# Recalculate WHZ during treatment

This question was posted the Management of wasting/acute malnutrition forum area and has 2 replies.

### Indi Trehan

Normal user

11 Sep 2023, 16:43

I am interested in hearing thoughts and experiences surrounding the issue of WHZ monitoring during wasting treatment and how this effects target ("graduation" / "recovery") weights.

For example: A child is enrolled in a severe wasting treatment program because of a WHZ of -3.2. They then do well in the program and gains some weight during the course of treatment and now several weeks into therapy, their WHZ is now above -2 based on their **enrollment length. **But at the same time, their recovery has been so good that their height/length has also increased and so if you re-calculate their WHZ based on the current length, their WHZ is still below -2.

*What do you do in this situation? Do you keep them enrolled for another week, recalculating their WHZ at each visit, or do you consider them recovered since they have achieved their target WHZ based on their enrollment length?*

I am curious to hear what national policies and NGO practices are on this question. Obviously there are advantages and disadvantages to both approaches. Thank you for your insights.

### Paul

Action Against Hunger UK

Technical expert

11 Dec 2023, 14:48

Hi Indi,

It would be good to have the opinions of others working in programmes to hear what they do in this situation. I can offer some relections from past work.

The standard practice in OTP was that height would be measured every 4 weeks as marked on the OTP card. It was common to see the linear growth you mentioned and the child would be kept in the programme based on their newly calculated weight for height - if that had been their admission criterion. It depended on the national guidance or the NGO practices whether both criteria were used for discharge.

The introduction of the 15% weight gain for discharge came about in part to unify the discharge criteria for MUAC and weight-for-height. Although it was abandoned due to the most malnourished children receiving the least treatment, it did make the calculation of a 'target weight' a standard procedure - which didn't require further height measurement.

Personally I am ambivalent about repeating height measurements in the programme context. In my opinion it is the most inaccurate measurement done at field level - especially between different measurers. When standardisation tests are done for survey enumerators it is usually fairly easy to to obtain 'consistency' for each type of measurement measurement. In my experience it is typically only weight (and sometimes MUAC) that pass the requirements for accuracy using the ENA for SMART / Habicht method parameters. I would also question whether the lying / standing addition or subtraction of 0.7cm is appropriately and consistently used in programme contexts.

Errors in surveys are probably compensated for to some extent by the sample size, but i'm not convinced that this makes for appropriate decision making for individual children where the measurers may vary from week to week. As a generalisation, NGO run programmes tend to be more rigorous than those without NGO involvement due to the increased level of training and supervision.

The new WHO guidance requiring both MUAC and weight-for-height to be used for discharge will change practices and i suspect lead to longer lengths of treatment in some cases. It will be interesting to see to what extent this affects overall RUTF demand when balanced against the reduced dosage.

I would be interested if others could also share their insights,

Paul

### AndrÃ© Briend

Frequent user

11 Dec 2023, 15:11

Dear Indi,

Dear Paul,

I share Paul's concern regarding repeated WHZ measurements with the effect of measurement errors. In this regard, we should be aware that measurement errors are important ofr height and have a great impact on WHZ calculation as it is entered as a squared term. For those who are interested, I explain the maths behind this in the short note below which is also available here with figures:

**Impact of measurement errors on weight and height on calculated weight-for-length/height z-score **

In a meta-analysis on the reliability of weight-for-length/height scores, Mwangome and Berkley reported that the intra-class correlation coefficient (ICC) of weight-for-length/height z-score (WLZ) was consistently lower than the ICC for weight or height taken separately (1). They noted that the effect in particularly important for young children. They speculated that individual errors on weight and height are compounded when presented as an index, but did not provide evidence in favour of this interpretation. This note provides a mathematical explanation for this observation.

**WLZ and BMI**

WLZ is calculated by the following formula:

WLZ = (Wtobs – Wtst) /SDst (i)

Wtobs : observed weight

Wtst : median weight for the observed height in WHO growth standard

SDst : standard deviation of weight for the observed height in WHO growth standard

SDst is highly dependent of height (Figure 1). The relmationship between SDst and height can be adequately desribed by the following log regression:

LN (SDst) = -9.337 + 2.091 LN (Heightcm); R2 = 0.9659 for girls

and

LN (SDst) = -0.931 + 2.070 LN (Heightcm); R2 = 0.9591 for boys

These equations are equivalent to:

SDst = e-9.337 x height2.091 = 8.81x 10-5 x height2.091 for girls (ii)

and

SDst = e-9.331 x height2.070 = 8.81x 10-5 x height2.070 for girls (iii)

These equations are presented Figure 1.

