Noncompartmental analysis
Summarize single-dose exposure without fitting a full compartmental concentration model.
Concepts and reasoning
Summarizing exposure without a compartment model
Noncompartmental analysis, NCA, summarizes a concentration–time profile using areas and other observed features. It does not require fitting a complete system of distribution compartments. That flexibility does not make it assumption-free: interpolation between samples and extrapolation beyond them still need justification.
The maximum observed concentration, Cmax, and its observation time, Tmax, depend on the sampling schedule. A sparse schedule can miss the true peak. AUC from the first observation to the last quantifiable observation measures observed exposure, subject to the chosen interpolation rule.
AUC to infinity adds an estimated tail after the last observation. That calculation assumes the selected terminal segment represents a log-linear decline that continues into the future. The terminal phase must be identified from the profile and pharmacology; simply choosing the final few numbers is not always valid.
Observed area and modeled tail
The linear trapezoid joins two concentrations with a straight line. For a decreasing positive segment, a logarithmic trapezoid instead assumes an exponential decline between the observations. A linear-up/log-down convention uses linear interpolation on rising segments and log interpolation on falling ones.
These choices matter when samples are widely separated. The PKNCA AUC documentation explains calculation rules and their intended use. NCA is most credible when the sampling design captures the peak, distribution, and terminal portions needed for the intended summaries.
Mathematical foundations
The core calculations
For adjacent times separated by Δt, the linear trapezoid is
When C₁ and C₂ are positive and unequal, log interpolation gives
At equal positive concentrations, the limiting result is C₁Δt. Zero concentrations cannot be inserted into a logarithm without a justified handling rule.
Fit a terminal line log C(t) = a − λz t to appropriate positive terminal observations. Then
The extrapolated percentage is 100 × (Clast/λz)/AUC∞. A small or poorly estimated λz can make the tail large and unstable.
For an intravenous dose, clearance is dose/AUC∞ under the relevant linear pharmacokinetic assumptions. For an extravascular dose, that ratio estimates CL/F, where F is bioavailability. Without independent information on F, clearance and bioavailability cannot be separated.
Worked example
Worked example: interpolation and extrapolation
Suppose concentrations decline from 10 to 5 mg/L over two hours. Linear interpolation gives an area of 2 × (10 + 5)/2 = 15 mg·h/L. Log interpolation gives 2 × 5/log 2 = 14.427 mg·h/L. The difference reflects an assumption about the path between measurements.
For a separate illustrative complete profile, suppose the summed observed AUC is 80 mg·h/L, the last concentration is 2 mg/L, and the estimated terminal rate is 0.1 per hour. Then:
| Quantity | Calculation | Value |
|---|---|---|
| Terminal half-life | log 2 / 0.1 | 6.931 h |
| Extrapolated AUC | 2 / 0.1 | 20.000 mg·h/L |
| AUC to infinity | 80 + 20 | 100.000 mg·h/L |
| Extrapolated fraction | 20 / 100 | 20% |
For an intravenous dose of 100 mg, clearance is 100/100 = 1 L/h. For the same oral dose and AUC, the identifiable ratio is CL/F = 1 L/h. If F were independently known to be 0.5, clearance would be 0.5 L/h; the oral profile alone does not establish that value.
If the estimated terminal rate were 0.05 rather than 0.1, the tail would double to 40 and AUC∞ would become 120. This shows why terminal-point selection deserves direct inspection rather than relying only on the final exposure table.
These are teaching calculations with hypothetical profiles. They do not establish an acceptable extrapolated fraction for every product or study objective.
Interpreting the results
Separate observed exposure from extrapolated exposure
Area under the concentration–time curve to the last sample summarizes measured exposure over that sampling interval. Area extrapolated to infinity adds a terminal tail estimated from the last concentration and terminal elimination slope. The latter is more dependent on assumptions about late behavior.
Cmax and Tmax are the largest observed concentration and its sampling time; the true peak may occur between samples. Terminal half-life reflects the fitted late log-linear phase and need not describe early distribution or absorption. A long half-life can coexist with limited measured exposure if sampling ends too early.
Clearance calculated after an extravascular dose is apparent clearance, CL/F, unless bioavailability F is known. Similarly, a terminal volume divided by F is not a directly observed anatomical volume. Report units, route, integration method, selected terminal points, and the extrapolated fraction with the parameter estimates.
Assumptions and limitations
Model independence has limits
Noncompartmental analysis avoids fitting a full compartmental curve, but still requires assumptions about interpolation, terminal behavior, dose, and sampling. A log-linear terminal slope must describe the actual terminal phase rather than absorption or an earlier distribution phase.
Sampling should adequately cover the peak and late decline. Concentrations below quantification and missing samples require a prespecified handling strategy; substituting zero or a detection limit changes both integration and terminal fitting. An observed curve assembled from different individuals does not automatically support the same interpretation as a densely sampled individual profile.
Dose and concentration units must be compatible for clearance and volume. Extravascular mean residence time includes absorption contributions, and terminal slopes may reflect absorption-limited kinetics. Repeated dosing, infusions, and steady-state intervals introduce additional choices beyond a simple single-dose profile.
Diagnostics and sensitivity analysis
Inspect the terminal phase visually and numerically
Plot concentration against time on ordinary and logarithmic scales and examine which points define the terminal line. A high adjusted R squared is not sufficient if those points belong to the wrong phase. Compare defensible terminal windows and record how half-life and extrapolated exposure change.
Check the fraction of total exposure attributed to the unobserved tail. A large fraction makes total exposure and derived clearance sensitive to small slope changes. Verify the integration over one interval manually, especially when the method changes between rising and declining concentrations.
Review sampling around the observed peak, unit conversions, and below-quantification handling. Do not select terminal points only to obtain a desired half-life. PKNCA's methodological documentation provides references on integration, terminal estimation, and calculation choices.
References and other material
Read the methodological references and supporting tutorials below. The examples in this lesson are original teaching calculations, not findings from these sources.
- PKNCA: noncompartmental analysis documentation — Free worked NCA articles, terminology and calculation references.