Monitoring After Missed or Delayed Doses

Why the Dose History Matters

A concentration is a measurement at one time, not a summary of the entire dosing history. A result below a target may reflect reduced exposure after a missed dose, but it may also reflect a sample collected later than intended. A result above a target could follow an extra dose or a delayed dose taken shortly before sampling. Interpreting the number without asking which doses were taken, and when can lead to a mistaken conclusion about the patient's usual exposure.

The key distinction is between the prescribed regimen and the actual dose history. For interpretation, record the amount and time of each dose before the sample, along with the sample time. Then ask whether the concentration is plausible under that history. The calculations below use a deliberately simple model to make the timing effects visible; they are not a substitute for a drug-specific model or clinical judgment.

Model and assumptions: For illustration, suppose the drug follows a one-compartment model with linear elimination, a constant elimination rate constant $k$, and instantaneous systemic input. A dose $D_j$ given at time $t_j$ contributes $D_j/V$ to concentration at that time, where $V$ is the apparent volume of distribution. At a later sample time $t$, the concentration is the sum of the remaining contributions from all doses already given: $$ C(t)=\sum_{j:t_j\leq t}\frac{D_j}{V}e^{-k(t-t_j)}. $$ Here $C(t)$ is concentration, $D_j$ is dose amount, and $k=\ln(2)/t_{1/2}$, where $t_{1/2}$ is the elimination half-life. This model assumes doses are accurately recorded, pharmacokinetics are time-invariant and linear, and no unrecorded input or major change in disposition occurs. For an oral drug, absorption may take time, so instantaneous input is only an approximation when absorption is not important to the question.

The sum in the equation is important: at a sample time, the measured concentration can reflect several earlier doses, not just the most recent one. Under the model, a missed dose removes that dose's contribution. A delayed dose contributes later than expected, while an extra dose adds another contribution. A dose taken as prescribed but sampled at an unexpected time can also produce a different concentration than the intended sampling time.

Why Timing Changes the Concentration

For a single dose, the model gives $C(t)= (D/V)e^{-kt}$ after the dose. If the same sample is taken $\Delta t$ hours later, its predicted concentration is multiplied by $e^{-k\Delta t}$. Thus, even when no dose was missed or added, a timing error can change the measured value. With repeated doses, the same principle applies to each dose's contribution.

A useful reference case is repeated dosing every $\tau$ hours. At steady state, with dose size $D$, the concentration immediately after a dose is the sum of the current dose and the residual contributions from all previous doses. Let $r=e^{-k\tau}$, the fraction remaining after one dosing interval. For $0<r<1$, the postdose concentration is a geometric series:

C_{\text{post}}=\frac{D}{V}(1+r+r^2+\cdots)=\frac{D/V}{1-r}, \qquad C_{\text{trough}}=rC_{\text{post}}=\frac{D}{V}\frac{r}{1-r}.

The trough is the concentration just before the next scheduled dose. This reference is only appropriate if the patient is actually following the regimen and the system is at steady state. After a missed or delayed dose, the nominal steady-state trough is no longer the right prediction: use the actual dose times instead.

Worked Example: A Missed Dose Lowers the Next Trough

Hypothetical data. A patient receives a 100 mg dose every 12 hours. Assume $V=10$ L and a 12-hour half-life. Immediately before the dose due at time 0, the concentration is 10 mg/L. That dose is missed. Find the concentration just before the next scheduled dose at 12 hours, assuming no other doses are taken.

The elimination rate is $k=\ln(2)/12=0.05776\ \text{h}^{-1}$. Over 12 hours, the fraction remaining is $e^{-k(12)}=0.5$. With no new dose, the concentration at 12 hours is:

C(12)=10\ \text{mg/L}\times 0.5=5.00\ \text{mg/L}.