For both girls and boys, the exponent of height can be rounded down to 2 and give a good approximation of SDst

As a result, equation (i) can be expressed as follows, with height² measured in m²:

WLZ = (Wtobs – Wtst)/0.881 x heightm2 = [(Wtobs/heightm²) – (Wtst/heightm²)]/0.881

or

WLZ = k x (BMIobs – BMIst)

With k = 1/0.881 and BMIobs = observed body mass index (BMI) and BMIst the BMI corresponding to the median weight in the WHO standard for the observed height.

The BMI corresponding to the median wieght of the WHO growth standard varies with age (Figure 2). It increases rapidly up to 65 cm and then declines very slowly. If these vairations of BMI with height are negleceted, WLZ can be regarded as obtained by a linear transformation of BMI. This can be regarded as a good approximation for heights above 65 cm.

**Effect of measurement errors on WLZ estimation**

Errors on weight and height have both an impact of terms of the difference (BMIobs – BMIst) which determine the final potential error on WLZ.

The first term of the difference is likely to be most affected by measurement error as it represents a fraction in which both weight and height, measured with some uncertainty, are present. The total percentage of uncertainty of a ratio is calculated by adding the percentgage of uncertainty of each measurement (2).

Weight is usually measured with great precision (3), but weight variations due to the time to the last meal and last passed urine or stool can be regarded as random errors. Weight is present in the difference only in its first term and with an exponenent of 1.

Height is more difficult to measure with precision and as it is present in both terms of the difference. It is present in the denominator of the first term of the difference as a squared term. The error of height is increased by a factor of 2 in this term, as when a measurement is raised to a power, then the percentage of uncertainty is multiplied by this power (2). If height is underestimated, the first term is overestimated and conversely, if height is over estimated, the first term of the difference is understimated.

The second term of the difference is affected only by measurement errors on height. The effect of a measurement error on height on this term is different below and above 65 cm. Under 65 cm, if height is underestimated, the second term is underestimated as well. This error is compounded with the effect on the first term, which is increased in this case and the overall difference is grossly overestimated. The opposite effect is seen when height is overestimated with again a compounding effect on the difference. Above 65cm, an underestimation of height will slightly increase the second term, thus minimising the effect of the increase of the first term on the difference. The opposite effect is seen when height is overestimated, minimising the difference. As the decline of the BMI with height above 65 cm is slow, these minimising effects, however, are minor.

**Discussion: **

The low ICC observed for WLZ compared to the ICC of weight and height can be explained by the presence of both weight and height in its calculation. The involvement of height as a squared term doubles the effect of measurement errors on height on the final error in determining WLZ. The variation of the BMI corresponding for the median weight for each height in the WHO growth standard may explain that this effect is greater for younger children. The difficulty of measuring height in young children may also contribute to the low level of ICC observed for them.

The effect of random measurement errors on height on the estimation of WLZ should lead to caution when using this index for assessing growth. Errors made during different measurement sessions are likely to occur randomly and the uncertainty will add up when assessing change in nutritional status by difference. This contrasts with the assessment of weight-for-age z-score (WAZ): if an error is made on age at the first assessment, the same error will be done on the next one, minimising the error when the difference between two WAZ at different times is calculated.

1. Mwangome MK, Berkley JA. The reliability of weight-for-length/height Z scores in children. Matern Child Nutr 2014;10:474–80.

2. Uncertainties and practical work. Available at: https://qualifications.pearson.com/content/dam/pdf/A%20Level/Physics/2015/Specification%20and%20sample%20assessments/Appendix%2010%20Updated.pdf

3. WHO Multicentre Growth Reference Study Group. Reliability of anthropometric measurements in the WHO Multicentre Growth Reference Study. Acta Paediatr Oslo Nor 1992 Suppl 2006;450:38–46.

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