Trapezoidal AUC integrates a paired (X, Y) curve, useful for any cumulative-effect curve such as concentration against time or dose against response.
The trapezoid rule approximates the integral ∫ y dx by summing trapezoidal areas between consecutive (x, y) points. Standard for AUC₀₋∞ in pharmacokinetics (drug concentration vs time), dose-response cumulative effect, and any other cumulative-area readout.
Linear-trapezoid uses straight-line interpolation between points; log-linear-trapezoid uses log-interpolation on the descending phase, which is more accurate when the underlying decay is exponential (typical for plasma drug clearance).
Pair-resampling bootstrap CIs on AUC respect the (x, y) pairing — resample paired observations, recompute the AUC, repeat. The percentile CI is the standard non-parametric uncertainty interval.
Numeric X + Y + method (linear / log-linear) + optional bootstrap reps.
AUC + pair-resampling 95% bootstrap percentile CI.
The trapezoid rule under-estimates the area for concave-up curves and over-estimates for concave-down — but the bias is small with closely-spaced sampling.