Single Multipoint Calibration Curve for Discovery Bioanalysis

Compensation for divergence during an analytical batch is a primary motive for including duplicate calibration curves that bracket the unknown samples being measured. The drawback is that this adds time to the analysis. A single calibration curve run with staggered calibrants bracketing the unknowns was compared to running complete duplicate calibration curves, one at the beginning and one at the end of unknown sample analysis in an effort to accelerate discovery bioanalysis. The data, in terms of correlation coefficient (r²) and the weighted residuals plot, show that a single calibration curve, with staggered calibrants bracketing the unknown samples, can be used successfully to accelerate discovery (nonregulated) bioanalysis.

Designing a robust and reproducible generic liquid chromatography–tandem mass spectrometry (LC–MS-MS) method that can support discovery (nonregulated) bioanalysis of different molecules on a daily basis requires balancing scientific rigor with adequacy. Data integrity remains the critical objective. The only assumptions made in the discovery environment are in regard to extraction efficiency, stability, and response function. In essence, the generic method has to be good, or "adequate," enough such that reliable information can be quickly returned to facilitate the decision making process.

The minimum acceptance criteria are a measure of systematic bias, or accuracy, and a measure of random error, or precision, the combination of which is a measure of total assay error (1). In addition to these requirements, reproducibility, sensitivity, and selectivity are the other key factors needed to cover the typical 1–10,000 ng/mL range commonly required in discovery pharmacokinetic (PK) bioanalysis. These factors are constrained by typical chromatographic run times of 2 min or less and a minimal sample cleanup step that is usually protein precipitation–based for in-vivo applications. All of this adds to the challenge of developing robust generic LC–MS-MS methods.

The Calibration Curve — Regression Analysis Considerations

The main role of LC–MS-MS bioanalysis PK studies is to provide drug concentration data for an accurate indication of the new chemical entity (NCE) exposure time profiles. The standard curve serves as a reference line against which the concentrations of the unknown samples are calculated. The standard curve itself is a result of regression analysis that takes into consideration the mean values of all x (concentration) and Y (area ratio) and the line of best fit through each data point to attempt to account for random error.

The most important consideration for bioanalysis spanning a broad range (1–10,000 ng/mL) is the choice of weighting factor. This is because LC–MS-MS bioanalytical data in almost all cases is heteroscadastic, a statistical term used for data in which the standard deviation changes within the range of measurements. In other words, the error is more or less proportional to concentration, and without proper weighting, the regression is inherently biased by the highest concentration (2). This is especially relevant in discovery bioanalysis where the high point on the curve can be as great as four orders of magnitude away, inherently introducing bias at the critical low end, near the limit of quantitation (LOQ), of the curve. Additionally, the coefficient of determination, or r² (regression coefficient), actually can be misleading and often is a poor measure of curve fit quality because it fundamentally assumes constant error at all concentrations, which is never the case in bioanalysis (3).

It is important to determine the best weighting factor, especially when covering the wide dynamic range typical in discovery bioanalysis. Statistically, the 1/x² weighting provides the best fit because it most correctly approximates the variance at the low end of the curve, and by doing so, normalizes the error across the range. This effectively allows for the best fit (2). Because unknown samples are bracketed between two standard curves (one run at the front and one run at the back), the weighting factor chosen also has to account for divergence. The divergence is especially important in LC–MS-MS as factors affecting response are continually changing. At this stage, stability of the NCE is still undetermined, column performance can degrade over time, and ion-source efficiency can be affected as the source becomes coated with sample components. All of these are typical considerations in discovery bioanalysis.

Running two curves to test for divergence, commonly referred to as standard technique (Figure 1b), takes time — and time is an important factor in discovery bioanalysis. Another approach to estimate divergence is to run calibrants across the same range in a scattered manner at the beginning and the end of the sample analysis, referred to as staggered technique (Figure 1a). In this case, calibrants at concentrations 1, 5, 50, 500, and 5000 ng/mL are run at the beginning and then 1, 2.5, 10, 100, 1000, and 10,000 ng/mL are run at the end. The 1-ng/mL calibrant is run twice because it is most susceptible to divergence (exceeding the ±20% CV criteria at the LOQ). This article attempts to correlate regression data obtained from the use of a single staggered calibration curve and compare it to the data obtained from the standard approach of running two full calibration curves, one at the beginning and one at the end of sample analysis. The goal of the experiment is to accelerate discovery bioanalysis without compromising data integrity.

Figure 1: (a) Staggered multipoint calibration curve set-up. Calibrants are prepared from a single stock solution and no QCs are used. The 1 ng/mL sample is repeated twice to ensure the LOQ criteria are met. (b) Standard method using duplicate standard (STD) curves and quality control samples (QCs). The QCs and STDs are from two independent stock solutions to ensure the integrity of the regression.

