Interpreting AUC, Peak, Trough, and Time-Above-Target Metrics

Why One Concentration Summary Is Not Enough

A concentration–time profile contains several kinds of information. Its overall area describes cumulative exposure over a specified interval; its highest and lowest concentrations describe extremes; and the duration above a target describes how long concentrations satisfy a particular threshold. These summaries answer different questions. A regimen can have the same AUC as another regimen yet have a higher peak, a lower trough, or less time above a target.

These metrics are meaningful only when the interval, concentration scale, and threshold are clear. For a repeated regimen, a common interval is one dosing interval of length \(\tau\), often considered at steady state. When comparing schedules, the concentration profiles should refer to comparable intervals and conditions. A metric summarizes the profile; by itself, it does not establish that a regimen is clinically effective, safe, or optimal.

What Each Metric Describes

AUC summarizes total concentration exposure across the selected interval. For example, if concentration is measured in mg/L and time in hours, AUC is reported in mg·h/L. Dividing by the interval length gives the average concentration over that interval, \(C_{\mathrm{avg}}=\mathrm{AUC}/\tau\). AUC does not reveal when exposure occurred or how sharply it varied.

Peak concentration describes the maximum value of \(C(t)\), often written \(C_{\max}\). When the profile is continuous, the peak occurs at a time \(t_{\max}\). With bolus dosing, concentration may jump at administration, so the convention should make clear that the post-dose value is included. Peak concentration may be relevant when high concentrations are associated with toxicity, but its interpretation depends on the drug and clinical context.

Trough concentration describes the minimum over a specified interval, or, in common therapeutic drug monitoring language, the concentration just before the next dose. These definitions coincide for many declining profiles between doses, but they need not coincide if a profile has multiple local minima or if the interval includes an unusual infusion or dose event. For repeated bolus dosing, it is often useful to denote the pre-dose trough as \(C(\tau^-)\), distinguishing it from a post-dose concentration at the interval boundary.

Time above target (sometimes expressed as a fraction of the interval) measures how long concentrations exceed a specified threshold. The threshold is not inferred from the profile: it must be supplied and justified for the application. The strict definition uses \(C(t)>C_{\mathrm{target}}\). If a decision instead treats equality as meeting the target, use \(C(t)\geq C_{\mathrm{target}}\) and say so. For a profile that only touches the threshold at isolated times, the strict and inclusive definitions give the same duration; for a profile that stays exactly at the threshold over a nonzero interval, they differ.

Calculating Metrics From Sampled Profiles

A concentration profile is often available only at discrete sampling times. With values \(C_i=C(t_i)\), a standard approximation to AUC is the linear trapezoidal rule:

This formula treats concentration as changing linearly between adjacent observations. To estimate time above target under the same assumption, identify each segment that crosses the target, interpolate its crossing time, and add the durations of the portions above target. If both endpoints are above the target, the full segment contributes; if both are below, none contributes, unless the assumed within-segment shape allows an unobserved crossing. That qualification matters: two below-target samples do not rule out an intervening peak in the true profile.

Why the Metrics Can Give Different Impressions

The distinction among these summaries follows directly from what each calculation retains. AUC integrates concentration over time, so it depends on the total area. Peak and trough depend only on the maximum and minimum. Time above target depends on where the profile lies relative to a threshold. Consequently, knowing one metric generally does not determine the others.

For example, consider two hypothetical 12-hour profiles. Profile A is triangular: it rises linearly from 0 mg/L at time 0 to 12 mg/L at 6 hours, then falls linearly to 0 mg/L at 12 hours. Profile B stays constant at 6 mg/L for all 12 hours. Both have AUC \(72\) mg·h/L: Profile A has triangular area \((12)(12)/2=72\), and Profile B has rectangular area \((6)(12)=72\). Yet their peaks and troughs differ: A has peak 12 and trough 0 mg/L, while B has peak and trough 6 mg/L. With a target of 5 mg/L, A crosses upward at 2.5 hours and downward at 9.5 hours, so it is above target for 7 hours. B is above target for all 12 hours. Equal AUC therefore does not mean equal time above target or equal profile shape.

The metrics are complementary rather than competing versions of the same summary. AUC is useful when total exposure is of interest. Peak and trough make the extremes explicit. Time above target is useful when duration above a defined concentration matters. Reporting more than one can prevent an important profile feature from being obscured by a single summary.

Assumptions, Diagnostics, and Common Pitfalls

Before interpreting a calculated value, check that the interval represents the question being asked. For a recurring regimen, a single interval at steady state may be appropriate; a first-dose interval or a loading-dose interval can have a different profile and should not be treated as interchangeable. Confirm concentration and time units, the target value and its units, whether the target is strict or inclusive, and whether the trough means the interval minimum or specifically the pre-dose value.

Inspect the sampling times relative to expected changes in concentration. Sparse sampling near a rapid rise or fall may miss the actual peak, shift an estimated crossing time, and distort AUC. A computed maximum among observations is not automatically the true \(C_{\max}\). AUC based on trapezoids is an approximation whose reliability depends on the sampling density and the adequacy of linear interpolation. If a profile is generated by a pharmacokinetic model, the model’s predicted continuous profile can support more direct integration, but uncertainty in the model and its inputs still matters.

Common mistake: “The two schedules have the same AUC, so they provide the same concentration control.” This reasoning confuses cumulative exposure with profile shape. Equal AUC implies equal interval-average concentration when the intervals have equal length; it does not imply equal peak, trough, or time above target. The correction is to calculate and report the metric that corresponds to the clinical question, using the same interval and explicit threshold conventions for each schedule.

Another pitfall is to report time above target without stating how it was obtained. A value calculated from a dense model-predicted curve and a value estimated by linear interpolation between a few samples have different evidential bases. State the method and its assumptions so the precision of the reported duration is not overstated.

Comparison and Limitations

No one metric is universally sufficient. AUC ignores the timing and distribution of exposure; peak and trough reduce the profile to extremes; and time above target depends on a threshold that may not capture the full exposure-response relationship. Measurement error, model misspecification, unobserved concentration changes, and uncertainty in the clinically relevant target can affect all four interpretations. These are descriptive summaries of a specified profile, not guarantees about an individual’s response.