Auditing Units and Conversion Steps in Dose Calculations

Why Unit Audits Matter

A dose calculation can contain correct-looking numbers and still be wrong because a conversion factor was inverted, a body weight was applied twice, or a concentration unit was confused with an exposure unit. In first-in-human dose selection, these errors can change a proposed amount by a large factor. An audit therefore follows each quantity from its source to its destination, writing units alongside every value and checking that the units cancel as intended.

This tutorial focuses on the arithmetic and dimensional consistency of body-weight, body-surface-area, clearance, concentration, and exposure conversions. A successful unit audit does not establish that the biological assumptions or the selected safety margin are appropriate. It establishes that the stated calculation actually implements those assumptions without a conversion error.

Weight-Based and Surface-Area Conversions

A dose of \(D\ \text{mg/kg}\) is an amount per kilogram, not an amount in milligrams. For a person weighing \(W\ \text{kg}\), the corresponding absolute dose is \(D \times W\), with units \((\text{mg/kg})\times\text{kg}=\text{mg}\). Conversely, dividing an absolute dose in mg by weight in kg gives a dose in mg/kg. This distinction matters when a calculation moves between a dose intensity and the quantity that would be administered.

A common body-surface-area conversion uses conventional \(K_m\) values, where \(K_m\) is body weight divided by body surface area and has units kg/m². If an animal dose is expressed in mg/kg, multiplying it by the animal \(K_m\) gives a dose per surface area. Equating that surface-area dose across species and dividing by the human \(K_m\) produces a human-equivalent dose (HED) in mg/kg.

The ratio of \(K_m\) values is dimensionless because both have units of kg/m². The result therefore remains in mg/kg. This conversion relies on the conventional surface-area scaling approach and the selected \(K_m\) values; it is not a direct demonstration that species have identical pharmacology or exposure. Use the factors specified for the calculation, and record their source in an actual analysis.

Worked Conversions

Clearance, Concentration, and Exposure

Clearance describes volume of fluid cleared of drug per unit time, commonly L/h. For a drug with linear pharmacokinetics and complete AUC measured over the relevant interval, intravenous dose divided by systemic clearance gives AUC. The units verify the relationship: mg divided by L/h equals mg·h/L. For oral dosing under linear pharmacokinetics, absolute bioavailability \(F\) accounts for the fraction of the administered dose reaching systemic circulation, so AUC is \(F\) times dose divided by clearance. These equations require that the stated clearance and bioavailability apply to the dose and conditions being considered.

Concentration and exposure are different quantities. Concentration may be reported as mg/L or ng/mL; AUC includes time, for example mg·h/L or ng·h/mL. Since 1 mg equals 1,000,000 ng and 1 L equals 1,000 mL, 1 mg/L equals 1,000 ng/mL. The same concentration conversion applies to AUC units when the time unit is unchanged: 1 mg·h/L equals 1,000 ng·h/mL.

A Practical Audit and Common Failure Modes

A reliable audit makes each conversion visible rather than relying on a calculator’s final output. Write the source quantity with its units, write the conversion factor with its units, cancel units explicitly, and confirm that the resulting unit is the one requested. Keep adequate precision in intermediate calculations, then round the final result. Also record the definitions used: for example, whether a dose is per kg per administration or per kg per day, and whether an AUC is expressed per dosing interval or over the total observation period.

The main alternatives are not interchangeable merely because each produces a dose. Direct mg/kg scaling preserves a dose per body weight; BSA conversion uses a dose per surface area and a specified BSA or \(K_m\) convention; exposure-based calculations use PK quantities such as dose, clearance, and bioavailability. The appropriate approach depends on the rationale and evidence supporting the calculation. A unit audit can expose a mismatch between the stated approach and the calculation performed, but it cannot decide which approach is biologically best.

Common failure modes include inverting the animal-to-human \(K_m\) ratio, applying body weight twice, using height in metres when an equation requires centimetres, dropping the time unit from AUC, and converting mg/L to ng/mL with a factor of one million instead of one thousand. Another frequent problem is rounding an intermediate value and then presenting a multiplication as though it used the rounded number when it actually used an unrounded one. Show enough digits or state explicitly that the final amount was calculated from the unrounded value.

A correct dimensional result has limits. It does not establish that the source dose, \(K_m\) values, BSA equation, clearance estimate, bioavailability, or scaling assumptions are scientifically suitable. Nor does it establish that the resulting amount is clinically safe. Those judgments require the broader pharmacology, toxicology, and risk rationale; the unit audit supports that reasoning by ensuring the arithmetic faithfully represents it.