JOURNAL OF COSMETIC SCIENCE 360 CONCLUSION Freeing sunscreen t esting from selection bias and from subversion bias would be a worth- while goal in enhancing the validity of SPF testing results. Currently, the FDA method (9) invalidates an SPF test if all subjects were of the same Fitzpatrick skin phototype. The correlation between Fitzpatrick skin phototype and MED is poor. A test could easily in- corporate SPF test values from nine values from Fitzpatrick skin phototype 1 and one value from Fitzpatrick skin phototype 2 while committing selection bias and/or subver- sion bias. External validity w ill be improved by requiring subjects across all MED values as sug- gested by Alejandria et al (5). They suggested that each valid SPF test includes at least three subjects with a MED of d15 mJ/cm2, at least three subjects with a MED between 15 mJ/cm2 and 40 mJ/cm2, and at least three subjects with a MED of ≥40 mJ/cm2. This would minimize the selection bias reported by Kawanda et al. (3), Damien et al. (4), and Alejandria et al. (5). External validity wil l also be improved by restricting the use of individual subjects. Using a subject, no more than six times per year and no more than once every 60 days would minimize, but not eliminate, the potential for subversion bias. Until selection bias and subversion bias are eliminated, variations in SPF values from different testing facilities will continue. REFERENCES (1) J.A. Lewis. Statistical principles for clinical trials (ICH e9): an introductory note on an international guideline. Statist. Med., 18, 1903–1942 (1999). (2) WHO, Handbook for Good Clinical Research Practice (GCP) (World Health Organization, Geneva, Switzerland, 2002), p. 30. (3) A. Kawada, T. Noda, M. Hiruma, A. Ishibashi, and S. Arai, The relationship of sun protection factor to minimal e rythema dose, Japanese skin type, and skin colour, J. Dermatol., 20, 514–516 (1993). (4) D. L. Damian, G. M. Halliday, and R. S. Barnetson, Sun protection factor measurement of sunscreens is dependent on minimal erythema dose, Br. J. Dermatol., 141, 502–507 (1999). (5) M. Alejandria, A. Marra, G. Roberts, and M. Caswell, Disparate SPF testing methodologies generate similar SPFs. II. Analysis of P2 standard control SPF data, J. Cosmet. Sci., 70, 181–196 (2019). (6) J. A. Hartigan and M. A. Wong, Algorithm AS 136: a K-means clustering algorithm, J. Roy. Stat. Soc. C Appl. Sta t ., 28, 100–108 (1979). (7) P. J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Compu t. Appl. Math. 20, 53–65 (1987). (8) R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Com- puting, Vienna, Austria, 2019), accessed January 21, 2020, www.R-project.org. (9) Department of Health and Human Services, Food and Drug Administration, Sunscreen drug products for over-the-counter human use proposed amendment of fi nal monograph proposed rule, Fed. Regist., 72, 49070–49122 (2007).

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