Why the Choice of Index Matters
A dose-selection target is only useful if its exposure measure represents the pharmacology that matters. AUC summarizes total concentration over a period, peak concentration describes the highest concentration, trough concentration describes the concentration immediately before a scheduled dose, and time above threshold describes how long concentration exceeds a specified level. These summaries can rank regimens differently, even when they are calculated from the same concentration-time profile.
The index should therefore be chosen from the exposure-response evidence and pharmacologic rationale, not because it is easiest to calculate or most familiar. An index associated with response in one set of regimens may be a proxy for another exposure feature that actually drives response. The objective is to select a summary that represents the relevant driver over the time window and at the site of action that matter.
The notation \(C(\tau^-)\) means the concentration just before the dose scheduled at time \(\tau\). This distinction matters: the concentration immediately after a dose may jump upward, so it is not the trough. AUC has units of concentration multiplied by time, peak and trough have concentration units, and time above threshold has time units. If the pharmacology depends on unbound drug, an active metabolite, or concentration at a target site, the index should be defined using that relevant concentration rather than automatically using total plasma concentration.
Assumptions and What the Indices Preserve
An index is interpretable only when its definition matches the comparison. Regimens should be assessed over comparable windows—for example, the same dosing interval at steady state if the target is a steady-state target. The threshold for a time-above-threshold index must be specified in the same concentration scale used for the profile. If the target is tied to a particular organism or patient characteristic, that context also belongs in the target definition.
Each index compresses a curve and therefore discards information. AUC preserves total integrated exposure but not its timing. A peak index preserves the maximum but not how quickly concentrations fall afterward. A trough preserves a single late-interval value but not necessarily the earlier profile. Time above threshold preserves duration above a specified level but does not distinguish, for example, a concentration just above the threshold from one far above it.
This identity says that AUC divided by the interval length is the average concentration over that interval. It does not imply that the average, peak, trough, and time above threshold are interchangeable. In particular, equal AUCs imply equal average concentrations only when the intervals are the same; they do not imply equal peaks, troughs, or durations above a threshold.
Worked Examples: Indices Can Rank Profiles Differently
Worked Example: Equal AUC, Different Peak and Time Above Threshold
Hypothetical data. Two regimens have concentrations in mg/L at the listed times in hours. Assume concentration changes linearly between adjacent times. Compare their AUCs, peaks, and time above a threshold of 10 mg/L.
| Time (h) | Regimen A (mg/L) | Regimen B (mg/L) |
|---|---|---|
| 0 | 0 | 0 |
| 2 | 20 | 8 |
| 6 | 8 | 15.2 |
| 12 | 0 | 0 |
For linear segments, the trapezoidal area is the interval width multiplied by the average of the endpoint concentrations. For regimen A:
For regimen B:
Both profiles therefore have the same AUC, 100 mg·h/L. Their peaks differ: \(C_{\max,A}=20\) mg/L and \(C_{\max,B}=15.2\) mg/L. For regimen A, the rising segment crosses 10 mg/L at 1 h. The segment from 2 to 6 h falls from 20 to 8 mg/L, a decrease of 3 mg/L per hour, so it crosses 10 mg/L at \(2+(20-10)/3=5.333\) h. Its time above threshold is \(5.333-1=4.333\) h.
For regimen B, the rising segment from 2 to 6 h crosses 10 mg/L after \((10-8)/(15.2-8)\times4=1.111\) h, at 3.111 h. The falling segment from 6 to 12 h crosses 10 mg/L after \((15.2-10)/15.2\times6=2.053\) h, at 8.053 h. Its time above threshold is \(8.053-3.111=4.942\) h. Thus the regimens have equal AUC but different peaks and different time above threshold. Which difference matters depends on the relevant pharmacology.
Matching an Index to the Pharmacologic Driver
Use the exposure-response evidence to decide which feature of the concentration profile is relevant. AUC is a natural candidate when the effect depends on cumulative exposure over a defined period. Peak concentration is relevant when the magnitude of the maximum concentration drives the effect or toxicity. Trough is useful when maintaining a minimum concentration near the end of each dosing interval is the key condition. Time above threshold is relevant when pharmacologic activity depends on remaining above a meaningful concentration for a sufficient duration.
These are not universal drug classes or automatic rules. The appropriate index depends on the drug, outcome, population, concentration measure, and time window. The evidence should support both the choice of index and the target value. A statistical association between an index and an outcome is informative, but does not on its own establish that index as the biological driver. For example, if AUC and peak are highly correlated across the regimens studied, either may appear associated with response. Evidence from regimens that separate those indices, together with pharmacologic knowledge, is more discriminating.
Worked Example: Choosing Time Above Threshold for a Hypothetical Drug
Hypothetical scenario. Suppose prior pharmacologic and exposure-response evidence for a drug indicates that antibacterial effect is related to the fraction of a dosing interval during which unbound concentration exceeds the organism's MIC. The MIC is 4 mg/L. Two simplified 24-hour profiles are assumed constant within each stated half-interval:
- Regimen X: unbound concentration is 10 mg/L for 12 h and 0 mg/L for 12 h.
- Regimen Y: unbound concentration is 5 mg/L throughout 24 h.
For regimen X, AUC is \((10\ \mathrm{mg/L})(12\ \mathrm{h})+(0\ \mathrm{mg/L})(12\ \mathrm{h})=120\ \mathrm{mg\cdot h/L}\). For regimen Y, AUC is \((5\ \mathrm{mg/L})(24\ \mathrm{h})=120\ \mathrm{mg\cdot h/L}\). The AUCs are equal. The peaks are 10 mg/L for X and 5 mg/L for Y.
