unclear. Generally underestimates weight, more so in older and heavier children. Differing accuracy in different ethnic, socio-economic and international populations. Age restriction 1 to 10 years of age | ||

Garwood formula | \( Wt=\frac{z}{4}+6 \) | Developed in a UK population from a sample of 1252 children in 2012. The initial validation study was fatally flawed, but this formula has been subjected to a validation study subsequently (showing poor performance). For children aged 1 to 16 years. | ||

Leffler formulas | \( Wt=\frac{z+8}{2} \) | For children <1 year of age | Also known as the Tintinalli formula, the original origin is unclear, but became popular after the Leffler study in 1997. Overestimates weight in younger children (≤ 6 years) and underestimates weight in older children (> 6 years). | |

Wt = (2 × Z) + 10
| For children aged 1 to 10 years | |||

Luscombe formula |
Wt = (3 × Z) + 7
| Developed in the UK in 2007 from a large database of nearly 14,000 children. Underestimates weight in most populations studied, but significantly overestimates weight in populations from developing countries. Age restriction 1 to 10 years. | ||

Michigan formula |
Wt = (3 × Z) + 10
| Derived by Ackwerh in 2010, but has not been evaluated fully. | ||

Nelson formulas (originally Weech’s formulas) | \( Wt=\frac{z+9}{2} \) | For infants 3 to 12 months | As described in Nelson’s Textbook of Paediatrics. The origin is probably from Weech’s formulas, first reported in 1954 in the USA. The Weech formula is still in use today as one of the standard measurement denominators for determining underweight status. Weight most often overestimated in infants and older children (> 6 years) and underestimated in younger children (≤ 6 years). | |

Wt = 2 × (Z + 4)
| For children aged 1 to 6 years | |||

\( Wt=\frac{\left(Z\times 7\right)-5}{2} \) | For children aged 7 to 12 years | |||

Park formulas | \( Wt=\frac{z+9}{2} \) | For infants ≤12 months of age | Derived in Korean population from a large database study (nearly 125,000 children). Poor accuracy in older children (> 6 years). | |

Wt = (2 × Z) + 9
| For children aged 1 to 4 years | |||

Wt = (4 × Z) − 1
| For children aged 5 to 14 years | |||

Shann formulas |
Wt = (2 × Z) + 9
| For children aged 1 to 9 years | Used in Australasia primarily. Origin is unclear. Underestimates weight increasingly with increasing age. | |

Wt = (3 × Z)
| For children aged >9 years | |||

Theron formula |
Wt = e
^{(0.175571 × Z) + 2.197099}
| Derived in 2005 in New Zealand from a small study of 900 children that included a large number of Pacific Island children (high weight-for-age). The developers intended it for use in children high in the weight-for-age centiles. Age restriction 1 to 10 years. Overestimates weight in most populations. | ||

Unknown |
Wt = (3 × Z) + 8
| This formula is mentioned in some weight-estimation studies with no reference to its origin. It is not known what restrictions apply. Mentioned in Dearlove, Bicer. | ||

Traub-Johnson formula (TJ) |
Wt = 2.05 × e
^{0.02X}
| Derived in 1980 from USA national growth data from 1959. This formula was used to estimate ideal body weight and adjusted body weight, which were used interchangeably. The formula was intended to estimate the 50th centile of weight-for-height. Underestimates total body weight. For children aged 1 to 18 years. | ||

Traub-Kichen formula (TK) |
Wt = 2.396 × 1.0188^{X}
| Derived in 1983 in the USA from data from more than 20,000 children in the National Centre for Health Statistics database. The formula was intended to estimate the 50th centile of weight-for-height which the developers regarded as an approximation of ideal body weight. Underestimates total body weight. For children over 74 cm and aged 1 to 17 years. | ||

Other length-based systems | Broselow tape (BT) | Weight estimated directly by placing tape next to child and measuring from head to heel. The estimated weight and colour zone is read off the tape. | Developed in 1985 in the USA from US growth data and first validated in a sample of just over 900 children in 1988. Several changes have been made over the years: the latest version is the 2011A edition. Underestimates weight except in populations with a high prevalence of poor nutrition. Inaccuracy increases with increasing length/weight. Increased underestimation of weight in obese and overweight individuals. Substantial number of children “too tall for the tape” but who are not at adult weight. Length restriction 46 to 143 cm. Maximum weight estimation 36 kg. | |

