Dose banding: a pragmatic approach

Dose banding is a system whereby drug doses that are calculated by any method are grouped and rounded to set of predefined doses for the convenience of the ‘users’. Each series of consecutive dose(s) is called a ‘band’, with the dose to which they are rounded towards being the ‘banded dose’¹

The usefulness of dose banding will be governed by the point of view and the method of dose banding which has been employed. Some methods will not create the full range of benefits.

Marsh et al. described a number of significant advantages of logarithmic banding,² including the ease of dose modification. Coincidentally, the increase from the ‘traditional’ 5% bands to 6% resulted in a reduction in product inventory. However, logarithmic banding is not without its disadvantages; ‘unmeasurable’ doses often being cited as the most problematic, closely followed by the concern that doses that unnecessarily include decimal places might introduce additional risk of error.

Rounding the doses to measurable values, for most drugs will reduce the appearance of decimal places and allow manufacturers and pharmacies to confidently produce and label a product with a dose that corresponds to the volume of drug measured.

However, the choice of actual doses to band in the Marsh et al. paper was based on an initial starting dose of 100mg, and for individual drugs, a different starting point may be more appropriate. If a single dose banding scheme (applicable to any drug) is desired, then the selection of starting dose for the bands to be formed from may be arbitrary and could result in a suboptimal scheme for a specific drug.³

In addition, and possibly of greater importance, while the standard logarithmic bands work well for 20% dose reductions, 25% reductions are also commonly mandated in chemotherapy protocols and are not so well served by the logarithmic system previously published.

In addition, logarithmic doses are not optimised to vial sizes. While this may not be an issue for those using dose banding to facilitate batch production, where vial sharing can minimise waste; where a single dose is required it can lead to situations where a large proportion of a part vial may be wasted. Furthermore, while logarithmic bands minimise inventory of drugs supplied in single containers the absence of a common denominator in the dose increments means that inventory for multiple syringe dosing is not optimised.

However, logarithmic dose banding does also lead us to question if there are mathematical solutions to the problem of optimising the bands. Conventionally, if the bands of 80, 90 and 100mg are in use, patients prescribed doses between 85.1 and 95mg would receive the 90mg dose and patients prescribed doses of over 95mg would receive the 100mg dose.

However, the variance for a patient with a calculated dose of 95mg who is given 90mg is a 5.55% reduction while giving 100mg would only result in a 5.26% increase. While such differences in variance are small, clearly using the mid-point between bands is not mathematically optimal, algebraically defining the variance by using the higher and lower bands and then integrating both expressions to determine the intercept defines that the optimal point where doses should be banded up instead of down is defined as the square root of the product of the two bands being considered.

In the example above the optimal point is 94.87mg rather than 95mg, minimising the variance to 5.4% in both cases, while this difference is unlikely to be significant it can be sufficient to allow a mathematical model to develop doses that minimise the number of bands required.

Traditionally a 5% variance has been used for dose banding. Again, there are several ways to calculate this, depending on which figure the variance is measured from (in other words, the ‘denominator’). It is considered correct that the denominator should be the actual dose calculated for the patient and the variance is how much the banded dose differs from this. For example, if the calculated dose was 95mg, and the banded dose 100mg:

The choice of positive or negative numbers in this situation does not make any different to the final percentage variance and is often quoted in either direction.

It is the nature of logarithms that the percentages going up a band and down a band are different.² As dosing methods for chemotherapy usually require dose reductions, the going down method is the variant we are most interested in.

If we have two bands – 90mg and 100mg, for example – using the variance method above we achieve the following two answers:

Using the same principle (choosing 95mg and 100mg to illustrate the point) dose decreases of 5% equate to increases on the same scale of 5.3%. These are small differences but must be born in mind when considering how the banding number set is chosen, especially when numbers are usually selected going up.

There is little evidence to support 5% being an absolute limit for rounding to the nearest dose band, although breaching this causes concern amongst some.⁴ However, in evaluating numbers, a small increase in variance in certain places in the number set to a maximum of 6.5% can have a useful effect in the numbers.

Take the example of the following dose set – 100mg, 110mg, 120mg etc. This would have to continue at 10mg increments all the way to 200mg (see Tables 1 and 2 above).

Allowing the variance to increase slightly and two dose bands can be omitted (170mg and 190mg). And with rounding variance to the nearest whole percentage, only two of these figures breach 5% – the jump between 160mg and 180mg. Extrapolating this principle up the entire table can remove a considerable number of bands. We removed approximately 30 bands in the range of 0.2 to 1100ml.

5% variance requires 10 bands over this section of graph (Figure 1). The 5% variance lines (blue) lie above and below the calculated heavy blue central line. Dose bands are in red.

Increasing the acceptable variance to 6.5% in the above example shows that the breach is tiny – see 160mg and 180mg in the graph (Figure 2). The 5% variance lines are left in place.

These benefits can also be displayed by the following reduction in potential inventory (Tables 3 and 4).

Currently, the data shows that Trusts in the North of England are buying eight drugs in 671 different dose presentations. Applying the dose banding principles we can reduce this to 61 lines, which will still cover 96% of items currently being bought as single container. Focusing on the higher usage product lines, it might be reasonable for the manufacturers to commit to the pre-planned production of 45 product lines (equating to 91% of all doses currently purchased).

Despite not having the data on the prescribed doses for the bolus chemotherapy, utilising the above banding structure will result in reducing the inventory for the four lines on the tender from 265 to 20, that is, five products for each of the bolus syringes

A fixed set of volumes has been calculated (as opposed to doses) to achieve all dose volumes required between 20 and 200ml. The volumes are a maximum of 10% apart so that bands will never have a variance of more than 5%. All that is required from here is to convert the volumes to doses based on the strength of the diluted drug to achieve a list of syringe doses that will be required to be kept in stock.

