Interpretation of SPF In vivo Results: Analysis and Statistical Explanation

Mar 1, 2011 | Contact Author | By: Marc Pissavini and Olivier Doucet, Coty-Lancaster; and Olivier Brack, Statistique Industrielle KHI2 Consulting (KSIC)
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Title: Interpretation of SPF In vivo Results: Analysis and Statistical Explanation
SPFx meanx standard deviationx confidence intervalx standard error mean (SEM)x
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Keywords: SPF | mean | standard deviation | confidence interval | standard error mean (SEM)

Abstract: Methods for determining SPF in vivo are based on a biological response by human skin. To overcome intrinsic variation in these methods, large numbers of volunteers and statistics are required; however, these concepts are often poorly understood or worse, misinterpreted. This article discusses how these values should be interpreted and explains what they mean to formulators.

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M Pissavini, O. Doucet and O Brack, Interpretation of SPF In vivo Results: Analysis and Statistical Explanation, Cosm & Toil 126(3) (2011)

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Currently in Europe, sun protection products must follow many recommendations and although they are not law, compliance is expected from the cosmetic industry by regulators, consumers and the industry itself. For example, the European Commission and Colipa recommend that products provide both UVB and UVA protection, with an SPF ratio of at least one-third. SPF claims are organized into four categories: low SPFs of 6 and 10; medium SPFs of 15, 20 and 25; high SPFs of 30 and 50; and very high SPFs of 50+.1, 2

In relation, in the United States in 2007, the US Food and Drug Administration (FDA) proposed an amendment to its Final Monograph relating to sun protection.3 The proposed rules are different than Europe’s for UVA but are similar in terms of SPF. The FDA has proposed: replacing its current category descriptors of minimal and moderate respectively with the terms low, meaning SPF 2 to < 15, and medium, meaning SPF 15 to < 30; and increasing the labeled SPF value to 50 for SPF 30–50, and 50+ for SPF 50+.

SPF is assessed based on the biological marker erythema, which is caused by a certain portion of UV radiation and is a generally accepted benchmark by which consumers choose sunscreen products. So while companies should test sunscreen products throughout the development process to ensure the desired SPF level is maintained, many also measure SPF in vivo during the development phase since the final SPF claimed is obtained in vivo. Oftentimes, in order to cut the costs of in vivo testing, companies reduce the number of volunteers from 10 to 5.

The purpose of this article is to provide product developers with a guide for interpreting in vivo SPF results. Values including the mean, standard deviation and confidence intervals are related to probability concepts that are often misunderstood or misinterpreted, which can lead to serious consequences since the screening value of the in vivo SPF has a direct effect on the product’s further development. Product developers should thus consider whether two SPF results being compared are similar.

All of these parameters will be explained and discussed here. From the SPF mean and standard deviation, the authors will show how to calculate the confidence percentage if a result obtained is different from the claimed SPF mean. Step by step calculation will be given in order to compare two means, and the impact of a decrease from 10 to 5 volunteers on the results will be discussed. Tools for decision support also will be communicated.

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Table 1. Example Evaluation of Shapiro and Wilk’s Test on Products A and B

Table 1. Example Evaluation of Shapiro and Wilk’s Test on Products A and B

In the simulated evaluation shown in Table 1, calculations comparing two products on 10 volunteers estimate that the SPF mean for product A is 36.97 and B is 33.69.

Table 2. Distribution Intervals of a Population

Table 2. Distribution Intervals of a Population

According to the normal law shape, Table 2 summarizes the areas of the bell curve in which SPF data collected from a population of consumers would be expected to be distributed.

Table 3. Distribution Interval for Products A and B

Table 3. Distribution Interval for Products A and B

For example, for 95% with 10 volunteers, the t-value equals 2.262 (see simulated example in Table 3).

Table 4. CI%, c, CI Lower and Upper Limits for Products A and B

Table 4. CI%, c, CI Lower and Upper Limits for Products A and B

In order to compare the variability of SPF products tested in vivo, or those assessed via different methods—e.g., in vivo and in vitro, the SEM is provided and is expressed as a percentage of the average (see simulated example in Table 4).

Table 5. Claimed SPFs

Table 5. Claimed SPFs

The sample products A and B from Table 1 are both claimed as SPF 30 (see Table 5).

Table 6. Comparison of the Two SDs

Table 6. Comparison of the Two SDs

However, if Fcalculated is greater than Fcritical, the two standard deviations are assumed to be significantly different and will be taken into account separately for the means comparison (see Table 6).

Table 7. Comparison of Two SPFs

Table 7. Comparison of Two SPFs

If the tcalculated is greater than tcritical, the two means are assumed to be significantly different (see Table 7).

Table 8. Comparison of %CI for 10 vs. 5 Volunteers

Table 8. Comparison of %CI for 10 vs. 5 Volunteers

Considering that with five volunteers the standard deviation will not change, one could estimate what this HR could be for an average of five volunteers (see Figure 1 and Table 8).

Table 9. Confidence for Products A and B

Table 9. Confidence for Products A and B

Figure 2 shows that the confidence for this claim is between 85–90% (88.26%, according to student table and Table 9), therefore the claim cannot be made without too high a level of risk, since a minimum 95% confidence is necessary to be sure the product SPF is in fact greater than the claimed SPF.

Figure 1. Confidence abacus for comparison between observed SPF and target 5 volunteers

Figure 1. Confidence abacus for comparison between observed SPF and target 5 volunteers

Considering that with five volunteers the standard deviation will not change, one could estimate what this HR could be for an average of five volunteers (see Figure 1 and Table 8).

Figure 2. Low and medium SPF confidence abacus comparing observed and target SPF (n = 5)

Figure 2. Low and medium SPF confidence abacus comparing observed and target SPF (n = 5)

Figure 2 shows that the confidence for this claim is between 85–90% (88.26%, according to student table and Table 9), therefore the claim cannot be made without too high a level of risk, since a minimum 95% confidence is necessary to be sure the product SPF is in fact greater than the claimed SPF.

Figure 3. Confidence abacus for comparison between observed SPF and target estimation for 10 volunteers, using the results from 5 volunteers

Figure 3. Confidence abacus for comparison between observed SPF and target estimation for 10 volunteers, using the results from 5 volunteers

Figure 3 also shows that below an SEM of 4, researchers can be confident with the hypothesis that the SPF should be greater than the revendication.

Footnote (CT1103 Pissavini)

a JMP SAS-Institute Software 8.01 is manufactured by SAS-Institute, Inc.

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