For comparison, under the regular regimen, a 100 mg dose contributes $100\ \text{mg}/10\ \text{L}=10\ \text{mg/L}$ immediately after dosing. The steady-state trough is $10\times 0.5/(1-0.5)=10$ mg/L. The missed dose therefore predicts a 5.00 mg/L concentration at this particular sampling time, rather than the 10 mg/L steady-state trough. This calculation does not establish the patient's average exposure over a longer period; it predicts the concentration at the stated time under the stated dose history.

Delayed Doses and Samples Taken at the Wrong Time

A delayed dose is not equivalent to a missed dose. It creates a period with no new dose contribution, followed by a later contribution. Consequently, a delayed dose can leave concentration lower than expected before it is taken and higher than expected soon after it is taken. The result depends on when the sample falls relative to both the scheduled and actual dose times.

Worked Example: A Delayed Dose Raises a Later Sample

Hypothetical data. Use the same 100 mg every-12-hour regimen, $V=10$ L, and 12-hour half-life. The concentration immediately before the dose due at time 0 is 10 mg/L. The dose is delayed until hour 8, and a sample is collected at hour 12, just before the next scheduled dose. Calculate the predicted concentration at hour 12 using the actual history.

The original 10 mg/L decays for 12 hours, leaving $10\times 0.5=5.00$ mg/L. The delayed dose contributes $100/10=10$ mg/L at hour 8, then decays for 4 hours. Its remaining fraction is $e^{-k(4)}=2^{-4/12}=0.7937$, so that contribution is $10\times0.7937=7.937$ mg/L. Add the two contributions:

C(12)=5.00+7.937=12.94\ \text{mg/L}.

If one incorrectly assumed a dose at time 0 and no delay, the expected steady-state trough would be 10 mg/L. The actual-history prediction is 12.94 mg/L because the delayed dose was taken only four hours before sampling. That higher sample does not mean the concentration was continuously high during the interval; the model predicts a different profile before the delayed dose.

A sample can also be mistimed even when every dose was taken correctly. The relevant comparison is between the actual sample time and the time intended by the monitoring plan. If a trough was intended, a sample taken before the next scheduled dose is not automatically a trough: it must be collected at the specified point relative to that dose.

Worked Example: An Early Sample Can Look Like a High Trough

Hypothetical data. A patient follows a 100 mg every-12-hour regimen with $V=10$ L and a 12-hour half-life. At steady state, the expected trough is 10 mg/L. The latest dose was taken on time, but the blood sample was collected 10 hours after that dose, two hours before the intended 12-hour trough. Predict the sample concentration.

The concentration immediately after the dose at time 0 is the steady-state trough plus the new dose contribution: $10+100/10=20$ mg/L. Ten hours later, the fraction remaining from that postdose concentration is $2^{-10/12}=0.5612$. Therefore:

C(10)=20\ \text{mg/L}\times 0.5612=11.22\ \text{mg/L}.

The predicted result is 11.22 mg/L, above the intended trough of 10 mg/L, even though the patient took the dose on schedule. The difference is explained by the sample being collected two hours early under this model. It would be incorrect to infer a sustained increase in exposure from this one mistimed sample.

Extra Doses and the Size of the Change

An extra dose adds to the contributions still present from earlier doses. Under linear pharmacokinetics, the added concentration at a later sample can be calculated separately and then added to the prediction without that dose. This does not mean every extra dose produces the same clinical effect: the magnitude and consequences depend on the drug, dose, timing, concentration, and patient. The arithmetic is a way to reconstruct a plausible profile, not a dosing recommendation.

Worked Example: An Extra Dose Adds a Residual Concentration

Hypothetical data. Just before a scheduled 100 mg dose at time 0, concentration is 10 mg/L. The patient takes the scheduled dose and an additional 100 mg dose at hour 4. A sample is collected at hour 8. Assume $V=10$ L and a 12-hour half-life. Compare the predicted concentration with and without the extra dose.

Without the extra dose, the starting 10 mg/L decays for 8 hours, and the scheduled dose contributes another 10 mg/L at time 0. Each contribution has the same remaining fraction, $2^{-8/12}=0.6300$. Thus the prediction without the extra dose is $(10+10)\times0.6300=12.60$ mg/L.

