Direct comparison
Trapezoidal AUC: Linear vs Log-Linear
Linear vs log-linear trapezoidal AUC in noncompartmental PK analysis: when each rule applies, the formulas, and why linear-up/log-down combines both.
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How do Linear trapezoidal, Log-linear trapezoidal compare side by side?
The table below compares Linear trapezoidal, Log-linear trapezoidal across 9 procurement-relevant dimensions, from interpolation between two points through typical nca software default.
Side-by-side comparison
| Dimension | Linear trapezoidal | Log-linear trapezoidal |
|---|---|---|
| Interpolation between two points | Straight line between (t1, C1) and (t2, C2) | Exponential curve (constant proportional decline per unit time) between the two points |
| Formula | AUC = (C1 + C2) / 2 x (t2 - t1) | AUC = (C1 - C2) / (ln C1 - ln C2) x (t2 - t1) |
| Underlying assumption | Concentration changes at a constant absolute rate between the two points | Concentration changes at a constant proportional (first-order) rate between the two points |
| Best-fit phase | Absorption / rising phase, and any segment where concentration is flat or increasing | Elimination / declining phase, where first-order elimination kinetics typically hold |
| Mathematical requirement | None -- works for any C1, C2 >= 0 | C1 > C2 > 0; undefined if either value is zero, or if C2 >= C1 |
| Bias if misapplied | Overestimates AUC across a declining, curving segment -- the straight-line trapezoid sits above the true concave exponential curve | Undefined if applied across a rising segment or a zero/BLQ concentration; cannot be used there at all |
| Handling a zero or BLQ concentration | Computable directly -- no restriction on zero values | Not computable -- the segment falls back to the linear rule instead |
| Role in the linear-up/log-down method | Applied to every segment where C2 >= C1 (rising or unchanged) | Applied to every segment where C2 < C1 and both concentrations are positive (declining) |
| Typical NCA software default | Available as an explicit "linear-only" method, but rarely the default across a full profile | Rarely used alone; linear-up/log-down (combining both) is the usual software default, not pure log-linear |
Common questions
Common questions about Linear trapezoidal vs Log-linear trapezoidal
What is the "linear-up/log-down" method, and why is it the default in most NCA software?
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It computes AUC segment by segment across a concentration-time profile, applying the linear trapezoidal rule wherever concentration is rising or unchanged between two consecutive sampling points, and the log-linear trapezoidal rule wherever it is strictly declining with both values positive. Because absorption is not well described by a single exponential while elimination usually is, this hybrid tracks the true underlying pharmacokinetic behavior more closely than using either rule alone across an entire profile -- which is why it is the standard default in noncompartmental analysis software such as Phoenix WinNonlin and PKNCA, and the method most commonly reported in FDA/ICH-facing NCA outputs.
Can the log-linear trapezoidal rule be used on a rising concentration segment?
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No, it should not be. The formula requires C1 > C2 > 0; on a rising segment (C2 >= C1) the denominator (ln C1 - ln C2) is undefined or non-sensical. Rising segments are handled by the linear rule instead, which is exactly why the hybrid linear-up/log-down method exists rather than one rule being used throughout an entire profile.
What happens when a concentration value is zero or below the limit of quantification (BLQ)?
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The log-linear rule is undefined at zero, since it requires taking a logarithm of the concentration. Standard NCA convention falls back to the linear trapezoidal rule for any segment touching a zero or BLQ-substituted value, rather than attempting a log-linear calculation across it.
Does the choice of method meaningfully change the calculated AUC in practice?
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It can, particularly for a compound with a rapid, clearly exponential decline and sparse sampling around Cmax and in the terminal phase -- the linear rule systematically overestimates AUC across such segments because the trapezoid sits above the true concave exponential curve. With dense sampling the two methods converge, since the gap between the curve and either trapezoid shrinks. The difference is largest exactly where it matters most: long, widely spaced terminal-phase intervals.
Which method should be reported in an NCA analysis for a regulatory submission?
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Linear-up/log-down is the de facto standard and the one most reviewers expect to see, but the method used should always be stated explicitly in the PK analysis plan and report, since a mismatch in reported AUC can arise between labs or software using different rules. This is a methodology-transparency requirement, not a single formula mandated by ICH/FDA guidance -- the expectation is a clearly stated, consistent method, not one specific universally required rule.
Going deeper
