170 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS We may summarize our conclusions as follows: (1) Baseline data, when available, should be utilized in the analysis to increase precision of the treatment effects. Baseline information is also useful for determining when a given subject is responding in an atypical manner. (2) Analysis of covariance is the recommended statistical procedure for incorporation of baseline data. It will give equal or better precision versus the competitive analysis based on simple change from baseline. (3) Logarithmic transformation of sweat rates is necessary to ensure that the assumptions of variance homogeneity and distribution normality are met. (4) Although repeated measurements do not greatly improve precision, they can be useful in data-checking. (5) The above conclusions apply to multitreatment studies (three or more treatments). DETAILED DISCUSSION In this section we present our results in detail after a review of statistical methodology presented by earlier writers. We first consider the analysis of post-treatment data alone and derive a simple model for the analysis of this data. We then discuss two methods of utilizing baseline data and compare the precision of all three methods based on analysis of past clinical studies. The final sections discuss other repeated-measures aspects of these studies and the required panel size. An outline for this section is as follows: ß Overview of current data analysis practice ß The need for the log transform of sweat measurements ß The POSTRT model for analyzing post-treatment data alone ß Design and analysis of multitreatment studies ß Results of POSTRT analysis on past studies ß A simpler POSTRT model ß The use of baseline data--the CHGBAS and ANCOVA models ß Comparison of the three analysis methods ß Multiple baselines and readings--Are they necessary? ß Determination of panel size ß Use of the SAS statistical package CURRENT PRACTICE•VERVIEW The "gravimetric" method for conducting antiperspirant efficacy studies was described by Majors and Wild (4). Current experimental design philosophy is based on the fact that, in the general population, average sweat rates from the right axilla are greater than those on the left axilla. Therefore, each pair of treatments is assigned such that an equal number of human subjects have a specified treatment on right and left axillae. The allocation of treatments to axillae within a panel of human subjects is made by random assignment. Test results are usually reported in terms of percent sweat reduction (PCTRED) of one treatment relative to another. For any two treatments, this is calculated as:

ANTIPERSPIRANT RESULTS 171 PCTREDofTversusC -- 100- (C - T)/C = 100- (1 - T/C) where T = sweat rate from the axilla treated with "test" product T, and C = sweat rate from the axilla treated with "control" product C. There are various statistical methods of treating the data to arrive at the mean sweat reduction and its statistical significance. FDA guidelines for antiperspirant efficacy (1-3) state that a product must attain strong evidence of a median sweat reduction (versus placebo or untreated) exceeding 20% in the user population to qualify as an effective antiperspirant (Category I). The antithesis is stated in terms of a statistical hypothesis as follows: Null hypothesis: Median sweat reduction is equal to or less than 20%. Rejection of this null hypothesis allows the experimenter to assert that the alternative hypothesis is true at a given confidence level, i.e., that the median sweat reduction is greater than 20%. The null hypothesis is tested at the significance level of 0.05 (one-sided). In competitive claims for advertising, the null hypothesis is that the sweat reduction of the candidate versus the competitor is equal to zero. If the hypothesis is rejected, then one of two alternative hypotheses are accepted: (a) that the sweat reduction exceeds zero, i.e., that the candidate has superior efficacy to the competitor, or (b) that the sweat reduction falls short of zero, i.e., that the competitor has superior efficacy. In this application, the null hypothesis is usually tested at the 0.05 significance level, two- sided. An early statistical method suggested by the FDA was the binomial test (1), but this method has fallen out of favor due to its low statistical power. Later, two other non- parametric tests were recommended by the FDA (3), based on the ranks of the ratios of sweat measurements of the right axilla to those of the left axilla: (a) the Wilcoxon rank sum test (Mann-Whitney test) on the ratios when no pretreatment data are taken, and (b) the Wilcoxon signed rank test on adjusted ratios when pretreatment data are taken. Both tests have reasonable statistical power, but unfortunately, neither test allows for easy calculation of confidence interval estimates for average percent sweat reduction. Another early method described by Majors and Wild (4) used the axillary sweat response ratios of test (T) to control (C) for each subject for normal-theory statistical tests, e.g., the Student t-test. These methods are currently in use, although criticized by Wood- ing (5) and Wooding and Finklestein (6) on the grounds that the T/C ratios do not have a normal distribution required for the valid use of such tests. A problem with arithmetic treatment of ratios is that the average result depends upon which treatment is placed in the denominator of the ratio. For example, consider the following results: Subject Sweat amount (mg) Ratio Ratio number Product A Product B A/B B/A 1 200 400 0.5 2.0 2 400 200 2.0 0.5 Average ratio 1.25 1.25 Average percent reduction 25 25