Because the stated driver is time above the MIC, calculate that duration directly. Regimen X is above 4 mg/L for 12 h, so its time above MIC is \(12/24=0.50\), or 50% of the interval. Regimen Y is above 4 mg/L for 24 h, so its time above MIC is \(24/24=1.00\), or 100% of the interval. Under the scenario's stated pharmacologic evidence, time above MIC is the relevant index, and regimen Y has the more favorable profile on that index. Equal AUC does not erase this distinction.
The piecewise-constant profiles are a deliberately simplified illustration. Real profiles change continuously, and the threshold duration would be calculated from the full concentration-time curve. Also, if the evidence concerns unbound concentration, using total concentration instead could misclassify time above the MIC.
Worked Example: Using Trough When Sustained Concentration Is the Target
Hypothetical data. At steady state, two regimens are simulated over a 24-hour interval. Concentrations are in mg/L. Assume the curve is linear between listed points and decreases monotonically from the post-dose value to the pre-dose value. Prior evidence supports a minimum effective trough of 2 mg/L.
| Time (h) | Regimen A (mg/L) | Regimen B (mg/L) |
|---|---|---|
| 0, immediately after dose | 8.0 | 6.5 |
| 6 | 4.5 | 4.8 |
| 12 | 2.8 | 3.5 |
| 18 | 1.9 | 2.8 |
| 24, just before next dose | 1.5 | 2.4 |
Calculate AUC by summing the four trapezoids. For regimen A:
For regimen B:
The troughs are the pre-dose concentrations at 24 h: 1.5 mg/L for A and 2.4 mg/L for B. Regimen A is below the 2 mg/L trough target, whereas regimen B is above it. Given the stated evidence that maintaining a minimum concentration is important, trough is the directly relevant index. Regimen B meets that target in this hypothetical comparison, although it also has a larger AUC. These two simulated regimens alone cannot determine whether trough or AUC is the causal driver; the choice of trough here follows the stipulated pharmacologic evidence.
Diagnostics, Alternatives, and Limitations
Before using an index for dose selection, inspect whether it is calculated from the intended concentration profile and over the intended interval. AUC depends on the window: AUC over one dosing interval is not automatically interchangeable with AUC over a day or over the full treatment course. Peak and trough depend on dose timing and sampling resolution. A peak estimated from sparse samples may be missed, and an apparent trough taken after rather than just before a dose is not the pre-dose trough. Time above threshold can be especially sensitive to uncertainty in both the profile and the threshold when concentrations spend substantial time near the threshold.
In NLME simulation, individual differences in parameters can produce a range of profiles and index values. A population-average profile is not generally enough to characterize individual index values: calculating an index from an averaged curve can differ from averaging the individual indices. Preserve the intended level of analysis when summarizing simulated outcomes. Also check whether the same index is being compared across relevant covariates, dosing conditions, and sources of variability.
Common warning signs include:
- The selected index changes when the analysis window is shifted without a pharmacologic reason.
- Two candidate indices are strongly correlated in the available data, so the evidence does not distinguish their roles.
- A profile is poorly resolved around its peak, trough, or threshold crossing.
- The exposure measure uses total concentration even though the target is defined for unbound or target-site concentration.
- A threshold is treated as exact despite uncertainty in its biological basis or measurement.
The main alternative is not another universal index, but another summary chosen to represent a different exposure feature. AUC is often robust to moderate timing shifts but hides profile shape. Peak directly represents maximum intensity but is sensitive to brief fluctuations and sampling. Trough is simple to interpret for sustained exposure but ignores most of the interval. Time above threshold captures duration but requires a defensible threshold and adequate curve resolution.
| Index | Most relevant when | Information it omits |
|---|---|---|
| AUC over a specified window | Cumulative exposure is supported as the driver | Timing, peak, and trough profile shape |
| Peak concentration | The maximum concentration is linked to effect or toxicity | Duration at high concentration and total exposure |
| Pre-dose trough | Maintaining a minimum late-interval concentration matters | Concentration earlier in the interval and cumulative exposure |
| Time above threshold | Duration above a supported pharmacologic threshold matters | How far above threshold concentrations rise |
No index can repair a misspecified exposure-response relationship, an inappropriate concentration measure, or a mismatch between the simulated regimen and the intended dosing situation. If the evidence does not clearly separate candidate indices, report that limitation rather than presenting one as established. The index choice is a scientific modeling decision, not merely a computational one.
Common Mistake
Correction: Equal AUC means equal integrated concentration over the specified window, not equal concentration-time profiles or equal values of other indices. If effect depends on peak, trough, or time above a threshold, those features must be assessed directly and supported by the relevant pharmacologic evidence.
Check Your Understanding
Answer each question using the stated definitions and assumptions.
- What are the units of AUC if concentration is measured in mg/L and time in hours?
- Two profiles have equal AUC over the same interval. Must they have equal peaks? Explain.
- A drug's supported driver is time above a threshold of 3 mg/L. A simulated unbound concentration remains above 3 mg/L for 18 hours of a 24-hour interval. What fraction of the interval is above threshold?
- At a scheduled 12-hour dose, a concentration sample is taken immediately after administration. Is it the trough? Why or why not?
- If AUC and peak are highly correlated in the exposure-response data, what limitation should be considered when choosing between them?
Solutions. (1) mg·h/L, because AUC is concentration multiplied by time. (2) No. Equal integrals constrain total area but do not require equal maxima; profiles can differ in shape while having the same area. (3) \(18/24=0.75\), so the concentration is above threshold for 75% of the interval. (4) No. The trough is the concentration immediately before the scheduled dose; a post-dose sample may reflect the increase caused by that dose. (5) The data may not distinguish which index is the driver: either may appear associated because they vary together. Evidence from profiles that separate AUC and peak, as well as pharmacologic rationale, is needed.