ANTIPERSPIRANT RESULTS 195 treatment comparisons have variance equal to that of the more efficient, direct com- parisons of the EVC design. Thus, for a given panel size and number of treatments (counting the control treatment), the RRB design is equivalent in efficacy to the EVC design for test-versus-control comparisons and twice as efficient as the EVC design for test-versus-test comparisons. USE OF THE SAS* STATISTICAL PACKAGE In the SAS statistical package, the analysis of variance (ANOVA) for the full-model two-treatment case can be effected by using the following statements: PROC GLM CLASS GROUP SUBJECT SIDE TREATMNT MODEL LOGSWEAT = GROUP SUBJECT(GROUP) TREATMNT SIDE TEST H = GROUP E = SUBJECT(GROUP) LSMEANS TREATMNT SIDE/STDERR PDIFF. The TEST statement allows for the correct hypothesis testing of the interaction (group) effect. The LSMEANS statement allows for estimation of the treatment and sides means and their standard errors. The Type III sums of squares should be used for significance testing. The full-model analysis of variance for multitreatment studies can be generated by the following SAS program statements: PROC GLM CLASS CELL GROUP SUBJECT SIDE TREATMNT MODEL LOGSWEAT = CELL GROUP(CELL) SUBJECT(CELL GROUP) TREATMNT SIDE TEST H = GROUP(CELL) E = SUBJECT(CELL GROUP) LSMEANS TREATMNT SIDE/STDERR PDIFF. The TEST statement provides for the testing of an overall interaction (group) effect over all treatment pairs. The LSMEANS statement provides for pairwise comparison of treatment differences. The simpler POSTRT analysis is readily set up in SAS for any number of treatments. First, create variables TRTA, TRTB,'TRTC, etc., so that, for a given subject: TRTA = 1, if treatment A is applied on the right axilla, TRTA = - 1, if treatment A is applied on the left axilla, and TRTA = 0, if treatment A is applied on neither axilla. The following SAS statements will illustrate the analysis of variance and the estimates of relative efficacy for each pair of three treatments, where POST is Pij: PROC GLM MODEL POST = TRTA TRTB TRTC ESTIMATE 'SIDES' INTERCEPT 1 ESTIMATE 'A_VS_B' TRTA 1 TRTB - 1 * Trademark of SAS Institute, Inc.

196 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS ESTIMATE 'A_VS_C' TRTA 1 TRTC - 1 ESTIMATE 'B_VS_C' TRTB 1 TRTC - 1. The ESTIMATE statements provide the estimates for the sides and treatment difference effects, together with their standard errors, t-statistics, and significance levels. The analysis can be extended to four or more treatments in an obvious way by adding additional TRTn terms in the MODEL statement and ESTIMATE statements for each additional pair of treatments. To conduct the change from baseline (CHGBAS) analysis of variance using SAS, CHNG = Cii is substituted for the post-treatment value POST in the SAS statements presented above. However, the sides effect is not estimated, so that the SAS statements should provide for no intercept (NOINT) in the MODEL statement and no ESTIMATE state- ment for the sides effect. PROC GLM MODEL CHNG = TRTA TRTB TRTC/NOINT ESTIMATE 'A_VS_B' TRTA 1 TRTB - 1 ESTIMATE 'A_VS_C' TRTA 1 TRTC -1 ESTIMATE 'B_VS_C' TRTB 1 TRTC - 1. To conduct analysis of covariance (ANCOVA) using SAS, the baseline value, BASE = Bij , is added in the model statement. PROC GLM MODEL POST = TRTA TRTB TRTC BASE ESTIMATE 'A_VS_B' TRTA 1 TRTB -1 ESTIMATE 'A_VS_C' TRTA 1 TRTC - 1 ESTIMATE 'B_VS_C' TRTB 1 TRTC - 1 ESTIMATE 'SLOPE' BASE 1. The last ESTIMATE statement will print the value of the slope estimate, its standard error, and a significance level for testing the hypothesis that the slope is zero. The intercept in this model will estimate the quantity •(1 - [3), which would usually not be of interest, and thus no estimate statement appears for the int.,•ercept. The change from baseline value may also be used as the response variable, substituting CHNG for POST in the MODEL statement. In this case the slope estimate b' will be obtained, but the treatment comparison estimates will be the same. A SAS computer program is available from the authors. REFERENCES (1) Food and Drug Administration, Antiperspirant drug products for over-the-counter human use (pro- posed rule), Federal Register, 46693-46732 (October 10, 1978). (2) Food and Drug Administration, Antiperspirant drug products for over-the-counter human use (ten- tative final monograph), Federal Register, 36492-36505 (August 20, 1982). (3) Food and Drug Administration, Guidelines for Effectiveness Testing of OTC Antiperspirant Drug Products, Dockets Management Branch [HFA-305] (August 1982). (4) P. Majors and J. Wild, The evaluation of antiperspirant efficacy, J. Soc. Cosmet. Chem., 25, 139-152 (1974). (5) W. Wooding, Interpretation of gravimetric axillar antiperspirant data, Proc. Joint Conf. on Cosmet. Sciences, 91-105 (1968).