Dose Rounding and Available Pediatric Formulations

From a Calculated Dose to a Measurable Amount

A model-based dose is a target amount, not necessarily an amount that can be administered exactly. A liquid may be measured only to particular volume increments, a tablet may not be suitable for splitting, and an infusion pump may have a minimum rate increment. The practical task is to choose an available amount that is both measurable and appropriate, then quantify the difference from the target.

Rounding should be considered after the intended dose and regimen have been established. Keep the prescribed dose basis clear: an amount per administration is not the same as a total daily amount. The comparisons in this tutorial are hypothetical and illustrate calculations, not patient-specific dosing recommendations. In practice, formulation suitability, device instructions, and applicable clinical guidance must also be checked.

Definition: Let $D^*$ be the calculated target amount per administration and $D_r$ the selected, measurable amount per administration. The signed dose-rounding error is $D_r-D^*$. The relative dose-rounding error is $$ e_D=\frac{D_r-D^*}{D^*}, $$ and its percentage form is $100e_D\%$. A negative value means the selected dose is below the target; a positive value means it is above. Both $D_r$ and $D^*$ must use the same units and refer to the same administration.

The feasible amounts depend on the product and the way it is administered. For an oral liquid with concentration $c$ in mg/mL, a measurable volume $V$ gives $D_r=cV$. If the measuring device allows only multiples of an increment $\Delta V$, candidate volumes are restricted to those increments, subject to any minimum volume or device-specific constraints. For a tablet, feasible amounts depend on the product strength and whether splitting into the intended portions is appropriate for that product. For an infusion, the feasible rate can be restricted by pump increments and the prepared concentration.

How Rounding Relates to Exposure

A dose error is not automatically the same as an exposure error. A direct comparison is available under a specific pharmacokinetic model: linear, time-invariant pharmacokinetics, unchanged bioavailability $F$, unchanged clearance $CL$, and the same dosing interval. At steady state, the interval AUC is

AUC_{\tau}=\frac{F D}{CL},

where $D$ is the amount administered during one interval and $\tau$ is the interval length. For a change from $D^*$ to $D_r$, with $F$ and $CL$ unchanged, the ratio of interval AUCs is therefore

\frac{AUC_{\tau,r}}{AUC_{\tau,*}} =\frac{F D_r/CL}{F D^*/CL} =\frac{D_r}{D^*}.

Thus, under these conditions, the relative interval-AUC change equals the relative dose change. This result concerns interval AUC; it does not say that the entire concentration-time profile is unchanged. A different dose can change concentrations, and changing the interval or infusion duration can change the profile, including peaks and troughs. In linear pharmacokinetics with unchanged $F$ and $CL$, the interval AUC relation remains $FD/CL$; it is the other exposure measures that may require a regimen-specific comparison.

Choosing Among Feasible Amounts

If the aim is to minimize absolute dose error and feasible amounts are equally spaced, compare the candidates immediately below and above the target. The closest candidate minimizes $|D_r-D^*|$; because the denominator $D^*$ is fixed and positive, it also minimizes $|e_D|$. That arithmetic rule is not a substitute for clinical constraints. A permitted dose range, a maximum dose, a minimum deliverable volume, or a product-specific restriction can rule out the numerically closest candidate. If an exposure target has a clinically important boundary, the decision may also require more than choosing the nearest amount.

Define the target precisely.
Record the target amount, units, and whether it is per dose, per day, or per unit time. Keep the interval and route explicit.

List feasible administered amounts.
Use the available concentration or strength and the actual measuring or delivery increments. Do not assume a tablet can be divided or a liquid measured to arbitrary precision.

Compare candidates and constraints.
Calculate signed and absolute errors for plausible choices, then exclude choices that violate product, device, or clinical constraints.

Interpret the result using the relevant exposure metric.
Use the dose-ratio result for interval AUC only when its assumptions hold. For other metrics or changed pharmacokinetics, evaluate the regimen using the relevant model and exposure measure.

Worked Example: Rounding an Oral Liquid Volume

Suppose a hypothetical child weighing 18.4 kg has a model-based target of 6 mg/kg per administration, given every 12 hours. The available liquid concentration is 40 mg/mL, and the oral syringe is graduated in 0.1 mL increments. Assume the formulation has the intended bioavailability and that rounding does not change the dosing interval.

Calculate the target amount. The target is $18.4\ \text{kg}\times6\ \text{mg/kg}=110.4\ \text{mg}$ per administration. At 40 mg/mL, the exact theoretical volume would be $110.4/40=2.76\ \text{mL}$, which is not a 0.1 mL increment.

Identify nearby measurable amounts. A volume of 2.7 mL supplies $40\times2.7=108$ mg; 2.8 mL supplies $40\times2.8=112$ mg. Their signed errors are $108-110.4=-2.4$ mg and $112-110.4=+1.6$ mg. Their relative errors are $-2.4/110.4=-0.02174$, or $-2.174\%$, and $1.6/110.4=0.01449$, or $+1.449\%$, respectively.

By absolute error, 2.8 mL is closer to the target. If the formulation and device are suitable and no other constraint changes the choice, the selected amount is 112 mg per administration. Under linear pharmacokinetics with unchanged $F$ and $CL$, its interval AUC is $112/110.4=1.01449$ times the target-dose interval AUC, a 1.449% increase. This conclusion is about interval AUC, not a guarantee that every concentration or exposure metric rises by exactly 1.449%.

Worked Example: A Splittable Tablet Strength

In a separate hypothetical case, the target is 37 mg per administration. A product is available as a 10 mg tablet, and product-specific instructions confirm that it may be split into equal halves. Assume that the intended route and bioavailability are unchanged. The feasible amounts are therefore multiples of 5 mg.

