Building a Dose Table From a Population Model

From a Population Model to a Practical Table

A population model can predict clearance for a person with specified covariates, but a practical recommendation often needs a manageable number of regimens rather than a unique calculated dose for every possible combination of age, weight, and kidney function. Building a dose table means choosing clinically interpretable groups, calculating the model-predicted clearance for each group, translating clearance into a dose for a stated exposure target, and rounding that dose to a usable regimen.

The table is a summary of model-based predictions, not a guarantee that every person in a group will have the same clearance or exposure. The grouping and rounding decisions therefore need to be explicit, and the resulting regimens should be checked against the assumptions and covariate range for which the model is intended.

Definition: A model-based dose table assigns a dose regimen to each defined covariate group using predicted pharmacokinetic parameters and a stated exposure target. Each row must identify the group, the representative covariates or prediction rule, the calculated target dose, the rounded regimen, and the predicted consequence of rounding.

Model, Target, and Assumptions

Consider a fully hypothetical teaching model for intravenous clearance, \(CL\), in L/h:

CL = 6\left(\frac{WT}{70}\right)^{0.75} \left(\frac{25}{AGE+24}\right) \left(0.30+0.007\,eGFR\right)

Here \(WT\) is weight in kg, \(AGE\) is age in years, and \(eGFR\) is kidney function in mL/min/1.73 m². The model is assumed to apply only over the hypothetical range age 5–16 years, weight 20–70 kg, and eGFR 30–120 mL/min/1.73 m². It is not a model for an actual drug or a clinical dosing recommendation. The renal multiplier equals 1 when eGFR is 100; the weight and age terms adjust clearance relative to their reference values.

For this illustration, assume linear pharmacokinetics, a fixed 24-hour interval, intravenous administration with bioavailability \(F=1\), and a target steady-state AUC over each interval of 10 mg·h/L. Under these assumptions, dose divided by clearance gives the AUC over the interval. The model is treated as the source of predicted typical clearance; unexplained individual variation and uncertainty are not included in the point predictions below.

AUC_{24}=\frac{Dose}{CL} \qquad\Longrightarrow\qquad Dose_{\text{target}}=AUC_{\text{target}}\times CL

If administration were oral with known bioavailability \(F\), the corresponding relationship would be \(AUC_{24}=F\times Dose/CL\), and the target dose would need to account for \(F\). The examples keep \(F=1\) so that the table construction is transparent. They also assume that the interval, route, target, and model are clinically appropriate; arithmetic cannot establish those assumptions.

Worked Example: Calculate a Target Dose for One Group

Suppose a hypothetical age-weight-kidney-function group is represented by a 5-year-old weighing 20 kg with eGFR 100 mL/min/1.73 m². Calculate predicted clearance and the unrounded dose for the target AUC.

Substitute the covariates into the stated model:

CL=6\left(\frac{20}{70}\right)^{0.75} \left(\frac{25}{5+24}\right) \left(0.30+0.007(100)\right)

The renal multiplier is \(0.30+0.70=1\), and \(25/(5+24)=25/29\). Thus:

CL=6(20/70)^{0.75}(25/29)(1) =2.021353\ \text{L/h}

The unrounded target dose is \(10\ \text{mg·h/L}\times2.021353\ \text{L/h}=20.21353\ \text{mg}\). If the available dose increment is 2.5 mg, the nearest increment is 20 mg. The predicted AUC after rounding is \(20/2.021353=9.8944\ \text{mg·h/L}\), or about 1.06% below the target. These calculations assume that the model applies at these covariates and that the stated target and 24-hour interval are suitable.

Build and Check the Rows

A dose table needs a rule for assigning a person to a row. Groups might be defined by age bands, weight bands, kidney-function bands, or combinations of these. For each row, specify how its representative covariates were chosen: for example, a clinically meaningful reference profile or a model prediction averaged over a clearly defined population. A single representative profile is convenient, but it does not describe every person in the row.

The next example uses three hypothetical profiles as the representatives for three proposed rows. Assume doses are rounded to the nearest 2.5 mg, with ties rounded upward. The calculations keep the interval fixed at every 24 hours.

Worked Example: Construct Three Rounded Table Rows

For each profile, calculate \(CL\), the target dose, and the AUC predicted after rounding. The model and assumptions are those stated above.

Row A: age 5 years, weight 20 kg, eGFR 100. From the preceding calculation, \(CL=2.021353\) L/h and the target dose is 20.21353 mg. Rounding to 20 mg gives \(AUC_{24}=20/2.021353=9.8944\) mg·h/L, approximately 1.06% below target.

Row B: age 12 years, weight 40 kg, eGFR 60. The renal multiplier is \(0.30+0.007(60)=0.72\), so:

CL=6(40/70)^{0.75}(25/36)(0.72) \approx1.97166\ \text{L/h}

The target dose is \(10(1.97166)=19.7166\) mg, which rounds to 20 mg. The resulting AUC is \(20/1.97166\approx10.144\) mg·h/L. Relative to the target, the deviation is \((10.144/10-1)\times100\%\approx1.44\%\) above target.

Row C: age 16 years, weight 60 kg, eGFR 30. The renal multiplier is \(0.30+0.007(30)=0.51\), giving:

CL=6(60/70)^{0.75}(25/40)(0.51) \approx1.70369\ \text{L/h}

The target dose is \(10(1.70369)=17.0369\) mg, which rounds to 17.5 mg. The resulting AUC is \(17.5/1.70369\approx10.271\) mg·h/L, about 2.718% above target.

