Overlap coefficient for assessing the similarity of pharmacokinetic data between ethnically different populations

Abstract

We developed a method to assess the similarity of pharmacokinetic data between ethnically different populations. An evaluation of confidence intervals for the mean difference in pharmacokinetic parameters, such as area under the concentration-versus-time curve (AUC), between populations is often used. We propose the use of the overlap coefficient (OC), which represents the proportion of overlap between two probability distributions, as a measure of the similarity between distributions. We considered five OC estimators – two parametric ones and three nonparametric ones. Simulation studies were conducted to compare the performance of the five OC estimators and their bootstrap confidence intervals. Results showed that nonparametric estimators with fixed-bandwidth kernel density estimation had a smaller mean squared error in almost all situations, and their coverage probabilities were close to the nominal level. The proposed method was applied to pharmacokinetic data from a bridging study of a combination therapy for metastatic colorectal cancer patients in the USA and Japan. From the analyses of this study, it was suggested that the distributions of the logarithmically transformed AUC for leucovorin and 5-fluorouracil were similar between the two populations.

References

1. ICH steering committee . International Conference on Harmonisation (ICH) harmonized tripartite guideline. Ethnic factors in the acceptability of foreign clinical data (E5). Federal Register, Food and Drug Administration 10 June 1998; 63(111): 31790-31790.

2. Peace KE . Estimating the degree of equivalence or nonequivalence: An alternative to bioequivalency testing. American Statistical Association, Proceedings of the Biopharmaceutical Section 1986; 63–69.

3. US Food and Drug Administration . Guidance on statistical procedures for bioequivalence using a standard two-treatment crossover design. Rockville, MD: Division of Bioequivalence, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, 1992.

4. US Food and Drug Administration . Guidance for industry: Statistical approaches to establishing bioequivalence. Rockville, MD: Division of Communications Management, Office of Training and Communications, Center for Drug Evaluation and Research, Food and Drug Administration, 2001.

5. Bradley EL . Overlapping coefficient. In Kotz S, Johnson NL, Read CB, eds. Encyclopedia of statistical science. New York: Wiley, 1985; 6: 546–547.

6. Rom DM , Hwang E . Testing for individual and population equivalence based on the proportion of similar responses. Stat Med 1996; 15: 1489–1505.

7. Inman HF , Bradley EL . The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Commun Statist Theory Methods 1989; 18: 3851–3874.

8. Stine RA , Heyse JF . Non-parametric estimates of overlap. Stat Med 2001; 20: 215–236.

9. Clemons TE , Bradley EL . A nonparametric measure of the overlapping coefficient. Comput Statist Data Anal 2000; 34: 51–61.

10.

10. Pazdur R , Douillad JY , Skillings JR et al. Multicenter phase III study of 5-fluorouracil (5-FU) or UFT in combination with leucovorin (LV) in patients with metastatic colorectal cancer. Proc Am Soc Clin Oncol 1999; 18: 263a-263a.

11.

11. Carmichael J , Popiela T , Randstone D et al. Randomized comparative study of ORZEL (Oral Uracil/ Tegafur (UFT) plus leucovorin (LV)) versus parenteral 5-fluorouracil (5-FU) plus LV in patients with metastatic colorectal cancer. Proc Am Soc Clin Oncol 1999; 18: 246a-246a.

12.

12. Hoff PM , Loehrer P , Abbruzzese JL et al. Joint United States of America (USA)/Japan study of UFT (uracil and tegafur) plus leucovorin (LV) in patients (pts) with metastatic colorectal cancer. Eur J Cancer 2001; 37(suppl. 6): s307-s307.

13.

13. Hyodo I , Ohtsu A , Shirao K . Joint United States of America (USA)/Japan study of oral Uracil/Ftorafur (UFT) plus leucovorin in patients with metastatic colorectal carcinoma. J Japan Soc Cancer Ther 2001; 36: 538-538.

14.

14. Simonoff JS . Smoothing methods in statistics. New York: Springer-Verlag, 1996.

15.

15. Silverman BW . Density estimation for statistics and data analysis. London: Chapman and Hall, 1986.

16.

16. Wand MP , Jones MC . Kernel smoothing. London: Chapman and Hall, 1995.

17.

17. Abramson IS . On bandwidth variation in kernel estimates: A square root law. Annal Stat 1982; 10: 1217–1223.

18.

18. Inman HF , Bradley EL . Hypothesis tests and confidence interval estimates for the overlap of two normal distributions with equal variances. Environmetrics 1994; 5: 167–189.

19.

19. Efron B , Tibshirani RJ . An introduction to the bootstrap. New York: Chapman and Hall, 1993.

20.

20. SAS . SAS/IML user's guide. Release 6.07. Cary, NC: SAS Institute Inc., 1990.

21.

21. Sheather SJ , Jones MC . A reliable data-based bandwidth selection method for kernel density estimation. J Roy Stat Soc B 1991; 53: 683–690.

22.

22. Balakrishnan N , Kocherlakota S . Robustness to nonnormality of the linear discriminant function: mixtures of normal distributions. Commun Statist Theory Methods 1985; 14: 465–478.

23.

23. Reiser B . Confidence intervals for the mahalanobis distance. Commun Statist Simul Comput 2001; 30: 37–45.

24.

24. Committee for Proprietary Medicinal Products . Note for guidance on the investigation of bioavailability and bioequivalence. London: The European Agency for the Evaluation of Medicinal Products, 26 July 2001.