The nearest feasible amounts are 35 mg and 40 mg. For 35 mg, the signed error is $35-37=-2$ mg and $e_D=-2/37=-0.05405$, or $-5.405\%$. For 40 mg, the error is $+3$ mg and $e_D=3/37=0.08108$, or $+8.108\%$. The 35 mg amount has the smaller absolute error.

If it is otherwise appropriate to use that tablet, the selected amount is 35 mg per administration. With linear pharmacokinetics and unchanged $F$ and $CL$, the interval-AUC ratio is $35/37=0.9459$, corresponding to a 5.405% decrease from the target-dose interval AUC. The calculation does not establish that a tablet can be split: that was an explicit product-specific assumption in this example.

Worked Example: Rounding an Infusion Rate

Consider a hypothetical continuous intravenous infusion with target rate 3.67 mg/h. The prepared concentration is 2 mg/mL, and the pump permits rate settings in increments of 0.1 mL/h. The corresponding drug-rate increment is $2\ \text{mg/mL}\times0.1\ \text{mL/h}=0.2\ \text{mg/h}$.

The nearest feasible rates are 3.6 mg/h and 3.8 mg/h. Their signed errors are $3.6-3.67=-0.07$ mg/h and $3.8-3.67=+0.13$ mg/h. Their relative errors are $-0.07/3.67=-0.01907$, or $-1.907\%$, and $0.13/3.67=0.03542$, or $+3.542\%$. The closest setting is 3.6 mg/h.

For a linear, time-invariant intravenous model at steady state, $C_{ss}=R_0/CL$, where $R_0$ is the infusion rate. If clearance is unchanged, the steady-state concentration ratio is $3.6/3.67=0.9809$, about 1.907% below the target-rate value. This conclusion assumes the same drug concentration in the prepared solution and accurate delivery at the selected pump setting.

When the Simple Exposure Calculation Does Not Apply

The direct dose-ratio calculation for interval AUC depends on the exposure relationship being proportional to dose and on $F$ and $CL$ being unchanged. If pharmacokinetics are nonlinear over the relevant dose range, the AUC ratio need not equal the dose ratio. If changing formulation changes bioavailability, interval AUC may change by more or less than the dose ratio suggests. In either case, compare the candidate regimens with a suitable pharmacokinetic model and the exposure metric of interest.

A change in dosing interval or infusion duration should be handled according to the question being asked. It can change average concentration and the concentration-time profile, including peaks and troughs. It does not, by itself, invalidate the interval-AUC equation $AUC_{\tau}=FD/CL$ under linear pharmacokinetics with unchanged $F$ and $CL$. If the comparison concerns a peak, trough, time above a threshold, or another profile feature, use an analysis that represents the actual regimen rather than treating dose ratio as a prediction for that metric.

Diagnostics and Common Pitfalls

Before accepting a rounded amount, check the arithmetic and the practical assumptions. A liquid calculation should convert volume to amount using the stated concentration; an infusion calculation should convert the pump setting using the prepared concentration. Confirm that the target and selected amount refer to the same administration, not one to a daily total and the other to a single dose. Check that the chosen increment is actually deliverable with the specified product and device.

Rounding before converting units. A target in mg cannot be compared directly with a volume in mL. Convert through the formulation concentration first.
Using a daily target as a per-dose target. Divide or allocate according to the prescribed regimen before rounding each administration; do not silently treat the daily total as a single dose.
Assuming any tablet can be split. Feasible tablet amounts depend on product-specific suitability and instructions, not just arithmetic divisibility.
Calling dose error the error for every exposure measure. The dose-ratio result applies to interval AUC only under its stated assumptions. It does not establish an identical proportional change in peak, trough, or time above a threshold.
Choosing the nearest amount without checking constraints. A mathematically closest amount may not be appropriate if it violates a product, device, or clinical limit.

For example, the reasoning “the dose was rounded up by 5%, so the peak concentration must rise by exactly 5%” is not justified by the interval-AUC equation. The correction is to identify the exposure measure first. AUC may scale with dose under the stated linear assumptions; peak concentration depends on the regimen and concentration-time profile, so it requires the appropriate model or calculation.

Key takeaway: Rounding is a constrained choice among amounts that can actually be administered. Quantify the dose error explicitly, and translate it into an exposure change only for a specified metric under assumptions that support that relationship.

Check Your Understanding

Answer each question, then compare with the solutions below.

A hypothetical target is 24 mg per administration. Feasible amounts are 22 mg and 25 mg. Calculate the signed and relative error for each and identify the closer amount by absolute error.
A liquid contains 30 mg/mL. What amount is delivered by 1.4 mL, and what volume increment corresponds to 3 mg?
Under linear pharmacokinetics with unchanged $F$ and $CL$, what is the interval-AUC ratio when the dose changes from 80 mg to 84 mg?
Does that AUC ratio alone establish the change in peak concentration if the interval is also changed? Explain.

Solutions. For question 1, the 22 mg error is $22-24=-2$ mg, so $e_D=-2/24=-0.08333$, or $-8.333\%$. The 25 mg error is $+1$ mg, so $e_D=1/24=0.04167$, or $+4.167\%$. The 25 mg amount is closer by absolute error. For question 2, $30\ \text{mg/mL}\times1.4\ \text{mL}=42$ mg; 3 mg corresponds to $3/30=0.1$ mL. For question 3, the ratio is $84/80=1.05$, a 5% increase in interval AUC under the stated assumptions. For question 4, no. The relation establishes the interval-AUC ratio, not the peak change; an interval change can alter the concentration-time profile, so peak concentration requires evaluation for the actual regimen.