Reconstructing Response From Real-World Dosing Histories

Why Dosing History Matters

In routine care, a prescription describes intended dosing, not necessarily the doses a person takes. A missed dose can lower exposure, while a delayed dose can shift exposure later without removing the dose entirely. Those histories can produce different concentrations—and therefore different response predictions—even when the prescription is identical. Treating prescribed doses as if they were taken can obscure this distinction.

This case study uses a fully hypothetical dataset from people prescribed a 100 mg oral dose every 12 hours. Electronic package records provide dose timestamps, and concentration and response measurements are collected during follow-up. The goal is not to infer whether a person was adherent from response. It is to use the available dosing records to reconstruct exposure under stated PK assumptions, then compare that reconstruction with one based on the prescription.

Reconstructing Concentration From Dose Times

For a transparent illustration, assume each 100 mg dose is absorbed instantaneously and contributes 5 mg/L to concentration immediately after dosing. Concentration then declines by first-order elimination, with half-life 12 hours. This is a simplified one-compartment model; it is useful here for making the effect of dose timing explicit, not as a claim that oral absorption is instantaneous in practice.

Let \(t_j\) be the time of dose \(j\), measured in hours from the start of the observation window, and let \(C(t)\) be concentration in mg/L. For \(t\) at or after a dose, that dose’s contribution is its initial concentration multiplied by the fraction remaining after elapsed time \(t-t_j\). By superposition, the concentration from a history of doses is the sum of those contributions:

The factor 5 applies because each dose in this case is 100 mg. A dose not yet taken contributes nothing before its recorded time. For doses of different amounts, each contribution would be scaled in proportion to its dose under the same linear PK assumption.

A useful check follows by integrating each dose’s concentration contribution over a window from 0 to \(T\). For a dose taken at \(t_j<T\), its contribution over the window \([0,T]\) is integrated from \(\max(0,t_j)\) to \(T\):

The full AUC over the window is the sum of these dose-specific areas. This result follows because integration is additive: the integral of the sum of dose contributions equals the sum of their integrals. A dose at exactly \(T\) contributes zero area within \([0,T]\); for a trough prediction at \(T\), it is also important to specify whether the value is immediately before or after any dose scheduled at that time.

Case Comparison: Prescribed and Recorded Histories

R17’s prescription is 100 mg at hours 0, 12, 24, and 36. The electronic package record lists doses at hours 0, 16, and 30; the hour-12 dose was delayed to hour 16, the hour-24 dose was delayed to hour 30, and no hour-36 dose is recorded by the end of follow-up. For calculations over hours 0–36, compare the prescribed doses at hours 0, 12, and 24 with the recorded doses at hours 0, 16, and 30. The prescribed dose at hour 36 is at the window boundary and contributes no area before that time; endpoint concentrations below are explicitly pre-dose at hour 36.

For these assumptions, the prescribed-history AUC is:

The recorded-history AUC uses elapsed times of 36, 20, and 6 hours since the three recorded doses:

Under this model, the recorded-history AUC is about 12.8% lower than the prescribed-history AUC. This comparison is about the modeled exposure over this particular 36-hour window; it does not establish that the recorded doses were actually swallowed or explain why the records differ from the prescription.

Translating Exposure Into a Response Prediction

Suppose the hypothetical PD model relates concentration to a response score as follows. The score is measured in response points, \(E_0=2\) points is the baseline, \(E_{\max}=8\) points is the maximum increase above baseline, and \(EC_{50}=4\) mg/L is the concentration producing half of that maximum increase. For this illustration, the model is assumed to apply at the hour-36 assessment and the response is modeled as an increasing function of concentration:

Using the prescribed-history concentration gives:

Using the recorded-history concentration gives:

Thus, the recorded-history prediction is higher by approximately \(6.713-6.179=0.534\) response points at hour 36. These are conditional model predictions under the stated PK and PD assumptions, not observed response values and not evidence that the later dose caused a clinical improvement.

Assumptions, Diagnostics, and Alternatives

A reconstructed history is only as credible as its dose records and structural assumptions. In this example, the calculations assume that the recorded times represent doses taken, each dose has the same amount and bioavailability, the one-compartment elimination model is adequate, elimination is linear and time-invariant, and the individual half-life and concentration scale are known. The response calculation additionally assumes the stated concentration-response relationship applies at the assessment time. These assumptions should be stated before interpreting predictions.

Several checks can reveal problems. Confirm that timestamps are in the correct time zone, that duplicate records are not counted twice, and that dose amounts and units are consistent. Compare reconstructed concentrations with measured concentrations at recorded sampling times. For example, the hypothetical R17 measurements at hours 12, 24, and 36 can be compared with the model predictions at those same times, using the correct immediately-before or immediately-after dose convention. Systematic prediction errors, implausible concentrations, or residual patterns over time may indicate incorrect records, an unsuitable PK model, or unmodeled variability. A fit to a few concentrations alone cannot prove that every recorded dose was taken.

The prescribed-dose model is a useful benchmark when the question concerns intended regimen exposure or when reliable dose timestamps are unavailable. The actual-dose model is more directly aligned with recorded use, but its apparent precision can be misleading if the records are incomplete or do not verify ingestion. Other approaches include using directly observed concentration data to inform exposure, or analyzing plausible alternative histories when dose timing is uncertain. These approaches answer different questions: measured concentrations inform exposure at sampling times, while a dose-history model fills in the intervening trajectory under its PK assumptions.

When a timestamp is uncertain, it is better to represent that uncertainty than to silently assign a precise time. For instance, if a dose may have been taken between hours 14 and 18, predictions can be calculated across that range or under clearly defined timing scenarios. The resulting spread reflects uncertainty in the reconstructed exposure, not a confidence interval for the response unless a formal uncertainty analysis has been performed.

Common Pitfall

A related mistake is to treat an electronic record as definitive evidence of ingestion. Such records may document package opening rather than swallowing, and unrecorded doses may also occur. The correction is to describe the history as recorded, explain how it was interpreted, and assess how plausible alternative histories change the prediction.