Experimental

Diphenhydramine (C₁₇H₂₁NO, FW: 256.2) was used as the test compound, with reserpine (C₃₃H₄₀N₂O₉, FW: 609.3; 10 ng/mL) as the analog internal standard (IS). Calibrants were diluted using K2-EDTA rat plasma, and the calibration standards were serially diluted using a Hamilton Starlet Liquid Handler (Hamilton Co., Reno, Nevada).

Plate 1 (Figure 1a) contained the multipoint staggered calibrants. Calibrants at 1, 5, 50, 500, and 5000 ng/mL were placed in the front of the plate, plasma blanks were placed in the middle, and calibrants 1, 2.5, 10, 100, 1000, and 10,000 ng/mL were placed at the end. Plate 2 (Figure 1b) contained duplicate sets of the calibrants in a low-to-high series, bracketing 50 plasma blanks in the middle, with interspersed quality control samples (QCs) at low, mid, and high concentrations. Both plates were repeated 10 times and the calibration curves were compared for divergence.

A model 1100 LC pump (Agilent Technologies, Santa Clara, California) was used to perform the chromatography with a CTC PAL autosampler (CTC, Basel, Switzerland). Mobile phase A was water (0.2% formic acid) and mobile phase B was acetonitrile (0.2% formic acid). A gradient was structured as follows, with starting conditions set at 5% B at 0 min and 45% B in 0.01 min with a flow rate of 0.8 mL/min. The % B was ramped to 95% in 1.4 min; the flow rate was increased to 1.3 mL/min. After holding these conditions for 0.2 min, the gradient was ramped back down to the starting conditions. The total run time was 1.8 min. The column used was an 30 mm × 2.1 mm, 3-μm Atlantis C18 column (Waters Corp, Milford, Massachusetts). Analysis was performed on a TSQ Quantum Ultra mass spectrometer using atmospheric-pressure chemical ionization (APCI, Thermo Fisher Scientific, San Jose, California) in the MRM mode using unit resolution in Q1 and Q3. The scan time for both transitions was 0.2 s (resperine, m/z 609→195 and diphenhydramine, m/z 257→167).

Results and Discussion

Figures 2a and 2b show the results for the staggered and standard multi-point calibration curves, respectively. Both techniques use linear r² (0.998 vs. 0.999) regression coefficients (coefficients of determination) and thus can be considered comparable. Although reporting r² is conventional practice, one should take into consideration that the regression coefficient assumes that error is fairly constant across the bioanalytical range, which is seldom the case in bioanalysis. A better way to compare the techniques is to look at the plot of the weighted residuals (Figures 3a and 3b), which is useful in determining divergence as a direct consequence of analytical sensitivity. Based on these graphs, the single calibration curve run in a staggered manner is comparable to duplicate calibration curves. The data thus indicate that the information content required for rigorous quantitation is relatively unaffected and that running a single calibration curve in a staggered setup can be used in discovery bioanalysis without compromising data integrity. One can almost argue that using a single calibration curve in a staggered manner is perhaps more rigorous in terms of adhering to guidelines that require simple statistical models (4). The larger question remains whether running a duplicate curve at the end of the sample analysis adds any significant value to the experimental end-point, which often determines bioavailability for an NCE.

Figure 2: Correlation coefficient (r2) results for the (a) staggered (r2 = 0.998) and (b) standard (r2 = 0.999) multipoint calibration curves, respectively. No difference is observed between these two regression techniques. Note that r2 can be a misleading indicator as it assumes a constant bias for each weighted point across the bioanalytical dynamic range, which is seldom the case.

Conclusion

Statistically, the 1/x² weighting provides the best fit because it most correctly approximates the variance at the low end of the curve and by doing so, normalizes the error at the high, low, and mid levels. No practical difference in the divergence was observed using the staggered technique in terms of r² (0.998 vs. 0.999), slope (1.089 vs. 1.077), or during the comparison of the weighted residuals versus the concentrations (Figures 3a and 3b). This indicates that running a single calibration curve using the staggered technique may be a viable alternative to running duplicate calibration curves.

Figure 3: The plot of the weighted residuals for the (a) staggered and (b) standard techniques. This plot is perhaps most useful in determining divergence as a result of the impact of sensitivity. Note the scale on the y-axis for the LOQ. Based on these data, a single calibration curve using the staggered technique provides comparable data and can be used in discovery bioanalysis.

Acknowledgments

The authors would like to thank Rohan A. Thakur for his contribution to this article. The authors also wish to thank Richard Lelacheur, Vice President, PharmaNet USA for his input and discussions.

References

(1) S. Bansal and A. Destefano, AAPS 9(1), E109–E114 (2007).

(2) A.M. Almeida et al., J. Chrom. 215–222 (2002).

(3) M. Kiser and J.W. Dolan, LCGC Europe 17(3), 138–143 (2004).

(4) "Guidance for Industry: Bioanalytical Method Validation," US FDA (2001).

Benjamin Begley is Analytical Chemist and Michael Koleto is Associate Director with PharmaNet in Princeton, New Jersey.