Peak-Trough Tradeoffs in Regimen Design

Why Average Exposure May Not Be Enough

Two dosing regimens can deliver the same amount of drug per unit time and therefore have the same average concentration at steady state, yet produce different concentration-time profiles. A longer interval with a larger dose generally creates a higher peak and a lower trough than a shorter interval with a smaller dose. The practical importance depends on how the concentration profile relates to the drug’s effects: efficacy may depend on maintaining concentrations above a minimum, while toxicity may rise when concentrations exceed a peak-related threshold.

The relevant comparison is not simply “higher” versus “lower” exposure. It is whether the concentration feature that matters for the clinical objective—such as average concentration, peak, trough, or time above a target—differs enough to affect the decision. The calculations below use a deliberately simple pharmacokinetic model to make that comparison explicit.

A Simple Model for Peak-Trough Comparisons

Assume repeated intravenous bolus doses of amount \(D\), administered every \(\tau\) hours, in a one-compartment model with volume of distribution \(V\), clearance \(CL\), and first-order elimination rate constant \(k=CL/V\). Assume linear, time-invariant pharmacokinetics, constant parameters, and that steady state has been reached. Concentration declines exponentially between boluses. This model has an abrupt concentration jump at each dose; it is useful for deriving the tradeoff, but does not represent every route or formulation.

At steady state, let \(C_{\max,ss}\) denote the concentration just after a dose. During the interval it falls to \(C_{\max,ss}e^{-k\tau}\), the trough. The concentration just after the next dose equals the residual concentration plus the new dose increment \(D/V\). Thus,

The average concentration over one steady-state interval follows from the interval area. Under linear pharmacokinetics, the area under the concentration-time curve over that interval is \(D/CL\); dividing by \(\tau\) gives the average. Set \(x=k\tau\), a dimensionless measure of the interval relative to the elimination time scale. Since \(CL=Vk\), the peak and trough can also be written in terms of the average:

For a fixed \(C_{\mathrm{avg},ss}\), increasing \(\tau\) increases \(x\), raising the peak relative to the average and lowering the trough relative to the average. In the limit of a very short interval, both ratios approach 1, so the profile becomes flatter in this model. The required dose per administration changes with interval: \(D=C_{\mathrm{avg},ss}CL\tau\). Equal average concentration therefore does not mean equal dose at each administration, although these regimens have the same average dose rate.

Connect the Profile to the Clinical Objective

A peak-trough comparison matters when the exposure-response relationship is sensitive to features other than average concentration. The decision rule must therefore specify which concentration feature is linked to the objective and how that feature is translated into a target or constraint. A trough-based efficacy target, for example, is not interchangeable with an average-concentration target.

For illustration, suppose efficacy requires the steady-state trough to be at least 5.00 mg/L and a peak-related toxicity constraint requires the peak to be no greater than 16.0 mg/L. These are hypothetical, deterministic thresholds for comparing the two regimens above. They do not include uncertainty or variation between patients.

Another useful quantity is the fraction of an interval spent above an efficacy threshold. Under exponential decline after a bolus, the time above a threshold \(C_{\mathrm{thr}}\), when the peak is above it and the trough below it, is \(\ln(C_{\max,ss}/C_{\mathrm{thr}})/k\). This gives a direct comparison for an effect assumed to require concentrations above that threshold.

Choosing the Right Summary and Checking the Model

The primary alternative to a peak-trough comparison is to compare average exposure, often represented by interval AUC or average concentration. That can be appropriate when the response is adequately described by average exposure. For example, if instantaneous effect is linear in concentration, \(E(t)=aC(t)\) for a constant \(a\), then its interval average is \(aC_{\mathrm{avg},ss}\); profiles with the same average concentration have the same average effect under that specific model. If effect is nonlinear in concentration, or depends on a threshold, a peak, or a trough, equality of average concentration alone does not guarantee equal average effect.

The full concentration-time profile is more informative than any single summary, but it also requires a suitable exposure-response model to connect concentrations to clinical outcomes. Peak and trough are practical summaries when their relevance is supported by pharmacology or clinical evidence; they should not be selected simply because they are easy to calculate. A regimen should be assessed against the exposure feature linked to the decision objective.

Before interpreting a peak-trough calculation, check whether its assumptions are credible. The one-compartment bolus model may be a poor approximation if absorption is gradual, distribution phases are important, clearance changes with concentration or time, or the drug has active metabolites. Oral absorption can delay and smooth the peak; an infusion produces a different profile. If steady state has not been reached, the steady-state equations do not describe the observed interval. A delayed or hysteretic concentration-effect relationship can also make the concentration at a particular time a poor proxy for effect at that time.

Diagnostics should focus on the parts of the profile that drive the conclusion. Compare predicted and observed concentrations around the expected peak and immediately before the next dose; verify dose and sample timing; and assess whether the model captures the decline across the interval. Sparse samples that miss the peak cannot directly confirm a peak prediction. A predicted trough close to a target also warrants caution because small errors in timing or model parameters may change whether the target appears to be met. These checks evaluate the regimen comparison under the assumed model; they do not replace clinical justification of the target.

Limits of the Comparison

Peak-trough calculations describe a modeled concentration profile, not a complete clinical decision. They do not by themselves establish the exposure-response relationship, the clinical meaning of a threshold, or the acceptability of a regimen. Nor does a favorable result for one patient-level profile establish that the regimen will meet a target across a population. Those conclusions require additional evidence and analyses.

For this tutorial’s model, the most direct comparison is between regimens with the same average concentration and different intervals. In practice, formulation, route, adherence, tolerability, and the ability to administer the regimen also matter. The key conclusion is narrower: when pharmacologic effects depend on concentration peaks or troughs, matching average exposure is not sufficient to establish that two regimens are equivalent.