A compact table of these calculations is:

Representative profile	Predicted CL (L/h)	Target dose (mg)	Rounded regimen	Predicted AUC (mg·h/L)
5 y, 20 kg, eGFR 100	2.021	20.214	20 mg every 24 h	9.894
12 y, 40 kg, eGFR 60	1.972	19.717	20 mg every 24 h	10.144
16 y, 60 kg, eGFR 30	1.704	17.037	17.5 mg every 24 h	10.271

The table reports predicted values for the representative profiles, not observed outcomes or guarantees for all members of the groups. The AUC deviations quantify only the effect of rounding under the assumed model and regimen.

Why Rounding Changes Exposure

With a fixed target AUC and interval, the unrounded dose is \(Dose_{\text{target}}=AUC_{\text{target}}\times CL\). After rounding to \(Dose_{\text{rounded}}\), the predicted AUC is \(Dose_{\text{rounded}}/CL\). Dividing the rounded AUC by the target AUC shows why the relative deviation is easy to calculate:

\frac{AUC_{\text{rounded}}}{AUC_{\text{target}}} = \frac{Dose_{\text{rounded}}/CL}{Dose_{\text{target}}/CL} = \frac{Dose_{\text{rounded}}}{Dose_{\text{target}}}

Therefore, the percentage deviation is \(100\times(Dose_{\text{rounded}}/Dose_{\text{target}}-1)\%\). It is positive when rounding increases the dose and negative when rounding decreases it. This calculation is an exposure comparison for the assumed target and model; it is not a probability statement or a clinical safety threshold.

A dose increment that seems small in milligrams may be large relative to a small target dose. Conversely, the same increment can have little relative effect for a larger dose. The table should report the rounded regimen and its predicted exposure consequence, rather than implying that the unrounded mathematical dose can be administered exactly.

Check Group Width, Diagnostics, and Alternatives

A representative profile can conceal meaningful differences within a row. One simple check is to evaluate model predictions at the covariate combinations that give the lowest and highest clearance in the proposed group. For the stated model, clearance increases with weight and eGFR and decreases with age over the specified ranges. If the same rounded dose is assigned across a broad group, the predicted AUC can therefore vary substantially across its members.

Worked Example: Test Whether One Row Is Too Broad

Consider a proposed row covering ages 8–12 years, weights 25–35 kg, and eGFR 60–100 mL/min/1.73 m². Suppose it assigns 20 mg every 24 hours. Within these ranges, the lowest predicted clearance occurs at age 12, weight 25 kg, and eGFR 60; the highest occurs at age 8, weight 35 kg, and eGFR 100.

At the low-clearance combination, the model gives \(CL=6(25/70)^{0.75}(25/36)(0.72)\approx1.386\) L/h. The predicted AUC from 20 mg is \(20/1.386\approx14.43\) mg·h/L, about 44.3% above the target.

At the high-clearance combination, \(CL=6(35/70)^{0.75}(25/32)(1)\approx2.787\) L/h. The predicted AUC is \(20/2.787\approx7.176\) mg·h/L, about 28.2% below target. Thus one 20 mg regimen does not keep the model-predicted AUC close to 10 mg·h/L throughout this proposed row. The result is a reason to reconsider the group boundaries or assignment rule, not proof that a particular clinical action is required.

Useful checks include verifying units and covariate definitions, confirming each row falls within the model's intended range, recalculating the dose-to-AUC arithmetic independently, and inspecting the predicted AUC at representative and boundary profiles. A discontinuous jump in dose at a group boundary can also be a warning that the categories are too coarse or that their rounded regimens need review. These checks do not replace evaluation of model fit, uncertainty, or clinical acceptability.

A table based on one representative profile is simpler than a table built from predictions across the full group, but it can hide within-group variation. A finer grid can represent covariates more closely, at the cost of more rows and possible complexity in use. A continuous formula can avoid abrupt category boundaries, but requires users to calculate doses and still needs practical rounding. A fixed dose-per-kilogram rule is simpler, but it will not necessarily reproduce a model that also includes age and kidney function. The choice is a balance of usability, model support, and acceptable predicted exposure variation.

Common pitfall: “The rounded dose is close to the target dose for the representative child, so everyone in that row will reach the target AUC.” This conclusion does not follow. Different clearances within the row produce different AUCs at the same dose; calculate or otherwise assess predictions across the group before treating one row as representative of all its members.

A model-based dose table is limited by the model's scope, the accuracy and interpretation of age, weight, and kidney-function measurements, and the chosen target and regimen assumptions. A population prediction is not an individual clearance estimate, and rounding agreement at a representative profile does not remove parameter uncertainty or unexplained variability. The table should be labeled as model-based, used only within its justified range, and reviewed for clinical suitability before use.

Check Your Understanding

Answer each question using the hypothetical model and assumptions in this tutorial. Concise solutions follow.

If predicted clearance is 2.5 L/h and the target AUC is 10 mg·h/L, what is the unrounded target dose?
For a target dose of 18.6 mg rounded to the nearest 2.5 mg, what dose is selected under the stated tie rule, and what is the percentage dose deviation?
Why can a dose that closely matches the target for a group's representative profile still produce substantially different AUCs elsewhere in the group?
For the stated model, which direction of change in age increases predicted clearance, holding weight and eGFR fixed?

Solutions. (1) \(Dose_{\text{target}}=10\times2.5=25\) mg. (2) The nearest 2.5 mg increment is 17.5 mg; the deviation is \(100(17.5/18.6-1)\approx-5.91\%\). (3) AUC at a fixed dose equals dose divided by clearance, and clearance varies with covariates within the group. (4) Decreasing age increases the age factor \(25/(AGE+24)\), and therefore increases predicted clearance when the other covariates are held fixed.