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Calculation: how many days of treatment will this patient receive?

Do you know how many days’ supply of antibiotic this patient should receive?

The following question relates to the ‘calculation’ sections of the General Pharmaceutical Council (GPhC) registration assessment framework. It is designed to help you practise calculations you may be asked to perform when checking and dispensing prescriptions as a pre-reg or, if you are already a pharmacist, to help you support your pre-reg as they prepare for the assessment.

Question: quantity of amoxicillin suspension to supply

A three-year-old girl, weighing 14kg, is prescribed amoxicillin 250mg/5ml oral suspension BP at a dose of 420mg three times daily x 252ml for acute otitis media. The instructions advise adding 64ml of potable water and shaking until all contents are dispersed. The reconstituted suspension has a shelf-life of seven days and should be stored at 2-8°C.

Click here for the correct working out and answer

This is one method to work out the answer to this calculation:

Reconstituted antibiotic concentration = 250mg/5ml = 50mg/1ml

As mentioned in the question, 50mg of antibiotic is in each millilitre. We can work out how many millilitres (V1) per dose (420mg) are required.

420mg/V1 = 50mg/1ml

420mg = (50mg/1ml) x V1

(420mg x 1ml)/50mg = V1

V1 = 8.4ml

To calculate how many days the suspension lasts, you need to work out total daily volume used.

8.4ml x 3 doses per day = 25.2ml per day

The total volume prescribed is 252ml

252ml/25.2ml = 10 days

Learning points
  • The question is asking for the number of days of treatment
  • Additional information is available in the question, such as patient age, volume of potable water and fridge temperature. You should ensure you recognise the information relevant to the question – you may want to highlight or circle key figures.

An example answer grid with instructions on how to use the grid can be found here.

 

Babir Malik is a teacher practitioner at Bradford University and lead at the Green Light Campus masterclass.

Mr Malik does not set or write questions for the GPhC registration assessment and he does not imply that these calculations will come up in the exam. However, the questions relate to the GPhC framework. The author adds that there may be other ways to work out these questions, but it does not matter how you work out a question as long as you get to the correct answer.

You can listen to C+D's podcast on preparing for the GPhC pre-reg exam below. Alternatively, subscribe to all of C+D's podcasts on iTunes by clicking here or by searching 'Chemist+Druggist podcast' on your preferred Android podcast app.

7 Comments
Question: 
Were you able to answer the above calculations?

Susan Lee, Superintendent Pharmacist

A great pre-Reg / newly qualified pharmacist can ensure the right size syringe is supplied to enable measurement of an 8.4ml dose, and demonstrate how to draw this up. Equally they can offer a ‘tared’ bottle for 64ml + dry powder as a solution to a mother who expresses a genuine inability to return for the remainder of the course. Also they should be able if necessary to discuss the risks & benefits with a prescriber of rounding up to 500mg TDS for a carer who they judge will be struggling with the syringe/8.4ml scenario.

They will also know the Drug Tariff/special container rules and be able to explain to a young dispenser trainee in understandable terms how adding 64ml water gives 100ml of end product. It really could be argued this question is more suited to a OSCE style competence assessment than a multiple choice exam.

Anyone agree?

Stephen Roth, Community pharmacist

The patient requires 30 doses over the course of 10 days. Each bottle contains 11 doses at 8.4ml per dose. If one bottle was supplied as the initial supply, this would last until the second dose on day 4. On day 4, two bottles could be supplied at the same time, for the remaining 19 or 20 doses, minimising patient/parent/carer inconvenience. An explanation about safe disposal of the remaining medicine would of course be provided (with both supplies).

 

Roy Sinclair, Community pharmacist

The C&D starts by asking - how many days’ supply of antibiotic this patient should receive?  The learning points section in the answer states - The question is asking for the number of days of treatment. These are not the same question.

Neither of these are included in the Question Text shown so it is not easy to know what was actually asked for in the question.

One problem arises from the fact that the question includes a 7 day expiry for the suspension to be dispensed. This excludes the use of the sugar free suspension with a 14 day expiry. I.e. the Standard suspension is to be used.

Here is my rather long answer which shows this question isn't  that simple and perhaps isn't worded as well as it could / should be  :- 

When reconstituted, each 5mls will contain         = 250mg               

So 420mg is contained in (5/250) x 420mls        = 8.4mls - to be taken TDS.

So each day the patient will require  3 x 8.4mls   =25.2mls

The amount prescribed is                                      = 252mls

Therefore the patient is prescribed (252/25.2)     = 10 days supply

You cannot supply 256mls in a single dispensing on day 1 as that would exceed the 7 day expiry (as stated in the question).

Whatever you do will require you to reconstitute 3 x 100ml bottles in the dispensing process.

The suspension only has a shelf life of 7 days

At 25.2mls per day,  3 days supply would be 3 x 25.2        = 75.6mls

And                           5 days supply would be 5 x 75.2        = 126mls

So 5 days is within the 7 day expiry.

The 252mls would therefore be supplied as follows:-

Dispense 1 x 130mls on Day 1

Advice - Use for 5 days and discard the small remainder. On Day 5, all and collect a second supply.

Dispense 1 x 130mls on day 5

Advice-  Use for 5 days and discard the small remainder.

This would allow for small errors in over- measuring the individual 8.4ml doses which presumably would require use of a suitable oral syringe - which also would need to be supplied.

 

Ben Merriman, Community pharmacist

OK, it's been a long day but here goes....

I think we all agree that the treatment NEEDED is 10 days, however, that ignores any limited expiry and special container factors.  Assuming the medicine is on an FP10, in the real world, as per Drug Tariff Part 2, Clause 13, 300mL would be supplied, 100mL @ t=0days, 100mL @ t=3 days, 100mL @ t=7days. 

Yes, you could only supply 52mL on say day 8 of treatment but you'd have to hope you'd be able to use the 48mL left over and that just doesn't happen.  As such, I'd give (and rightly be paid for) 300mL which would be 11.9 days, of course counselling the patient/carer that any remainder should be returned for disposal.

Finally, how (and why?!) would you supply 130ml when they come in 100ml bottles?  You'd only be paid for 300mL in total, not for the 70mL you're hoping to use (i.e. disposing of) on the second dispensing, unless the prescriber wrote two seperate forms for the first and second supply (again, part 2, clause 13).

Now, where's the port?

Roy Sinclair, Community pharmacist

Ben, you are right. I avoided dealing with payments as that is not covered in the question -plus as I mentioned, the question is really badly worded. Calculation questions should as much as possible ensure that they are truly representative of the real world. 

One 100ml bottle would last for 3 days. So you could supply one bottle and ask the patient (or their relative) to return every third day for a new bottle. This would require three  supplies that would provide three days each and then a final supply for the 10th day. You would still end up using 400mls but would inconvenience the patient more - double the journeys.

My suggestion was 130mls in a new 150ml bottle - more additional costs !

If this prescription was received in the real world, I would (try and) negotiate with the prescriber to rewrite the prescription to ensure  I was fully re-imbursed. Get them to write - Dispense two x 130mls at 5 day intervals??

I would find it no wonder that pre-regs would struggle with this!

Ben Merriman, Community pharmacist

There's more than one answer, surely...?

C A, Community pharmacist

Learning point - the sugar free version has an expiry of 14 days and is the solution to this problem... ;)

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