310 JOURNAL OF COSMETIC SCIENCE ICS as well, it is obvious that the effect of ITA° is dampened by the negative effects of dINT and dbStar. Had the dark spots showed more reduction in the clinical study, the improvement in ICS would have been more pronounced. Finally, it also was of interest to note that, because the derivation of the ICS model stemmed from panel-perception results, by taking the inverse function (logistic function) of the log-odds, we also inferred that the probability of people preferring the skin complexion after 8 weeks’ treatment to that of the baseline increased by roughly 27%. DISCUSSION Complexion is one of the top qualities of beauty and skin health readily recognized and perceived among people in their daily lives. Understanding consumer preference and basic components of the phenomenon helps the industry provide effective interventions to consumers for beauty management. Investigating the phenomenon by means of large- panel perception, objective measurement of multiple skin attributes, and mathematical modeling made it possible to characterize the desired skin properties and to help develop a daily skincare regimen for effective management of skin conditions. In this study, we identified the causal effect of objectively derived skin parameters including skin color, Figure 11. Detection of treatment efficacy in a clinical study using the ideal complexion model. X-axis: time point of the study y-axis: ICSs calculated from the clinical images using Equation 3. A statistically significant improvement in ICS values was detected after 4 weeks’ use of the test formulation, and the improvement became more pronounced at the 8-week time point. Table VI Changes of the Individual Parameters During the Clinical Study Parameters Time point BSL Time point W04 Time point W08 p Value W04/BSL p Value W08/BSL ITA° 26.82 30.21 42.19 6.38E-14 1.33E-37 dINT 28.06 27.92 27.31 5.34E-01 5.76E-03 daStar 5.17 5.15 4.96 8.34E-01 4.70E-02 dbStar 4.14 4.18 4.37 2.86E-01 8.23E-07

311 Characterizing and Modeling Complexion spots, and shine in determining people’s preferences for ideal complexion, and investigated their combined effects via a multivariate regression model, which provides a key tool for us to quantitatively describe ideal complexion. By analyzing facial images from a large female Chinese population (N =480), we show that this newly defined skin parameter of ideal complexion is normally distributed in the studied population with the vast majority exhibiting ICS values between 10% and 90% quantile (3.93–7.40) while the rest tailed off in the high and low ends (90% and 10% quantiles). The visual differences in high and low levels of ICS shown in Figure 10 agreed well with the general perception of Asians toward ideal complexion that is, skins with fair and even skin tone, fine texture, and free of pigmentary blemishes are preferred. This study helped provide data for adequate understanding of how ideal complexion is perceived by Chinese women as well as for objective quantification of the consumer-perceivable skin properties. The results of treatment efficacy evaluation provided data to demonstrate that a product claim of obtaining ideal complexion could be substantiated and the consumer preference likelihood could be quantitatively estimated based on the changes of the objectively measured skin properties. Regarding modeling complex skin properties, one general question that often arises is whether the multivariable model has added benefit in predicting a phenomenon when compared to each of the individual parameters. The added benefit was evident in this study. As shown in Figure 12, individually, the highest correlation coefficient was 0.5318, which was much less than that of the model, 0.9866, as shown in Figure 6. One thing worth noticing, however, is the behavior of dINT. While it correlated poorly with Bradley–Terry P individually (r =0.1268), significant contribution to Bradley–Terry P was shown in the multivariable model, owing to its interactions with other parameters to minimize residuals (Figure 7B). SVS showed a similar behavior but in an opposite direction—individually it correlated well with Bradley–Terry P (r =0.5008), but its contribution was not statistically significant in multiple regression analysis (Figure 7E). CONCLUSIONS From this study we concluded that skin complexion, a subjective and consumer-perceivable property of skin, could be characterized, quantified, and predicted with a linear model by using objectively measured basic visual attributes of facial skin. Use of paired comparison coupled with logit function, image analysis of basic skin parameters, and the Bradley–Terry Figure 12. Multivariate analysis showing correlations of individual skin attributes with the panel preference rank (Bradley–Terry P). Table on top: correlation coefficient of Bradley–Terry P and DRR, SVS, ITA°, etc. Charts on bottom: scatterplots with density ellipses and regression line showing each correlation.