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# W/h in rickets

This question was posted the Assessment and Surveillance forum area and has 5 replies.

### Mark Myatt

Epidemiologist at Brixton Health

Frequent user

7 Feb 2012, 21:57

The short answer is "NO". The long answer is to use a proxy for height. This is common when using BMI in the elderly who have a lot more kyphosis and scoliosis (spinal curvatures) than younger people. It is common to use knee-height (no good for this application), armspan, or half-armspan. You need to do a small study first with about 60 children measuring both armspan and height. A correcting formula is then found using ordinary least squares regression. When you come across a child with rickets you measure the armspan and use the correcting formula to estimate height and use this estimate when calculating WHZ or WHM. Using MUAC is so much easier. Does this help?

### Mark Myatt

Epidemiologist at Brixton Health

Frequent user

11 Feb 2012, 15:03

Let me know if you'd like a worked example of the procedure for find a suitable correction factor.

### Mark Myatt

Epidemiologist at Brixton Health

Frequent user

15 Feb 2012, 11:10

I will do a "toy example" with only a few data points. Is is a "toy example" in the sense that I will use only 10 pairs of measurements. In practice you'd want to use a sample size of 60 pairs. The example here is for finding a correction that can be applied to half-armspan (demispan) to estimate height in elderly Somalis. We have ten pairs of measurements taken from elderly Somalis without capable of standing upright without rickets, kyphosis, and scoliosis. Here are the data: ``` height demispan ------ -------- 173.3 91.5 166.6 86.7 158.9 83.5 158.1 82.3 156.8 80.5 155.3 78.3 175.6 92.8 153.0 76.2 160.6 83.6 154.5 79.2 ------ -------- ``` If we plot these as a scatterplot with height on the x-axis and demispan on the y-axis we get something like this: ``` 95 -+ | | * | * | 90 -+ | | | | * 85 -+ | | * * | * | 80 -+ * | * | * | | * 75 -+ +---------+---------+---------+---------+---------+--- | | | | | | 150 155 160 165 170 175 ``` The points lie (more or less) on straight line. If they don't then you will have to use a more complicated procedure but this is not usually required. The analysis is ordinary least squares (OLS) linear regression. All statistics packages and spreadsheets can do this. You nee to be sure that the height is the dependent (y) variable and demispan (or what-have-you) is the predictor (x) variable when you specify the regression. Here I use R to do the analysis: ``` > lm(height ~ demispan) Call: lm(formula = height ~ demispan) Coefficients: (Intercept) demispan 42.491 1.423 ``` In this example the formula for estimating height from demispan is: ``` height = 42.491 + 1.43 * demispan ``` If we need to estimate height in a person with a demispan of 86.7 cm we would use: ``` height = 42.491 + 1.43 * demispan height = 42.491 + 1.43 * 86.7 height = 166.47 ``` It is important to note that the relationship between limb length and height varies between populations and, in children, with age (i.e. younger children tend to have higher sitting to standing heights). This means that you need to do this for each population. It also means that for children you should collect age and include age in the regression and in the formula used to estimate height. This will need a larger sample size. A useful rule of thumb is: ``` n = 10p + 50 ``` where "p" is the number of predictor variables. With (e.g.) demispan and age (i.e. two predictors) the minimum sample size would be: ``` n = 10p + 50 n = 10 * 2 + 50 n = 70 ``` I hope this helps.