Only five fixed syringe volumes are required to make all doses in the table below. Note that not all volumes will be needed for any particular drug so the number of syringes required to be stocked may be less (Table 5). The following syringe sizes will make up any dose in the table below with no more than three being required for any specific dose: 2.5ml, 10ml, 25ml, 30ml and 50ml.

If we use the example of 75mg/m2 and 100mg/m2 epirubicin in the breast EC protocols, the banded doses range from 100–240mg (or 50 to 120ml as epirubicin in 2mg/ml). Only four syringe sizes (10ml, 25ml, 30ml and 50ml) are required to supply all doses for these protocols.

Maximum syringe fill volumes need to be taken into account. The recommendation from the NHS Pharmaceutical QA Committee is that no syringe should be filled beyond 85% of its nominal capacity. In addition, the standard volumes used in the multi-syringe system should always be measured to the nearest appropriate mark on the syringe. Therefore 2.5ml can be drawn up in a 3ml or 5ml syringe, 10ml in a 20ml syringe, 25ml in a 30ml syringe, and 30 and 50ml in a 60ml syringe.

For those wishing to use a capped volume of 30ml due to local practice it is also possible to produce this table without requiring the 50ml volume. In many cases, however, more syringes will be required to make up each dose.

Since dose banding was originally developed as a concept for ‘traditional’ cytotoxic agents4 there have been other drugs released to market that have followed similar dosing patterns but offer different difficulties in light of their formulation.

Monoclonal antibodies have traditionally been dosed in the same way as other systemic anticancer therapy (SACT) which has often been thought of as a rational approach. The rationale behind this approach would be that there would be reduced inter-patient variability using this dosing method has since been questioned – and there are a number of marketed mAbs that have flat fixed doses that were once dosed according to body size parameters (for example, trastuzumab and rituximab).⁵

The main point to consider with all therapeutic drugs is to maximise response with minimum adverse effect – and with many of this class of drug the adverse effects are achieved at levels much higher than the therapeutic effect.⁶

With these points considered and an incessant need to reduce wastage through vial sharing potential by moving to a model whereby the doses of these drugs are rounded to a greater variance then this can be achieved.

Increasing the variance to a level of ±10% will lead to more of the doses representing whole vial sizes or half vial sizes – which lead to more efficiency through less need to vial share and less wastage from non-vial sharing. As these drugs display a wide therapeutic index and the fact that these drugs work at molecular level then the need to dose as specifically as ±5% is probably not necessary.^5,6

This is supported by research relating to specific mAbs such as bevacizumab,⁷ and also the current model for increasing the variance to ±10% has already been adopted in some centres in the UK and is written in to the Scottish Oncology Pharmacy Practice Group (SOPPG).⁸ There may be some occasions where a greater than 10% variance is necessary to be agreed in order either eliminate waste or enable ease of vial sharing. All things considered the model of moving to a 10% variance for all mAbs may well lead to further research in the dose rationalisation of these products in the future.

Having evaluated the existing schemes, and attempted to make minor modifications such as rounding the volumes of logarithmic dose banding we remained dissatisfied that any of the systems could cover all of our desires for a dose banding scheme. We therefore created a new banding system, trying to take the benefits of log banding, but minimise the disadvantages.

Our new scheme, for cytotoxic drugs uses a 6% variance when the variance is rounded to one significant figure. The same underlying variance used in logarithmic banding, allowing fewer dose bands for a given drug, resulting in optimal inventory. Unlike logarithmic banding, we have not focused on the ability to dose reduce; however, it should be possible to make a 20–25% dose reduction with our scheme. Doses would be measurable, with the ability to measure agreed by NHS production colleagues nationally.⁹

Volumes consistent with normal vial sizes have been used to minimise waste where possible. Bands are defined by ‘measurable’ drug volume rather than a dose in milligrams, and hence can be applied to any drug. For the multi-dose syringes the same principles were applied but with an awareness of the presentation and the maximum fill volume. For the mAbs, an attenuated logarithmic system was chose with a 10% variance which also focused on whole or half vial sizes. This work has now been endorsed nationally by NHS England.

1. Plumridge R, Sewell GJ. Dose-banding of cytotoxic drugs: a new concept in cancer chemotherapy. Am J Health Syst Pharm 2001;58:1760–4.
2. Zavery B, Marsh G. Could logarithmic dosing change the way cytotoxics are prescribed? Pharm J 2011;3:116–8.
3. Mathijssen RH et al. Flat-fixed dosing versus body surface area based dosing of anticancer drugs in adults: does it make a difference? Oncologist 2007;12(8):913–23.
4. Kaestner SA, Sewell GJ. A National survey Investigating UK Prescribers’ Opinions on Chemotherapy Dosing and Dose Banding. Clin Oncol 2009;21:320–8.
5. Wang DD et al. Fixed dosing versus body size-based dosing of monoclonal antibodies in adult clinical trials. J Clin Pharmacol 2009;49(9):1012–24.
6. Bai S et al. A guide to rational dosing of monoclonal antibodies. Clin Pharmacokinet 2012;51(2):119–35.
7. Flak AT et al. Bevacizumab: A dose review. Crit Rev Oncol Hematol 2015;94(3):311–22.
8. Scottish Cancer Pharmacy Group; Guidelines for Dose Banding of Cancer Chemotherapy June 2015.
9. NHS Pharmaceutical Quality Assurance Committee, 2013. Guidance document: Protocols for the Integrity Testing of Syringes [online] Stockport: Quality control North West. www.qcnw.nhs.uk. Last accessed April 2016.