Missed Doses And Interrupted Infusions

Why the Administration Record Is Part of the Model

A concentration–time model needs an account of when drug entered the patient, not merely the regimen that was prescribed. A missed dose changes the input to the body; an interrupted infusion changes both the amount delivered and its timing. If the model is given the intended schedule instead of the best-supported actual history, it may attribute a concentration discrepancy to pharmacokinetics. For example, underestimating delivered dose can make a fitted clearance appear too large.

The task is therefore to reconstruct an administration history from available records, translate it into model input, and fit the concentration observations against that input. “Actual” here means the best-supported delivered history, not necessarily a perfectly observed one: pump logs can be incomplete, clocks can disagree, and a record of a scheduled dose does not establish that it was taken.

Representing the Delivered History

For a one-compartment model with linear elimination, let \(A(t)\) be the amount of drug in the body, \(C(t)=A(t)/V\) the concentration, \(V\) the apparent volume of distribution, and \(CL\) the clearance. A bolus dose \(D_j\) at time \(t_j\) adds \(D_j\) to the amount. Between boluses, a time-varying infusion rate \(R(t)\), in mass per time, enters the model as an input. The elimination rate is \(CL\,C(t)\).

Here \(R(t)\) is zero while an infusion is stopped. For a constant infusion rate \(R\) from time \(t_0\) to \(t_1\), with no bolus in that interval, the concentration at \(t_1\) is \(C(t_1)=C(t_0)e^{-k(t_1-t_0)}+\frac{R}{CL}(1-e^{-k(t_1-t_0)})\). After the infusion stops, the input term is zero and concentration declines according to elimination. Multiple infusion segments and boluses can be combined by applying the model over each interval and adding the bolus at its recorded time.

A practical reconstruction begins with an event table: one row per dose, start, stop, restart, or relevant correction. Retain the planned time and amount as separate fields from actual start and stop times, delivered amount, and the source of the record. Convert all times to a common reference and units before fitting. For an infusion with constant rate, the delivered amount over an uninterrupted segment is rate multiplied by duration; if the rate changes, calculate and sum the segment amounts. Do not count both a pump-delivered amount and a manually recorded total as separate doses.

The model should use the most defensible record for each event. A missed dose should be represented as absent input, not as a dose given later unless a later administration is documented. Likewise, a recorded interruption should create a zero-input interval; it should not be smoothed into a lower constant rate unless that is a deliberate approximation supported by the record.

Deriving the Exposure Consequence

For a linear model, the link between delivered dose, clearance, and total exposure follows from the amount balance. Integrate the amount equation over a time interval from 0 to \(T\), including any bolus jumps in the interval. Take \(A(0)\) just before any bolus at 0 and \(A(T)\) just after any bolus at \(T\). Since \(A(t)=V C(t)\), the change in body amount equals total input minus eliminated amount.

If the interval captures all relevant input and the drug is followed until the amount returns to its starting amount (in particular, both are zero for a single dose followed to completion), then \(A(T)-A(0)=0\). Writing total delivered dose as \(D_{\mathrm{delivered}}=\int_0^T R(t)\,dt+\sum_{j:\,0\le t_j\le T}D_j\), where the sum is over boluses in the interval, the area under the concentration curve is \(AUC_{0-T}=D_{\mathrm{delivered}}/CL\). At periodic steady state, the same balance applies over a dosing interval because the amount at the end equals the amount at the start; the input is the delivered dose in that interval. The result assumes linear elimination and a correctly defined interval. For a finite interval with unequal starting and ending amounts, the amount-change term must not be ignored.

This identity gives a useful exposure-level check on a reconstructed dose. If measured concentration data support an AUC and the model assumes a dose larger than the amount actually delivered, clearance may be overestimated. Conversely, entering too little dose can lead to an underestimated clearance. With sparse observations and a dynamic fit, the exact bias also depends on sample timing, which parameters are estimated, and the model structure; the simple dose-to-AUC ratio is not a universal formula for every fit.

Quantifying Dose-History Bias in Exposure

Fitting, Diagnostics, and Alternatives

Once the event history has been reconstructed, fit the concentration data using the appropriate input function and the usual observation model for the analysis. The dose and infusion records determine model input; they do not by themselves establish the structural PK model, residual error model, or which parameters can be identified. State which events are observed, which are uncertain, and which parameters are fixed or estimated. In particular, a sparse profile may not separate clearance, volume, and dose-history uncertainty.

Several checks help reveal a bad reconstruction or an unsuitable input representation:

• Check chronology and units. Verify that start times precede stop times, interruptions do not overlap active infusion segments, and recorded rates multiplied by duration agree with delivered amounts. Resolve clock offsets before interpreting discrepancies.
• Compare independent records. Reconcile pump logs, medication-administration records, and source notes. Treat a scheduled dose as planned input unless there is evidence it was administered.
• Inspect residuals by event time. If predictions depart systematically after an interruption or missed dose, the input history may be wrong. A systematic pattern can also indicate model misspecification, so it is a diagnostic signal rather than proof of an administration error.
• Check plausible parameter shifts. Large changes in clearance when a single uncertain event is toggled suggest that the data do not robustly distinguish PK from dose history. Report that sensitivity rather than selecting the preferred result solely because it gives a better-looking parameter.
• Check exposure boundaries. Confirm that the AUC interval accounts for residual drug at its beginning and remaining drug at its end. Applying dose/AUC to a truncated profile without an appropriate amount-balance adjustment can misstate clearance.

The preferred approach is to use documented delivery times and amounts directly when those records are credible. If timing is uncertain, fit plausible alternative histories as sensitivity analyses and compare concentration predictions, clearance, and exposure. A latent-adherence or joint model can represent uncertainty probabilistically, but it requires defensible assumptions and enough information to distinguish adherence from PK variation. Excluding affected observations or participants is simpler, but can discard useful data and may select a nonrepresentative subset. Using the prescribed schedule for every patient is not a neutral alternative: it can systematically misattribute input errors to PK parameters.

Reconstructed histories matter whenever a model is used to estimate individual parameters, describe exposure, or project a regimen. A biased clearance estimate can distort exposure predictions even when the model fits the observed concentrations. Keeping prescribed and delivered histories distinct makes the source of that bias visible and supports transparent sensitivity analysis when records are incomplete.