Accuracy of methods for integrating overlapping chromatographic peaks: A systematic evaluation

The accurate integration of overlapping chromatographic peaks is essential for reliable quantification, especially in pharmaceutical Quality Control (QC). Despite long-recognized concerns about accuracy, the quantitative conditions under which different rule-based integration methods perform adequately have not been systematically mapped over a broad parameter space. To address this, six rule-based integration methods were evaluated using 40,000 simulated chromatograms containing two noise-free, symmetric Gaussian peaks with equal peak widths (σ₁ = σ₂) over broad ranges of peak resolution (R_s = 0.5 - 2.1) and peak area fraction (0.1 - 99.9%). Of these, the 35,465 chromatograms in which a valley was present between the peaks were integrated and analyzed. Within this parameter space, the results establish a clear performance hierarchy. The Valley-to-Valley method (V2V) showed the poorest performance, with errors exceeding 5% in 99.8% of the cases analyzed. The Perpendicular Drop Method (PDM) showed intermediate performance and systematically underestimated the minor peak, with the magnitude of the error increasing as resolution and minor-peak area fraction decreased. No single threshold governs its applicability; the boundary depends on the tolerated integration error. Within the investigated parameter space, the PDM minor-peak integration error remained within 1% when R_s ≥ 1.1 and the minor-peak area fraction was ≥ 30%. Tangential skim and exponential skim did not outperform PDM under the equal width Gaussian conditions investigated, whereas Gaussian skim was more accurate than PDM within a bounded region at low minor-peak fractions; this crossover depends on the specific implementation of Gaussian skim. Corresponding error maps are also provided in terms of the directly measurable peak height fraction and relative valley height for practical assessment of overlapping peaks. Among the six methods under the investigated conditions, the proposed Peak Height-Area method (PHA) showed the best overall accuracy, with errors ≤ 0.1% in 84.9% and ≤ 1% in 95.6% of the analyzed cases and the maximum error was 5.01%. These findings demonstrate that PHA performs very well for the specific case investigated here: two overlapping, noise-free, symmetric Gaussian peaks of equal width. They do not establish its general superiority for routine chromatographic quantification. Unequal peak widths, asymmetric or otherwise dissimilar peak shapes, noise and baseline drift, overloaded main peaks with narrow rider peaks, and groups of more than two overlapping peaks were not examined and require separate evaluation.