The extra dose contributes 10 mg/L at hour 4 and decays for 4 hours. Its fraction remaining is $2^{-4/12}=0.7937$, so its contribution at hour 8 is $10\times0.7937=7.937$ mg/L. Including it gives:

C(8)=12.60+7.937=20.54\ \text{mg/L}.

The model predicts a substantial increase at the sample time compared with the 12.60 mg/L prediction without the extra dose. In practice, an unexpected extra dose warrants drug-specific assessment; this calculation alone cannot determine toxicity or the appropriate next dose.

A Practical Interpretation Sequence

Before attributing an unexpected result to a lasting change in exposure, reconstruct the circumstances that generated it. A compact sequence helps keep dose deviations and sampling deviations separate.

Establish the intended comparison.
Identify whether the result is being compared with a trough, a postdose target, or another defined sampling time. Use the target and timing conventions established for that drug.

Write the actual history.
List the dose amounts and actual administration times before the sample. Mark doses that were missed, delayed, repeated, or taken at an uncertain time; do not silently substitute the prescribed schedule.

Check the sample time.
Calculate the elapsed time from the most relevant dose and compare it with the intended sampling time. A sample outside the intended window may not be comparable with the target.

Predict from the actual history.
When a suitable model is available, calculate the expected concentration from the actual dose times. Ask whether the observed result is directionally and quantitatively plausible under that history.

Decide what remains unexplained.
If the result does not fit the documented history, verify the records and consider other explanations, including model mismatch or a change in patient status. Avoid changing a regimen solely to make a mistimed result match a target.

What the Reconstruction Can and Cannot Show

The model clarifies why the timing pattern matters. A missed dose generally removes a contribution that would otherwise be present. A delayed dose shifts a contribution later in time. An extra dose adds a contribution. A mistimed sample changes the point on the concentration-time profile being observed. These explanations can produce similar single concentrations, so dose and sample timing are essential for distinguishing them.

The model has important limitations. Real concentration profiles may not follow instantaneous input or one-compartment elimination; absorption, distribution, metabolites, changing clearance, nonlinear kinetics, and uncertain dose records can all matter. The calculations also assume the stated dose was actually taken and that the relevant pharmacokinetic parameters are known. If those assumptions are doubtful, a drug-specific model or additional appropriately timed measurements may be needed. A single level cannot, by itself, establish a patient's usual exposure or prove adherence.

A common mistake is to compare every measured concentration with a steady-state target as though the patient had taken every dose on schedule and the sample had been collected at the intended time. That reasoning ignores the very history that determines the concentration. The correction is to interpret the value conditional on the actual dose and sample times first, then decide whether it is suitable for the intended monitoring decision. Do not advise a patient to “make up” a missed dose or alter the next dose based on these generic equations; follow the drug-specific instructions and clinical plan.

Check Your Understanding

Use the simple model in this tutorial where stated. Each situation is hypothetical.

A dose has a 10 mg/L concentration contribution when given. If the half-life is 8 hours, what contribution remains 8 hours later?
A 50 mg dose is missed. Under linear kinetics, what happens to the dose's predicted concentration contribution at later times compared with taking it on schedule?
A patient takes a dose four hours late and is sampled soon afterward. Why could the result be higher than the expected concentration for the nominal sampling time?
A trough sample is collected early, and the measured value is above the trough target. What timing information should be checked before concluding that exposure is persistently high?

Solutions. (1) One half-life has elapsed, so the remaining contribution is $10\times 0.5=5.00$ mg/L. (2) The missed dose contributes zero; relative to taking it, the predicted concentration is lower by the amount that dose would have contributed after elimination to the sample time. (3) The delayed dose has had less time to be eliminated before sampling than a dose taken at the nominal time, so more of its contribution may remain. (4) Check the actual dose time, actual sample time, and elapsed time between them, and compare these with the intended trough timing. A concentration collected early may be above the true trough even when dosing was on schedule.