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Effect of different mathematical methods on etoposide area under the curve estimations and pharmacodynamic response predictions


Different methods to calculate interval area under the curve (AUC) data may produce substantial error. The purpose of this study was to compare methods of calculating etoposide AUC and determine the effect of these values on white blood cell (WBC) count nadir predictions calculated from a previously reported equation. Three AUC calculation methods were used: (1) the linear trapezoidal method, (2) a combination of the linear and logarithmic trapezoidal methods, and (3) the Lagrange method. Since none of the methods for determining the AUC could be considered the standard, the methods were evaluated by comparing differences between pairs of calculated AUC values by each method. The 95% CI for differences between all pairs of AUC values were greater than zero (no difference) indicating significance. Consistent with the smoother fitting function between data points, the Lagrange method tended to produce a larger AUC, lower clearance values, and lower WBC nadir count predictions than the other methods. The largest difference encountered was between the Lagrange and the linear-log AUC methods with a mean value of 16.9 μg h/ml (95% CI 9.4–24.3) This difference would account for approximately 11% of the total AUC. Using a previously published equation, where WBC nadir=−0.057+0.048×etoposide clearance, with clearance determined as dose/AUC, mean differences in calculated WBC nadir count values between the three AUC methods ranged from 80 to 220 cells/μl, which would be expected to be of little clinical consequence. The precision of this equation, using data derived from linear trapezoidal AUC calculations, had a mean absolute error of 0.93×103/μl (95% CI 0.53–1.32). Our findings suggest that any of the three mathematical methods studied would produce similar etoposide AUC values and pharmacodynamic predictions. Further, these findings also suggest that the major limitation in predicting etoposide leukopenia lies with the imprecision of the pharmacodynamic model more so than the ability to accurately determine the AUC. However, our findings may not be applicable if other factors intervene which dramatically alter the shape of the etoposide concentration-time curve.

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Author information

Correspondence to Bert L. Lum.

Additional information

Supported by National Institutes of Health grants numbers R01 CA 52168 and M01 RR 00070 (General Clinical Research Centers)

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McCauley, D.L., Lum, B.L. & Sikic, B.I. Effect of different mathematical methods on etoposide area under the curve estimations and pharmacodynamic response predictions. Cancer Chemother. Pharmacol. 37, 286–288 (1995). https://doi.org/10.1007/BF00688330

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Key words

  • Etoposide
  • Pharmacokinetics
  • Area under the curve