Calculating the right dose for children

27th January 2006 at 00:00
Q I have an extremely bright Year 5 pupil who has just recovered from tonsillitis. She asked me if I know the maths behind "5ml, four times a day". Can doctors get it wrong?

A Your letter sent me on a voyage of discovery. I thought that the dosage for children was worked out by their age, but there is a lot more to it than that. Children, as we all know, don't come in standard sizes. I found some very interesting facts along the way. About 40 per cent of children's prescribed medication has never been tested on children, with a figure of 65 per cent for newborn babies.

"Errors in prescribing and administration of medicines to children are at least as common as in adults. However, the consequences of these errors can be more serious. A study of admissions to neonatal and paediatric intensive care units found an error rate of 1 every 6.8 admissions (14.7 per cent).

The risk of error in children is often compounded by the need for additional calculations to determine the dose. Lack of formulations of licensed medicines for children frequently necessitates the use of products made for adults and hence the need for the calculation of doses and accurate measurement of small liquid dose volumes. A common source of error is misplacement of decimal points in dose calculations. Sometimes complex manipulations are necessary to prepare doses for very small babies," says the Department of Health (www.dh.gov.uk).

Your pupils need to know that the dosage will have been calculated for adults from medical research that has been carried out over time, hence the importance of statistics and mathematics in partnership.

Now for the calculations. Please note I am not a doctor and no one should be prescribing medication unless qualified and licenced to do so. Not only do the medical professionals have to take great care in performing these calculations with the patient's details in mind, they also have to consider the medicine they are prescribing as some medicines (and herbal remedies) should not be given to children at all.

The main assumption I have used here is that the doses approved for adults are accurate. Clark's rule (based on a child's weight) is relatively simple to apply and is used for infants and children with a proviso that the child has a normal lean body mass and normal body development. An approximate child dose is found by dividing the weight in pounds by 150 and then multiplying by the adult dose. So, with an adult prescription of 50 drops taken four times a day, a 30lb child would only take 10 drops four times a day or 1Z5 of the adult dose x adult dose = 30Z150 x 50 = 1Z5 x 50 = 10).

There seemed to be a more accurate calculation based on a child's body surface area.

* found three rules based on the child's age:

* Fried's rule (children from 1 year to 12 years) x adult dose;

* Young's rule (1 year to 12 years) x adult dose;

* Cowling's rule (I couldn't find an age range for this) x adult dose.

Since the 1950s medicine doses in adults have used the Body Surface Area (BSA) in the calculations. This is calculated using height and weight with a number of different formulae employed to work out the BSA. More recently West's nomogram provides a calculation of the BSA and is used as another way to calculate children's doses. The formula is BSAZ1.73 x adult dose.

It is also suggested that the smallest dose is chosen as this is considered the safest, but this can lead to not enough of the medication being administered for the condition.

An interesting investigation for your bright Year 5 pupil would be to create these different formulae on a spreadsheet and look at results for infants through to children of 12 years old. Extend this to looking at the BSA formula for a sample of pupils throughout the school (www.halls.mdbody-surface-areabsa.htm). This could be researched for the different BSA calculations.

In my searches I came across a book full of calculations from the US Army Medical Center and school, Houston, Texas

(www.freeinfosociety.compdfsscienceDrugdosage.pdf). The medic soldier has to learn the abbreviations of prescriptions, "Tab ii stat, then tab i bid", which reads "2 tablets at once, then 1 tablet twice a day."

There is an extremely long list of abbreviations. However, there is also an excellent resource containing real applications of ratio, fractions and other calculations. I would suggest these could be used at key stage 34.

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