Blantyre tape | Weight estimated directly by placing tape next to child and measuring from head to heel. The estimated weight is read off the tape. | Developed in Malawi using values 85% of the 50th centile of the American National Centre for Health Statistics weight-for-length growth charts. Validated on a sample of 729 children. The developers reported a reasonable accuracy between 4 and 16 kg, but the reporting of data was fatally flawed and is unverifiable. Length restriction of 45 to 130 cm. | ||

Oakley table | Age or length is used to estimate weight from a graph. | Developed in the USA in 1988 from averaged boy-girl medians of unspecified growth charts. Overestimates weight in infants and older children (> 6 years). Age restriction 0 to 14 years and length restriction 50 to 160 cm. | ||

Habitus-modified systems | Erker formulas |
Wt = (2 × Z) + 6
| For “thin” children | Developed in 2014 in the USA using regression formulas to estimate the 5th, 50th and 95th centiles of the Centre for Disease Control weight-for-age growth charts. Has not yet been shown to be accurate. |

Wt = (3 × Z) + 6
| For “normal” (average) children | |||

Wt = (4 × Z) + 6
| For “thick” (fat) children | |||

Yamamoto formulas |
See reference 11 different logarithmic formulas.
| Developed in 2009 in the USA from a sample of 542 children. A different length-based formula is selected for one of five (under 3 years of age) or six (over 3 years of age) icons, which represent an assessment of the body habitus. The reporting of the validation against the Broselow tape is flawed and does not permit verification. This technique has not been subsequently validated. | ||

Wozniak formulas |
Wt = (1.443 × U) + (1.596 × M) − 32.963
| Developed in Botswana in 2012 from a sample of 777 children with a high prevalence of HIV infection and growth retardation. Measurements of mid-arm circumference and ulna length or tibia length are used to estimate weight using the formula. The accuracy of the method decreases in children <10 kg and children > 40 kg. | ||

Wt = (0.86 × T) + (1.715 × M) − 30.426
| ||||

Devised weight estimating method (DWEM) | Length measured and then habitus assessed as “Slim”, “Average” or “Heavy” and weight read off a chart. A pre-marked tape was developed but is not widely available. | Developed in 1986 in the USA based on standard growth data available in 1983 and validated in a small sample of 258 children. Underestimates weight, especially in taller children. Length restriction 50 to 175 cm. Maximum weight estimation 70 kg. | ||

PAWPER tape | Weight estimated directly by placing tape next to child and measuring from head to heel. A habitus score (1 to 5) is assigned to the child based on body habitus (1 = very thin, 3 = average, 5 = very fat). The estimated weight for that length and habitus score is read off the tape. | Developed in 2004 in South Africa based on WHO weight-for-length growth charts and validated on a sample of 453 children in 2013. Estimates weight uniformly across length range of tape. Performs well in children who are under- or overweight. Length restriction 43 to 153 cm. Maximum weight estimation 47 kg. The extended PAWPER tape accommodates children up to 180 cm in length, a maximum weight estimation of 116 kg and with a 7-point habitus score assessment (habitus scores 6 and 7 were added to accommodate children above the 95% centile of weight-for-length, i.e. for obese and severely obese children). | ||

Mercy method (MM) | Humerus length and mid-arm circumference are measured and then used to determine “segmental weights” from a table. Specifically desgined tapes “2D” and “3D” tapes may be used which eliminates the need for a data table. | Developed in the USA from a database of 19,625 children and validated across several centres in 2012, 2013 and 2014, including in developing countries. Consistently good weight estimation across age and habitus ranges. Decreased accuracy in younger children (< 2 years). | ||

Other | Cattermole MAC formula |
Wt = (M − 10) × 3
| A mid-arm circumference-based formula developed in Hong Kong ethnic Chinese children in 2010 from a sample of 1370 children. Decreased accuracy in children < 6 years and underestimation of weight in older children. Recommended by developers to restrict use to children aged 6 to 11 years. | |

Haftel formula |
Wt = (5.176 × LW) + 3.487
| The “hanging-leg weight” formula developed in the USA in 1990 from a small sample of 100 anaesthetised children aged 2 months to 15 years. The accuracy of weight estimation was worst in infants and increased with age. No subsequent studies have been reported. | ||

Bavdekar formula |
Wt = − 5.15 + (FL × 1.35)
| Developed in India in 2006 from a sample of 500 infants < 2 years of age. Fatal flaws in the methodology do not permit the interpretation of the accuracy of this formula. No subsequent studies have been reported. For infants ≤ 2 years. |